Micromechanical effective elastic moduli of continuous fiber-reinforced composites with near-field fiber interactions

A higher-order micromechanical framework is presented to predict the overall elastic deformation behavior of continuous fiber-reinforced composites with high-volume fractions and random-fiber distributions. By taking advantage of the probabilistic pair-wise near-field interaction solution, the interacting eigenstrain is analytically derived. Subsequently, by making use of the Eshelby equivalence principle, the perturbed strain within a continuous circular fiber is accounted for. Further, based on the general micromechanical field equations, effective elastic moduli of continuous fiber-reinforced composites are constructed. An advantage of the present framework is that the higher-order effective elastic moduli of composites can be analytically predicted with relative simplicity, requiring only material properties of the matrix and fibers, the fiber?Cvolume fraction and the microstructural parameter ??. Moreover, no Monte Carlo simulation is needed for the proposed methodology. A series of comparisons between the analytical predictions and the available experimental data for isotropic and anisotropic fiber reinforced composites illustrate the predictive capability of the proposed framework.     

Modeling of progressive damage in aligned and randomly oriented discontinuous fiber polymer matrix composites

Damage constitutive models based on micromechanical formulation and a combination of micromechanical and macromechanical damage criterions are presented to predict progressive damage in aligned and random fiber-reinforced composites. Progressive interfacial fiber debonding models are considered in accordance with a statistical function to describe the varying probability of fiber debonding. Based on an effective elastoplastic constitutive damage model for aligned fiber-reinforced composites, micromechanical damage constitutive models for two- and three-dimensional (2D and 3D) random fiber-reinforced composites are developed. The constitutive relations and overall yield function for aligned fiber orientations are averaged over all orientations to obtain the constitutive relations and overall yield function of 2D and 3D, random fiber-reinforced composites. Finally, the present damage models are implemented numerically and compared with experimental data to show the progressive damage behavior of random fiber-reinforced composites. Furthermore, the damage models will be implemented into a finite element program to illustrate the dynamic inelastic behavior and progressive crushing in composite structures under impact loading.     

A computational approach to the investigation of impact damage evolution in discontinuously reinforced fiber composites

 A micromechanical damage constitutive model for discontinuous fiber-reinforced composites is developed to perform impact simulation. Progressive interfacial fiber debonding and a crack-weakened model are considered in accordance with a statistical function to describe the varying probability of damage. Emanating from a constitutive damage model for aligned fiber-reinforced composites, a micromechanical damage constitutive model for randomly oriented, discontinuous fiber-reinforced composites is developed. The constitutive damage model is then implemented into a finite element program DYNA3D to simulate the dynamic behavior and the progressive damage of composites. Finally, numerical simulations for a biaxial loading test and a four-point bend impact test of composite specimens are performed to validate the computational model and investigate impact damage evolution in discontinuous fiber-reinforced composite structures. Furthermore, in order to address the influence of Weibull parameter S _o on the damage evolution in composites, parametric analysis is carried out. Received 29 April 2000     

Multiscale finite element modeling of failure process of composite laminates

A multiscale nonlinear finite element modeling technique is developed in this paper to predict the progressive failure process for composite laminates. A micromechanical elastic–plastic bridging constitutive model, which considers the nonlinear material properties of the constituent fiber and matrix materials and their interaction and the damage and failure in fibrous composites at the fiber and matrix level, is proposed to represent the material behavior of fiber-reinforced composite laminates. The micromechanics constitutive model is employed in the macroscale finite element analysis of structural behavior especially progressive failure process of the fiber-reinforced composites based on a 4-node 24-DOF shear-locking free rectangular composite plate element.     

A two-scale homogenization framework for nonlinear effective thermal conductivity of laminated composites

In this study, we formulate the effective temperature-dependent thermal conductivity of laminated composites. The studied laminated composites consist of laminas (plies) made of unidirectional fiber-reinforced matrix with various fiber orientations. The effective thermal conductivity is obtained through a two-scale homogenization scheme. A simplified micromechanical model of a unidirectional fiber-reinforced lamina is formulated at the lower scale. Thermal conductivities of fiber and matrix constituents are allowed to change with temperature. The upper scale uses a sublaminate model to homogenize temperature-dependent thermal conductivities of only a representative lamina stacking sequence in laminated composites. The effective thermal conductivity of each lamina, in the sublaminate model, is obtained using the simplified micromechanical model. The thermal conductivities from the micromechanical and sublaminate models represent average nonlinear properties of fictitiously homogeneous composite media. Interface conditions between fiber and matrix constituents and within laminas are assumed to be perfect. Experimental data available in the literature are used to verify the proposed multi-scale framework. We then analyze transient heat conduction in the homogenized composites. Temperature profiles, during transient heat conduction, in the homogenized composites are compared to the ones in heterogeneous composites. The heterogeneous composites, having different fiber arrangements and sizes, are modeled using finite element (FE) method.     

Predictions of viscoelastic strain rate dependent behavior of fiber-reinforced polymeric composites

A viscoelastic damage model for aligned and 3D randomly oriented discontinuous fiber-reinforced polymeric composites is proposed. The model, which predicts the effective viscoelastic stress-strain behavior of the composites, is based on a combination of the Laplace-transformed superposition principle and the ensemble-averaged micromechanics. The Weibull’s damage function is incorporated into the model for the modeling of the evolution of damaged fibers. An inverse analysis based on experimental data is adopted to simulate the strain rate sensitivity of the model. A series of numerical simulations based on the proposed model are performed to examine the influence of damage parameters, fiber orientations, strain rates, and the aspect ratio of discontinuous fibers on the behavior of the composites. In addition, experimental comparisons are made to illustrate and assess the predictive capability of the proposed model.     

Progressive failure of triaxial woven fabric (TWF) composites with open holes

A computational approach to the investigation of crack evolution and interaction effects of microcracks and particles on the overall behavior of particle-reinforced brittle composites (PRBCs) is presented. To account for interactions of microcracks and particles, and their effects on the overall mechanical behavior, approximate solutions of a micromechanical model considering second-order, ensemble-volume averaged perturbations are employed. By combining the micromechanical framework with a fracture-mechanics based damage model, an evolutionary damage model of PRBCs is subsequently developed and the evolutionary damage model is implemented into a finite element code. The proposed computational damage model is exercised from benchmark examples on PRBCs to illustrate the capability of the proposed damage models for predicting the progressive crack evolution in PRBCs.     

A cohesive crack model to study the fracture behaviour of fiber-reinforced brittle-matrix composites

A cohesive crack model analysis of the fracture resistance and ductility of fiber-reinforced brittle-matrix composites was performed. The bulk material is assumed to behave as a linear elastic solid. The constitutive equation for the cohesive crack is obtained through micromechanical considerations based on the shear lag model of fiber-matrix interaction and on the statistical nature of fiber failure. A parametrical study of the influence of fiber volume fraction, fiber strength and flaw distribution, interfacial shear stress and specimen geometry on the fracture resistance of these composites was carried out. The results illustrate the role of each of these factors in overall composite toughening, and suggest various strategies to improve the composites' performance.     

Progressive damage modeling in fiber-reinforced materials

This paper presents an anisotropic damage model suitable for predicting failure and post-failure behavior in fiber-reinforced materials. In the model the plane stress formulation is used and the response of the undamaged material is assumed to be linearly elastic. The model is intended to predict behavior of elastic-brittle materials that show no significant plastic deformation before failure. Four different failure modes – fiber tension, fiber compression, matrix tension, and matrix compression – are considered and modeled separately. The onset of damage is predicted using Hashin’s initiation criteria [Hashin Z, Rotem A. A fatigue failure criterion for fiber-reinforced materials. J Compos Mater 1973;7:448; Hashin Z. Failure criteria for unidirectional fiber composites. J Appl Mech 1980;47:329–34] and the progression of damage is controlled by a new damage evolution law, which is easy to implement in a finite element code. The evolution law is based on fracture energy dissipation during the damage process and the increase in damage is controlled by equivalent displacements. The issues related to numerical implementation, such as mesh sensitivity and convergence in the softening regime, are also addressed.     

Modelling and simulation of the mechanical behavior of ceramic matrix composites as shown by the example of SiC/SiC

Modelling of the mechanical behavior of unidirectionally fiber-reinforced ceramic matrix composites (CMC) is presented by the example of SiC/SiC. The starting point of the modelling is a substructure (elementary cell) which includes on a micromechanical scale the statistical properties of the fiber, matrix and fiber–matrix interface and their interactions. The substructure is chosen in such a way that a macrostructure representative of the whole structure can be modelled from a suitable number of substructures. The typical damage behavior of ceramic composites is modelled by taking fiber and matrix cracks into account. Cracks are inserted into the substructure by reducing the elastic coefficients of the material. The fracture criterion used is a surface represented by a spheroid in the principal stress space. The crack direction is determined by the criterion of the energy release rate. Interfacial behavior is simulated by consideration of fiber–matrix debonding and frictional sliding. The numerical evaluation of the model is accomplished by means of the finite element method (FEM). The effect of important parameters such as the fiber volume fraction or the fiber Weibull-shape parameter on the nonlinear behavior of the substructure is examined. Finally, a macrostructure is modelled to show the effects of these important parameters on the mechanical behavior of the whole structure.     

A rate-independent elastoplastic constitutive model for biological fiber-reinforced composites at finite strains: continuum basis, algorithmic formulation and finite element implementation

 This paper presents a rate-independent elastoplastic constitutive model for (nearly) incompressible biological fiber-reinforced composite materials. The constitutive framework, based on multisurface plasticity, is suitable for describing the mechanical behavior of biological fiber-reinforced composites in finite elastic and plastic strain domains. A key point of the constitutive model is the use of slip systems, which determine the strongly anisotropic elastic and plastic behavior of biological fiber-reinforced composites. The multiplicative decomposition of the deformation gradient into elastic and plastic parts allows the introduction of an anisotropic Helmholtz free-energy function for determining the anisotropic response. We use the unconditionally stable backward-Euler method to integrate the flow rule and employ the commonly used elastic predictor/plastic corrector concept to update the plastic variables. This choice is expressed as an Eulerian vector update the Newton's type, which leads to a numerically stable and efficient material model. By means of a representative numerical simulations the performance of the proposed constitutive framework is investigated in detail. Received: 12 December 2001 / Accepted: 14 June 2002 Financial support for this research was provided by the Austrian Science Foundation under START-Award Y74-TEC. This support is gratefully acknowledged.     

Micromechanical simulation of tensile failure of discontinuous fiber-reinforced polymer matrix composites using Spring Element Model

The micromechanical damage and strength of discontinuous fiber-reinforced polymer matrix composites was simulated by the Spring Element Model (SEM), and SEM was compared with Periodic Unit-Cell (PUC) simulation to clarify the potential of SEM. Tensile failure simulations indicate that SEM can be effectively used to predict the strength of long discontinuous fiber reinforced composites. The transition between matrix cracking mode and fiber breaking mode is also discussed to clarify the fiber length at which SEM can be used to predict strength. In addition, the strengths predicted with SEM are compared with the results of experiments on long discontinuous fiber-reinforced thermoplastic composites.     

A micromechanics based multiscale model for nonlinear composites

A micromechanics model for fiber-reinforced composites that can be used at the subscale in a multiscale computational framework is established to predict the effective nonlinear composite response. Using a fiber–matrix concentric cylinder model as the basic repeat unit to represent the composite, micromechanics is used to relate the applied composite strains to the fiber and matrix strains by a six by six transformation matrix. The resolved spatial variations of the matrix fields are found to be in good agreement with corresponding finite element analysis results. The evolution of the composite nonlinear response is assumed to be governed by two scalar, strain-based variables that are related to the extreme value of an appropriately defined matrix equivalent strain, and the matrix secant moduli are used to compute the composite secant moduli for nonlinear analysis. The results from the micromechanics model are compared well with a full finite element analysis. The predictive capability of the proposed model is illustrated by two distinct fiber-reinforced material systems, carbon and glass, for the fiber volume fraction varying from 50 to 70 %. Since fully analytical solutions are utilized for the micromechanical analysis, the proposed method offers a distinct computational advantage in a multiscale analysis and is therefore suitable for large-scale progressive damage and failure analyses of composite material structures.     

Effective transverse elastic moduli of three-phase hybrid fiber-reinforced composites with randomly located and interacting aligned circular fibers of distinct elastic properties and sizes

A higher-order multi-scale structure for three-phase hybrid fiber-reinforced composites containing randomly located yet unidirectionally aligned circular fibers is proposed to predict effective transverse elastic moduli based on the probabilistic spatial distribution of circular fibers, the pairwise fiber interactions, and the ensemble-area homogenization method. Specifically, the two inhomogeneity phases feature distinct elastic properties and sizes. Two non-equivalent formulations are considered in detail to derive effective transverse elastic moduli of three-phase composites leading to new higher-order bounds. Numerical examples and comparisons among our theoretical predictions and other analytical predictions are rendered to illustrate the potential capability of the present method.     

Development of a new constitutive model considering the shearing effect for anisotropic progressive damage in fiber-reinforced composites

A corrected Linde's criterion considering the shearing effect for anisotropic progressive damage is developed to describe the elastic-brittle behavior of fiber-reinforced composites. Based on this criterion, a new three-dimensional (3D) nonlinear finite element model for static damage of unidirectional fiber-reinforced composites is proposed within a framework of continuum mechanics. The model is validated by taking 3D braided composites as example to study the relationship between the damage of materials and the effective elastic properties. The impregnated unidirectional composites are treated as homogeneous and transversely isotropic materials, whose properties are calculated by the Chamis' equations. The more accurate failure mechanisms of composites are revealed in the simulation process, and the effects of braided parameters on the uniaxial tensile behavior of 3D braided composites are investigated. Comparison of numerical results and experimental data is also carried out, which shows a better agreement than that of former study using the 3D Hashin's criterion.     

Green's function vs. shear-lag models of damage and failure in fiber composites

A Green's function method (GFM) for simulating fiber damage evolution and tensile strength in fiber-reinforced composites is compared in detail to the predictions of the standard shear-lag model (SLM) widely used in the literature. The GFM extracts the in-plane stress concentration factors describing how a broken fiber redistributes in-plane load to surrounding unbroken fibers from more-detailed micromechanical models, such as finite-element models, and uses this limited information to then calculate the propagation of fiber damage up to composite failure. The GFM only approximately includes the three-dimensional nature of the stress transfer and uses an approximate superposition method, but reduces the computational problem significantly. Here, elastic and elastic/plastic 3D SLM are used to provide the stress-transfer input to the GFM, and then predictions for composite behavior from the GFM are compared directly to those from the SLM. For exactly the same starting configuration of stochastic fibers, the GFM predicts (i) evolution of the fiber damage and the formation of critical clusters that are nearly identical to, (ii) composite tensile strengths within 2% of, (iii) a Weibull modulus for the composite strength essentially equal to, that of the SLM, all while requiring over an order of magnitude less computational time for modest-size composites. The approximations made in the GFM are found to have little effect on composite properties. These results support the use of the GFM approach with stress transfer input from accurate detailed finite element studies rather than from approximate SLM. Furthermore, the GFM is well-suited for tackling a wide range of problems that cannot easily be studied using the SLM; e.g. bending deformation and failure, matrix crack propagation, fatigue crack growth, and other situations in which the fiber stress distribution is nonuniform even in the absence of any fiber damage.     

Micromechanics and effective elastic moduli of particle-reinforced composites with near-field particle interactions

A micromechanical framework is proposed to predict effective elastic moduli of particle-reinforced composites. First, the interacting eigenstrain is derived by making use of the exterior-point Eshelby tensor and the equivalence principle associated with the pairwise particle interactions. Then, the near-field particle interactions are accounted for in the effective elastic moduli of spherical-particle-reinforced composites. On the foundation of the proposed interacting solution, the consistent versus simplified micromechanical field equations are systematically presented and discussed. Specifically, the focus is upon the effective elastic moduli of two-phase composites containing randomly distributed isotropic spherical particles. To demonstrate the predictive capability of the proposed micromechanical framework, comparisons between the theoretical predictions and the available experimental data on effective elastic moduli are rendered. In contrast to higher-order formulations in the literature, the proposed micromechanical formulation can accommodate the anisotropy of reinforcing particles and can be readily extended to multi-phase composites.     

双随机分布细观分析模型与复合材料性能预报

发展了一种细观力学有限元分析方法——拟真实的参数化双随机分布模型, 该模型综合考虑了纤维增强树脂基复合材料的真实微结构特点和纤维单丝综合力学性能测试结果的离散性特征, 模拟了复合材料中纤维排列和强度分布的随机性。借助移动窗口法研究了该参数化双随机分布模型的可靠性, 确定了其代表性体积单元的尺寸。基于能量法原理推导了单向复合材料的弹性模量预测公式, 结合能量法和渐进失效分析方法, 利用该细观力学有限元方法分别预测了单向纤维增强树脂基复合材料T300/5228的弹性模量和强度性能。数值模拟结果和大部分试验结果吻合良好, 表明发展的细观力学有限元方法能够较好地预测复合材料的力学性能。      

含缺陷平纹机织复合材料拉伸力学行为数值模拟

基于平纹机织复合材料的细观结构单胞模型, 考虑其制备过程中产生的孔隙缺陷为随机分布的特征, 通过引入两参数Weibull分布函数, 应用Python语言实现了ABAQUS的二次开发, 并采用Linde等提出的失效准则, 建立了含孔隙缺陷平纹机织复合材料的渐进损伤模型, 利用有限元数值方法模拟了其拉伸应力-应变行为, 针对该模型, 讨论了孔隙缺陷对材料拉伸应力-应变行为的影响, 并阐述了该平纹机织复合材料单胞模型在经向拉伸载荷作用下其纤维束的损伤及演化过程。结果表明, 该模型给出的数值模拟结果与实验数据吻合较好, 证明了模型的有效性, 为该类材料的优化设计及其力学性能分析提供了一种有效方法。      

二维编织陶瓷基复合材料偏轴拉伸力学性能预测

基于二维编织C/SiC复合材料的细观结构,建立了碳纤维丝/热解碳界面/SiC基体和纤维束/表层SiC基体两种尺度下的细观单胞模型,通过有限元方法计算碳纤维丝/热解碳界面/SiC基体模型的等效弹性常数和强度,然后代入纤维束/表层SiC基体模型中计算,并引入Tsai-Wu失效准则,考虑不同失效模式的损伤,建立了二维编织C/SiC复合材料的渐进损伤模型,模拟了其偏轴拉伸应力-应变行为。针对该模型,阐述了二维编织C/SiC复合材料单胞模型在复杂应力状态下其纤维束的损伤过程。数值模拟结果与实验数据吻合较好,验证了模型的有效性,为该种材料的力学性能分析提供了一种有效方法。