Effect of fiber,matrix and interface properties on the in-plane shear deformation of carbon-fiber reinforced composites

The effect of fiber, matrix and interface properties on the in-plane shear response of carbon-fiber reinforced epoxy laminates was studied by means of a combination of experiments and numerical simulations. Two cross-ply laminates with the same epoxy matrix and different carbon fibers (high-strength and high-modulus) were tested in shear until failure according to ASTM standard D7078, and the progressive development of damage was assessed by optical microscopy in samples tested up to different strains. The composite behavior was also simulated through computational micromechanics, which was able to account for the effect of the constituent properties (fiber, matrix and interface) on the macroscopic shear response. The influence of matrix, fiber and interface properties on each region and on the overall composite behavior was assessed from the experimental results and the numerical simulations. After the initial elastic region, the shear behavior presented two different regions, the first one controlled by matrix yielding and the second one by the elastic deformation of the fibers. It was found that in-plane shear behavior of cross-ply laminates was controlled by the matrix yield strength and the interface strength and was independent of the fiber properties.     

Modeling the tensile stress–strain response of carbon nanotube/polypropylene nanocomposites using nonlinear representative volume element

This paper presents a finite element model for predicting the mechanical behavior of polypropylene (PP) composites reinforced with carbon nanotubes (CNTs) at large deformation scale. Existing numerical models cannot predict composite behavior at large strains due to using simplified material properties and inefficient interfaces between CNT and polymer. In this work, nonlinear representative volume elements (RVE) of composite are prepared. These RVEs consist of CNT, PP matrix and non-bonded interface. The nonlinear material properties for CNT and polymer are adopted to solid elements. For the first time, the interface between CNT and matrix is simulated using contact elements. This interfacial model is capable enough to simulate wide range of interactions between CNT and polymer in large strains. The influence of adding CNT with different aspect ratio into PP is studied. The mechanical behavior of composites with different interfacial shear strength (ISS) is discussed. The success of this new model was verified by comparing the simulation results for RVEs with conducted experimental results. The results shows that the length of CNT and ISS values significantly affect the reinforcement phenomenon.     

Numerical characterization of CNT-based polymer composites considering interface effects

Carbon nanotubes (CNTs) possess exceptional mechanical properties and are therefore suitable candidates for use as reinforcements in composite materials. Load transfer in nanocomposite materials is achieved through the CNT/matrix interface. Thus, to determine nanocomposite mechanical properties, the interface behavior must be determined. In this investigation, finite element method is used to investigate the effects of interface strength on effective CNT-based composite mechanical properties. Nanocomposite mechanical properties are evaluated using a 3D nanoscale representative volume element (RVE). A single nanotube and the surrounding polymer matrix are modeled. Two cases of perfect bonding and an elastic interface are considered. For the perfect bonding interface, the no slip conditions are applied. To better investigate the elastic interface behavior, two models are proposed for this type of interface. The first elastic interface model consists of a thin layer of an elastic material surrounding the CNT. In the second elastic interface model, a series of spring elements are used as the nanotube/matrix interface. The results of numerical models indicate the importance of adequate interface bonding for a more effective strengthening of polymer matrix by CNT’s.     

Defect propagation at a circular interface

In this paper a nonlinear, nonuniform cohesive zone is employed to study the detailed features of quasi-static defect evolution in a simple, planar elastic system consisting of a circular inclusion embedded in an unbounded matrix subject to different remote loading configurations. The inclusion–matrix interface is assumed to be described by Needleman-type force-separation relations characterized by an interface strength, a characteristic force length and a shear stiffness parameter. Interface defects are modeled by an interface strength which varies with interface coordinate. Infinitesimal strain equilibrium solutions, which allow for rigid body inclusion displacement, are sought by eigenfunction approximation of the solution of the governing interfacial integral equations. For equibiaxial tension, quasi-static defect initiation and propagation occur under increasing remote load. For decreasing characteristic force length, a transition occurs from more or less uniform decohesion along the bond line to propagation of a crack-like defect. In the later case a critical failure load is well defined and interface failure is shown to be defect dominated (brittle decohesion). For interfaces with large characteristic force length, the matrix “lifts off” the inclusion accompanied by a delay in defect propagation (ductile decohesion). The decohesion modes ultimately give rise to a cavity with the inclusion situated within it on the side opposite to the original defect. Results for small characteristic force length show consistency with England’s results for the sharp arc crack on a circular interface (England AH (1966) ASME J Appl Mech 33:637–640) Stress oscillation and contact at the tip of the defect are observed primarily for small characteristic force lengths under extremely small loading. Results for remote tension, compression and pure shear loading are discussed as well. In the final section of the paper the results obtained in the first part are utilized to estimate the plane effective bulk response of a composite containing a dilute distribution of inclusions with randomly oriented interface defects.     

矩形橡胶复合材料层合板几何非线性分析

文中应用简单高阶剪切层合理论和大变形理论对各向异性纤维增强的矩形橡胶复合材料层合板进行了几何非线性分析.与线性理论相比,本文作者进行的层合板大变形状态的几何非线性分析和所计算的层板应力分布,更具有准确性.     

Nonlinear finite element modeling of concrete deep beams with openings strengthened with externally-bonded composites

This paper aims to develop 3D nonlinear finite element (FE) models for reinforced concrete (RC) deep beams containing web openings and strengthened in shear with carbon fiber reinforced polymer (CFRP) composite sheets. The web openings interrupted the natural load path either fully or partially. The FE models adopted realistic materials constitutive laws that account for the nonlinear behavior of materials. In the FE models, solid elements for concrete, multi-layer shell elements for CFRP and link elements for steel reinforcement were used to simulate the physical models. Special interface elements were implemented in the FE models to simulate the interfacial bond behavior between the concrete and CFRP composites. A comparison between the FE results and experimental data published in the literature demonstrated the validity of the computational models in capturing the structural response for both unstrengthened and CFRP-strengthened deep beams with openings. The developed FE models can serve as a numerical platform for performance prediction of RC deep beams with openings strengthened in shear with CFRP composites.     

基于离散宏单元的砌体结构高效非线性分析方法

砌体结构由力学性能不同的块体和砂浆构成,材料的各向异性使结构非线性行为体现出高度复杂性。砌体结构非线性分析模型主要包括分离式和整体式两种:分离式模型将块体、砂浆及二者粘结界面分开建模,可以精细化揭示砌体非线性行为和破坏形态,但非线性分析计算量大,多用于局部构件的细部分析和模拟;整体式模型将块体和砂浆假定为连续的匀质体,建模过程简单、易行,适用于整体结构的宏观分析。无论是分离式还是整体式,结构非线性计算分析中大规模刚度矩阵的实时更新与分解降低了分析效率。该文提出了一种基于整体式空间离散宏单元模型的砌体结构高效非线性分析方法,该方法采用剪切单元模拟砌体墙的斜截面剪切破坏模式,采用无厚界面单元模拟砌体墙的正截面弯曲破坏模式、正截面剪切滑移破坏模式和平面外剪扭破坏模式,进一步将剪切单元等效斜向弹簧的轴向变形和无厚界面单元上下表面的相对变形分解为线弹性和非线性两部分,并引入塑性自由度描述分离出的非线性部分,可将任意时刻的切线刚度矩阵表示为初始弹性刚度矩阵的低秩摄动形式,引入Woodbury公式进行求解,该文方法避免了大规模整体刚度矩阵的迭代更新,非线性分析的主要计算量仅集中于小规模非线性矩阵的更新与分解,显著提升了计算效率。     

Assessment of interfacial bonding between polymer threads and epoxy resin by transverse fibre bundle (TFB) tests

Two experimental approaches were employed to assess the fibre/matrix adhesion between polymer threads and epoxy resin by transverse fibre bundle (TFB) tests. The first approach was to measure interfacial bonding strength of the fibre/matrix interface in dog-bone-shaped tensile specimens by applying normal stress until failure, simulating the Mode I failure mode. The second approach was to determine the fibre/epoxy interfacial bonding strength in shear (simulating the Mode II failure mode) by means of a V-notched beam shear testing method, i.e. a modified Iosipescu test. In both methods, polymer threads were transversely incorporated in the middle section of the specimens. It was found that both methods were simple, reliable, and sensitive to changes in the fibre/matrix adhesion conditions, though interpretation of the test results was somewhat complex. The two experimental approaches were able to produce consistent results and can thus be adopted as alternative methods for determining the interfacial bonding properties between fibres and matrix in composite systems where conventional micro-mechanical or macro-mechanical testing methods cannot be used.     

Micromechanical modeling of interface damage of metal matrix composites subjected to transverse loading

A three-dimensional finite element micromechanical model was developed to study effects of thermal residual stress, fiber coating and interface bonding on the transverse behavior of a unidirectional SiC/Ti–6Al–4V metal matrix composite (MMC). The presented model includes three phases, i.e. the fiber, coating and matrix, and two distinct interfaces, one between the fiber and coating and the other between coating and matrix. The model can be employed to investigate effects of various bonding levels of the interfaces on the initiation of damage during transverse loading of the composite system. Two different failure criteria, which are combinations of normal and shear stresses across the interfaces, were used to predict the failure of the fiber/coating (f/c) and coating/matrix (c/m) interfaces. Any interface fails as soon as the stress level reaches the interfacial strength. It was shown that in comparison with other interface models the predicted stress–strain curve for damaged interface demonstrates good agreement with experimental results.     

Load transfer in a composite containing a broken fiber with imperfect bonding

The effect of interface behavior on the local deformation field is studied by analyzing a composite consisting of a broken fiber imperfectly bonded to its surronding matrix. The fiber-matrix interface is modelled by constitutive relations that specify the value of the shear stress in terms of the relative displacements of the fiber and the matrix along the interface. Two different forms of constitutive relations are considered, one corresponding to an elastic interface model, another to a plastic interface model with possible debonding at sufficiently large interface displacement. The latter model is used to study the process of interface crack growth and fiber pull out. Analytic and numerical solutions are presented for the both models.     

Study on fracture behavior of particulate reinforced magnesium matrix composite using in situ SEM

The fracture behavior of SiCp/AZ91 magnesium matrix composite fabricated by stir casting is investigated using the in situ SEM technique. Experimental results show that (1) the dominant microcrack nucleation mode is interface decohesion in particle-dense regions because of the weak interface formed during the solidification process of the composite and large stress concentrations caused by particle segregation, (2) microcracks coalesce by the failure of matrix ligaments between microcracks while additional microcracks are initiated in the particle-dense region ahead of the coalesced microcracks, and (3) cracks propagate by coalescence of microcracks or along the particle/matrix interface. And so we come to the conclusion that the fracture mechanism of SiCp/AZ91 composite is interface-controlled. The in situ SEM observations are verified by complementary SEM studies of the fractured specimens of conventional tensile tests. And so, the in situ SEM observations can be qualitative representation on the fracture behavior of bulk SiCp/AZ91 composite.     

基于细观有限元方法的复合材料横向力学性能分析

横向断裂是制约复合材料结构设计的关键点,传统细观模型因为不能充分考虑组分性能、体积分数和纤维形状及分布情况而不能有效预测材料横向力学性能。采用改进的随机序列吸收算法建立具有随机纤维分布的复合材料代表性体积单胞模型,考虑基体破坏和界面脱粘两种失效模式和固化过程中产生的残余应力,对模型在横向拉、压、剪3种载荷下的力学行为进行仿真计算。分析了不同界面强度对复合材料力学性能的影响规律。仿真结果与实验数据对比表明:横向模量预测误差在7%以内,压缩和剪切的强度误差在8%以内,结果一致性较好,表明该模型能够有效预测复合材料横向力学性能。     

Experimental testing of wood‐concrete and steel‐concrete composite elements in comparison with numerical testing

The paper presents the results of experimental tests with a numerical comparison of some typical composite element systems. Two different kinds of elements were tested: composite steel‐concrete and composite wood‐concrete elements. Deflections at midspan under monotonously increasing static load on simply supported beams were measured. The affects of different types of composite connections on the results were researched. In numerical tests the structure was modeled with two‐dimensional plane elements. The composite surface was modeled with two‐dimensional contact (interface) elements for the continuous connection simulation and modified beam elements for the discrete connection simulation. The applied material models include the most important nonlinear effects of concrete, steel and wood behavior, as well as the nonlinear behavior of the composite surface at the connection. The achieved results of the developed numerical model were compared with the results obtained through the experimental test.     

Coupled heat conduction and thermal stress analyses in particulate composites

This study introduces two micromechanical modeling approaches to analyze spatial variations of temperatures, stresses and displacements in particulate composites during transient heat conduction. In the first approach, a simple micromechanical model based on a first order homogenization scheme is adopted to obtain effective mechanical and thermal properties, i.e., coefficient of linear thermal expansion, thermal conductivity, and elastic constants, of a particulate composite. These effective properties are evaluated at each material (integration) point in three dimensional (3D) finite element (FE) models that represent homogenized composite media. The second approach treats a heterogeneous composite explicitly. Heterogeneous composites that consist of solid spherical particles randomly distributed in homogeneous matrix are generated using 3D continuum elements in an FE framework. For each volume fraction (VF) of particles, the FE models of heterogeneous composites with different particle sizes and arrangements are generated such that these models represent realistic volume elements “cut out” from a particulate composite. An extended definition of a RVE for heterogeneous composite is introduced, i.e., the number of heterogeneities in a fixed volume that yield the same expected effective response for the quantity of interest when subjected to similar loading and boundary conditions. Thermal and mechanical properties of both particle and matrix constituents are temperature dependent. The effects of particle distributions and sizes on the variations of temperature, stress and displacement fields are examined. The predictions of field variables from the homogenized micromechanical model are compared with those of the heterogeneous composites. Both displacement and temperature fields are found to be in good agreement. The micromechanical model that provides homogenized responses gives average values of the field variables. Thus, it cannot capture the discontinuities of the thermal stresses at the particle-matrix interface regions and local variations of the field variables within particle and matrix regions.     

State space formulation for composite beam-columns with partial interaction

A state space formulation is established for analyzing static responses of composite members with partial shear interaction under the combined action of an arbitrary transverse load and a constant axial force. Three generalized displacements (deflection, rotation angle, and interface slip) and three generalized forces (bending moment, shear force, and axial force) are combined into a state vector, which satisfies a state equation whose solution is easily obtained using matrix theory. The interfacial normal contact stress between the two subelements of a composite member is derived in order to check the validity of the basic assumption of identical deflection (or curvature) possessed by the two subelements. We find that, when a concentrated load alone acts on clamped–clamped or clamped–free beam-columns, tensile normal contact stress does appear at certain part of the interface. The formulation is then readily extended to analyze continuous composite beam-columns and inhomogeneous composite beam-columns. In particular, a non-continuous model of slip stiffness along the interface with discrete rectangular pulses is incorporated into the analysis, and the numerical results indicate a significant effect of slip stiffness ununiformity on the critical axial load as well as internal actions of the composite members.     

Numerical simulation of interface debonding with a combined damage/friction constitutive model

 Experimental studies for pull-out tests in fiber-reinforced composites reveal a softening behaviour due to interface crack growth between fiber and matrix followed by a contact friction behaviour on the cracked area. In this contribution this debonding process is modelled within the framework of interface damage mechanics, where the displacement discontinuities during the progressive decohesion are related to constitutive equations extended by an anisotropic damage model. The contact/friction behaviour after complete separation is described by a friction model analogously to the classical theory of plasticity. The simulation of the load-displacement curve in the pull-out test with the drop-off behaviour is achieved by introducing a Hermite polynomial. The numerical simulations are performed for glas/polystyrol fiber-reinforced composites, thus illustrating the progressive debonding and friction between both constituents and demonstrating a good agreement with experimental data of a pull-out test. Received 18 November 1999     

Failure mechanisms and fracture energy of hybrid materials

A shear-lag model of hybrid materials is developed. The model represents an alternating arrangement of two types of aligned linear elastic fibres, embedded in a linear elastic matrix. Fibre and matrix elements are taken to fail deterministically when the axial and shear stresses in them reach their respective strengths. An efficient solution procedure for determining the stress state for arbitrary configurations of broken fibre and matrix elements is developed. Starting with a single fibre break, this procedure is used to simulate progressive fibre and matrix failure, up to composite fracture. The effect of (1) the ratio of fibre stiffnesses, and (2) the ratio of the fibre tensile strength to matrix shear strength, on the composite failure mechanism, fracture energy, and failure strain is characterised. Experimental observations, reported in the literature, of the fracture behaviour of two hybrid materials, viz., hybrid unidirectional composites, and double network hydrogels, are discussed in the framework of the present model.     

Modeling progressive delamination of laminated composites by discrete element method

Discrete element method (DEM) was used to model progressive delamination of fiber reinforced composite laminates. The anisotropic composite plies were constructed through a hexagonal packing of particle elements. Contacts between the particles were represented by parallel bonds with the verified normal and shear elastic properties. The ply interface was characterized by a contact softening model with a bilinear elastic behavior which is similar to the cohesive zone model in the continuum mechanics. DCB, ELS and FRMM tests were simulated by the DEM model to assess its capability of modeling mode I, mode II and mix mode fracture of delamination, respectively. Good agreements were observed between the DEM and existing numerical and experimental results of loading curves, which confirmed that the DEM model can be used to simulate initiation and propagation of composite delamination, with more insights into microscopic material behavior, such as damage extension and plastic zone.     

Numerical model for composite structures with experimental confirmation

The paper briefly presents a numerical model for the simulation of composite structures. The main structure is modeled with two‐dimensional plane finite elements. The composite surface is modeled with two‐dimensional interface elements for the continuous connection simulation and modified beam elements for the discrete connection simulation. The applied material model’s primary purpose is the simulation of reinforced concrete structures. It includes the most important nonlinear effects of reinforced concrete behavior: yielding in compression and opening and propagation of cracks in tension, with tensile and shear stiffness of cracked concrete, as well as the nonlinear behavior of reinforced steel. It also includes nonlinear behavior of the composite surface and the connection elements. The model was confirmed in experimental tests of composite concrete Omnia slabs, which are in common usage. The achieved test results were compared with the results obtained through the developed numerical model.