Analysis of extension propagation process of interface crack between belts of a radial tire using a finite element method

A radial tire is a very complex structure made from rubber elastomers and fiber–rubber composite materials. During its use, extension propagation of interface crack between belts can occur, which obviously affects its durability and life. In the present paper, a new mathematical model of extension propagation of interface crack in complex composite structures is presented. The model can reveal the extension propagation dependence of interface crack on the relative size of energy release rates at the left and right crack tips and on the interfacial material properties. The extension propagation model of interface crack, Irwin’s virtual crack close technique and the finite element analysis method are used together in simulating numerically the extension propagation process of a interface crack between belts of a radial tire. The present study numerical results show that the extension propagation model of interface crack proposed in this paper can more realistically characterize the complexity of the extension propagation process of interface crack in complex composite structures.     

温差影响下的局部滑移接触行为的研究

针对不同温度装配件间接触界面的局部滑移问题,建立了三维稳态热弹性局部滑移接触的半解析求解模型.基于热弹性理论与热传导方程,构建了半空间受热流载荷和力载荷作用下的频响函数并建立了相应的影响系数矩阵.借助离散卷积-快速Fourier变换等数学工具,实现了针对高温压头与热弹性半空间局部滑移接触问题的高效求解.接触界面间的热量传递满足Fourier热传导定律,并且黏/滑状态由Coulomb定律确定.基于该半解析模型分析了不同荷载及温差对表面法向压力分布、摩擦力分布、刚体位移及接触区黏/滑演化行为的影响.研究结果表明,当法向荷载和切向荷载一定时,温差的上升会导致接触区域的减小,引起接触面法向压力及摩擦力的峰值增大,并且会显著影响黏着区与滑移区的分布情况.     

Creep of Heat-Resistant Composites of an Oxide-Fiber/Ni-Matrix Family

A creep model of a composite with a creeping matrix and initially continuous elastic brittle fibers is developed. The model accounts for the fiber fragmentation in the stage of unsteady creep of the composite, which ends with a steady-state creep, where a minimum possible average length of the fiber is achieved. The model makes it possible to analyze the creep rate of the composite in relation to such parameters of its structure as the statistic characteristics of the fiber strength, the creep characteristics of the matrix, and the strength of the fiber-matrix interface, the latter being of fundamental importance. A comparison between the calculation results and the experimental ones obtained on composites with a Ni-matrix and monocrystalline and eutectic oxide fibers as well as on sapphire fiber/TiAl-matrix composites shows that the model is applicable to the computer simulation of the creep behavior of heat-resistant composites and to the optimization of the structure of such composites. By combining the experimental data with calculation results, it is possible to evaluate the heat resistance of composites and the potential of oxide-fiber/Ni-matrix composites. The composite specimens obtained and tested to date reveal their high creep resistance up to a temperature of 1150°C. The maximum operating temperature of the composites can be considerably raised by strengthening the fiber-matrix interface.     

On the calculation of crack face opening displacements in fiber reinforced composites under plane loading

This paper concerns with the calculation of the crack face opening displacement in fiber reinforced composites using analytical, semi-analytical and numerical approaches. Crack bridging is one of the most characteristic effects of fibers on the material behavior of the composite. Knowing the crack face opening displacement the additional strain due to cracks can be calculated and used in homogenization procedures. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Simple Model for the Simulation of Delamination in Fiber-ReinforcedComposite Laminates under Mixed-Mode Loading Conditions

For a reliable prediction of the mechanical behavior of unidirectional fiber-reinforced composite laminates (FRCL), it is inevitable to take into account various damage and fracture mechanisms. In this work, delamination under arbitrary mixedmode loading conditions is examined in the framework of the finite element method. Delamination is assumed to be caused by failure of the resin-rich area in the interface between two layers of FRCL's. In this work, a cohesive interface elementin terms of natural stress-strain relationships which allows to describe the interlaminar mechanical behavior of FRCL's is introduced. The proposed model prevents the restoration of cohesion in the interface. The interpenetration of the crack faces is avoided by incorporating a simple contact algorithm. A representative numerical example shows the applicability of the proposed concept. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Determination of effective thermal expansion coefficients of unidirectional fibrous nanocomposites

We present an efficient numerical scheme (based on complex variable techniques) to calculate the effective thermal expansion coefficients of a composite containing unidirectional periodic fibers. Moreover, the mechanical behavior of the fibers incorporates interface effects allowing the ensuing analytical model of the composite to accommodate deformations at the nanoscale. The resulting ‘nanocomposite’ is subjected to a uniform temperature variation which leads to periodic deformations within the plane perpendicular to the fibers and uniform deformations along the direction of the fibers. These deformation fields are determined by analyzing a representative unit cell of the composite subsequently leading to the corresponding effective thermal expansion coefficients. Numerical results are illustrated via several physical examples. We find that the influence of interface effects on the effective thermal expansion coefficients (in particular that corresponding to the transverse direction in the plane perpendicular to the fibers) decays rapidly as the fibers become harder. In addition, by comparing the results obtained here with those from effective medium theories, we show that the latter may induce significant errors in the determination of the effective transverse thermal expansion coefficient when the fibers are much softer than the matrix and the fiber volume fraction is relatively high.     

Predicting the elastoplastic response of fiber-reinforced metal matrix composites

This paper aims to investigate the effect of microstructure parameters (such as the cross-sectional shape of fibers and fiber volume fraction) on the stress–strain behavior of unidirectional composites subjected to off-axis loadings. A micromechanical model with a periodic microstructure is used to analyze a representative volume element. The fiber is linearly elastic, but the matrix is nonlinear. The Bodner–Partom model is used to characterize the nonlinear response of the fiber-reinforced composites. The analytical results obtained show that the flow stress of composites with square fibers is higher than with circular or elliptic ones. The difference in the elastoplastic response, which is affected by the fiber shape, can be disregarded if the fiber volume fraction is smaller than 0.15. Furthermore, the effect of fiber shape on the stress–strain behavior of the composite can be ignored if the off-axis loading angle is smaller than 30°.     

基于随机电阻网络碳毡复合层力阻建模

基于碳纤维单丝力阻效应影响因素的统计规律,揭示了碳毡复合层力阻传感特性的导电网络定量化模型．对碳纤维单丝相互搭接后的长度进行了讨论,得到关于纤维均长、纤维密度、纤维根数等多参量间的统计关系;在假设毡内纤维随机均匀分布且搭接点正态分布的情况下,分别对4种不同尺寸的碳纤维毡复合层的电阻进行了估测,并通过箱线图分析表明实测值在相应的估测范围内,说明本模型可较好地对碳纤维随机乱相分布的碳毡复合层电阻进行估测;最后,基于碳毡电阻网络的统计模型,对碳毡复合层的力阻特性进行了研究,通过比较理论电阻变化率与实测电阻变化率发现模型给出的复合层力阻效应灵敏系数较为稳定,从而表明随机电阻网络模型可较好的模拟碳毡受载荷时的力阻行为．     

A RVE-based micro mechanical model for short fiber reinforced plastic materials including matrix damage and fiber fracture

The representative volume element (RVE) method is applied to a fiber reinforced polymer material undergoing matrix damage and fiber fracture. Results of RVE computations are compared to uniaxial tensile tests performed with the composite material. It is shown that the macroscopic behavior of the composite material can accurately be predicted by RVE computations. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the simulation of textile reinforced concrete using a multi scale approach

Textile reinforced concrete (TRC) is a composite of textile structures made of multi-filament yarns (rovings) within a cementitious matrix. Experimental investigations of textile reinforced concrete specimen show very complex failure mechanisms on different length scales. Therefore mechanical models on the micro, meso and macro scale are introduced. The paper presents a hierarchical material model of TRC on three scales. While on the micro scale the individual filaments of the fiber bundles are distinguished to determine an effective roving behavior, models on the meso scale are used to predict the macroscopic response of the composite material. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

High-Temperature Creep of Fibrous Metal-Matrix Composites under Varying Stresses

The present paper is aimed at testing the hypothesis about the failure of the relatively weak fiber/matrix interface under cyclic loading, which causes an increase in the steady-state creep rate. The hypothesis is tested qualitatively by comparing the creep behavior of composite specimens with various interface strengths under the conditions mentioned (loading-unloading-loading to the original level). The hypothesis is tested semi-quantitatively by estimating the interface strength in relation to the action decreasing the strength. The latter requires the use of a microstructural calculation model. Both the approaches are used in the paper, and the results found support this hypothesis. The experimental data obtained are an additional argument for the necessity of developing metal-matrix composites with a strong interface, which can be a basis for real creep-resistant high-temperature composites.     

介质与结构三维动力相互作用分析的半解析边界元—半解析有限元结合法

本文将半解析边界元一半解析有限无结合法用于介质与结构的动力相互作用研究:用半解析边界元法分析具有复杂地表面的半无限介质,用半解析有限元法分析具有任意截面形状的柱体结构,利用介质与结构交界面上的位移相容条件和力平衡条件,将介质与结构联系起来。联立京解上述半解析边界元方程和半解析有限元方程,对应每一时间步进,可同时求出介质与结构交界面上的位移、速度、加速度和相互作用力以及地表面的运动情况.与目前广泛研究的边界元—有限元结合法相比,本方法在介质与结构二个个区域各降低了一维空间,因而离散单元数和计算工作量大幅度减少,人工输入数据非常简单.文中还考虑了地下结构的长跨比效应、厚度效应和介质效应.     

Analysis of wave propagation in functionally graded piezoelectric composite plates reinforced with graphene platelets

This paper presents a semi-analytical approach to investigate wave propagation characteristics in functionally graded graphene reinforced piezoelectric composite plates. Three patterns of graphene platelets (GPLs) describe the layer-wise variation of material properties in the thickness direction. Based on the Reissner-Mindlin plate theory and the isogeometric analysis, elastodynamic wave equation for the piezoelectric composite plate is derived by Hamilton’s principle and parameterized with the non-uniform rational B-splines (NURBS). The equation is transformed into a second-order polynomial eigenvalue problem with regard to wave dispersion. Then, the semi-analytical approach is validated by comparing with the existing results and the convergence on computing dispersion behaviors is also demonstrated. The effects of various distributions, volume fraction, size parameters and piezoelectricity of GPLs as well as different geometry parameters of the composite plate on dispersion characteristics are discussed in detail. The results show great potential of graphene reinforcements in design of smart composite structures and application for structural health monitoring.     

Numerical investigations in structures with imperfect material interfaces and cracks

Natural fiber reinforced bio-polymers are in the focus of many research projects to understand and improve the mechanical behavior subjected to different process parameters during production. To provide safe and reliable light weight constructions, special interest is directed towards the damage and fracture behavior of such composite materials. Here, the material's behavior at the imperfect material interface between fiber and matrix plays an essential role and governs inelastic effects at the interfaces on the one hand, and the behavior of growing cracks on the other. The reduction of the elastic potential is related to both energy consuming processes in the system and in general is going along with a reduction of the crack tip loading and a shift of the crack growth direction. In this paper, the crack tip loading analysis in structures with perfect and imperfect material interfaces is presented and applied to different specimens. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling large amplitude vibration of pretwisted hybrid composite blades containing CNTRC layers and matrix cracked FRC layers

A modeling of the large amplitude free vibration of pretwisted hybrid composite blades is studied by considering the laminated structure which is composed of carbon nanotube reinforced composite (CNTRC) layers and matrix cracked fiber reinforced composite (FRC) layers. Two assumptions are made to facilitate this vibration study of hybrid nanocomposite: (1) CNTs are distributed across the layer thickness uniformly or functionally graded, and (2) the parallel slit matrix cracks disperse in the matrix homogeneously. Based on the theory of differential geometry, a novel shell model for pretwisted hybrid nanocomposites blade is developed. The von Kármán strains are adopted to capture the geometrically nonlinear behaviors of blades. The established governing equations are solved accurately and efficiently via the IMLS-Ritz method. The proposed numerical model is verified by making comparison studies and then the influence of crack density, pretwisted angle, CNT distribution and volume fraction, aspect ratio, width-to-thickness ratio, and ply-angle on the large amplitude vibration characteristics of matrix cracked pretwisted hybrid composite blade are scrutinized systematically. The present study serves as a useful benchmark to researchers who intend do further research in this topic.     

Boundary-value problem in the correlative approximation of the method of quasi-periodic components for a unidirectional fiber composite

The boundary-value problem in the correlative approximation of the method of quasi-periodic components and a numerical algorithm based on the boundary element method for determining the nonuniform stress fields in the matrix of a unidirectional fiber composite with a disordered structure are considered. The numerical results and analysis of the probability density function, for example, for normal stresses at some points of the interface of absolutely rigid fibers of the composite are presented. Perm State Technical University, Russia. Translated from Mekhanika Kompozytnykh Materialov, Vol. 35, No. 5, pp. 629–642, September–October, 1999.     

Modeling of microscopic failure in heterogeneous materials

The proper modeling of state-of-the-art engineering materials requires a profound understanding of the nonlinear macroscopic material behavior. Especially for heterogeneous materials the effective macroscopic response is amongst others driven by damage effects and the inelastic material behavior of the individual constituents [1]. Since the macroscopic length scale of such materials is significantly larger than the fine-scale structure, a direct modeling of the local structure in a component model is not convenient. Multiscale techniques can be used to predict the effective material behavior. To this end, the authors developed a modeling technique based on representative volume elements (RVE) to predict the effective material behavior on different length scales. The extended finite element method (XFEM) is used to model discontinuities within the material structure independent of the underlying FE mesh. A dual enrichment strategy allows for the combined modeling of kinks (material interfaces) and jumps (cracks) within the displacement field [2]. The gradual degradation of the interface is thereby controlled by a cohesive zone model. In addition to interface failure, a non-local strain driven continuum damage model has been formulated to efficiently detect localization zones within the material phases. An integral formulation introduces a characteristic length scale and assures the convergence of the approach upon mesh refinement [3]. The proposed method allows for an efficient modeling of substantial failure mechanisms within a heterogeneous structure without the need of remeshing or element substitution. Due to the generality of the approach it can be used on different length scales. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimization of piezoelectric fiber distribution in composite smart materials

A new approach to obtain macroscopic properties of fiber‐matrix composite materials is given by the optimization of the fiber distribution for a given pair of materials. The optimization was carried out by Evolution Strategies using an interface to the finite‐element‐software ANSYS. To cover the effects of varied micro level parameters, a homogenization algorithm was included in the optimization process. Two applications verify the correct implementation of the software. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlinear finite element analysis and modeling of a precast hybrid beam–column connection subjected to cyclic loads

In this work, a detailed three-dimensional (3D) nonlinear finite element model is developed to study the response and predict the behavior of precast hybrid beam–column connection subjected to cyclic loads that was tested at the National Institute of Standards and Technology (NIST) laboratory. The precast joint is modeled using 3D solid elements and surface-to-surface contact elements between the beam/column faces and interface grout in the vicinity of the connection. The model takes into account the pre-tension effect in the post-tensioning strand and the nonlinear material behavior of concrete. The model response is compared with experimental test results and yielded good agreement at all stages of loading. Fracture of the mild-steel bars resulted in the failure of the connection. In order to predict this failure mode, stress and strain fields in the mild-steel bars at the beam–column interface were generated from the analyzed model. Such fields of stresses and strains are hard to measure in experimental testing. In addition, the magnitude of the force developed in the post-tensioning steel tendon was also monitored and it was observed that it did not yield during the entire loading history. Successful finite element modeling will provide a practical and economical tool to investigate the behavior of such connections.     

On the simulation of textile reinforced composites and structures

This paper presents experimental and numerical methods to perform simulations of the mechanical behavior of textile reinforced composites and structures. The first aspect considered refers to the meso-to-macro transition in the framework of the finite element (FE) method. Regarding an effective modelling strategy the Binary Model is used to represent the discretized complex architecture of the composite. To simulate the local response and to compute the macroscopic stress and stiffness undergoing small strain a user routine is developed. The results are transfered to the macroscopic model during the solution process. The second aspect concerns the configuration of the fiber orientation and textile shear deformation in complex structural components. To take these deformations which affect the macroscopic material properties into account they are regarded in a macroscopic FE model. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)