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.     

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。      

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.     

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。      

A meso-scale finite element model for simulating free-edge effect in carbon/epoxy textile composite

Textile composites are well known for their excellent through thickness properties and impact resistance. In this study, a representative unit cell model of a triaxial braided composite is developed based on the composite fiber volume ratio, specimen thickness and microscopic image analysis. A meso-scale finite element (FE) mesh is generated based on the detailed unit cell dimensions and fiber bundle geometry parameters. The fiber bundles are modeled as unidirectional fiber reinforced composites. A micromechanical finite element model was developed to predict the elastic and strength material properties of each unidirectional composite by imposing correct boundary conditions that can simulate the actual deformation within the braided composite. These details are then applied in the meso-mechanical finite element model for a 0°/+60°/−60° triaxially braided T700s/E862 carbon/epoxy composite. Model correlations are conducted by comparing numerical predicted and experimental measured axial tension and transverse tension response of a straight-sided, single-layer (one ply thick) coupon. By applying a periodic boundary condition in the loading direction, the meso model captures the local damage initiation and global failure behavior, as well as the periodic free-edge warping effect. The failure mechanisms are studied using the field damage initiation contours and local stress history. The influence of free-edge effect on the failure behaviors is investigated. The numerical study results reveal that this meso model is capable of predicting free-edge effect and allows identification of its impact on the composite response.     

Micromechanics based analysis of randomly distributed fiber reinforced composites using simplified unit cell model

The geometry of the simplified unit cell (SUC) model [Aghdam MM, Smith DJ, Pavier MJ. Finite element micromechanical modeling of yield and collapse behavior of metal matrix composites. J Mech Phys Solids 48 (2000) 499–528] is extended to study effects of random fiber arrangement on the mechanical and thermal characterizations of unidirectional composites. The representative volume element (RVE) considered in the model consists of an r × c unit cells in which fibers are surrounded randomly by matrix cells. The presented model is general and can be used to predict the behavior of a fibrous composite subjected to thermal and mechanical, normal and shear, loading. The model also is capable of analyzing various combinations of these loading conditions such as off-axis test of unidirectional coupons. Both random and repeating fiber arrays can be considered in the model. Results for the overall thermal and elastic properties of a SiC/Ti metal matrix composite (MMC) show good agreement with both the finite element and other analytical models with repeating fiber arrays. Results of transverse properties also revealed that hexagonal array assumption for fiber arrangement is more realistic than square array assumption.     

连续石墨纤维增强铝基复合材料准静态拉伸损伤演化与断裂力学行为

针对连续石墨纤维增强铝基(CF/Al)复合材料,采用三种纤维排布方式的代表体积单元(RVE)建立了其细观力学有限元模型,采用准静态拉伸试验与数值模拟结合的方法,研究了其在轴向拉伸载荷下的渐进损伤与断裂力学行为。结果表明,采用基体合金和纤维原位力学性能建立的细观力学有限元模型,对轴向拉伸弹性模量和极限强度的计算结果与实验结果吻合良好,而断裂应变计算值较实验结果偏低。轴向拉伸变形中首先出现界面和基体合金损伤现象,随应变增加界面发生失效并诱发基体合金的局部失效,最后复合材料因纤维发生失效而破坏,从而出现界面脱粘后纤维拔出与基体合金撕裂共存的微观形貌。细观力学有限元分析结果表明,在复合材料制备后纤维性能衰减而强度较低条件下,改变界面强度和刚度对复合材料轴向拉伸弹塑性力学行为的影响较小,复合材料中纤维强度水平是决定该复合材料轴向拉伸力学性能的主要因素。     

Micromechanical analysis of stress relaxation response of fiber-reinforced polymers

The paper describes a micromechanical method to determine the stress relaxation response of polymer composites consisting of linearly viscoelastic matrices and transversely isotropic elastic fibers. A representative unit cell is subjected to some prescribed axial and shear loadings to study and quantify the time-dependent behavior of composite materials. Closed-form analytical expressions are derived describing the anisotropic viscoelastic response of composite materials as functions of matrix and fiber properties. The present analytical expressions are employed to determine the stress relaxation behavior of a graphite/epoxy composite and the results are compared with the finite element analysis of the micromechanical model. Very good correlation between analytical expressions and numerical results is illustrated for the linearly anisotropic viscoelastic response of composite materials.     

Explicit cross-link relations between effective elastic modulus and thermal conductivity for fiber composites

Explicit cross-link relations between effective elastic modulus and thermal conductivity for composites with different fiber orientation are derived with help of Mori-Tanaka micromechanical method. Numerical cross-link relations are also established by digital-image-based finite element method, and they compare favorably with the analytical cross-link relations especially for the composite with aligned fibers and planar randomly oriented fibers. Both analytical and numerical cross-link relations agree well with the experimental results available in the literature. For the composite with space randomly oriented fibers, the numerically obtained cross-link relations are insensitive to the fiber’s shape, and the analytical cross-link relations are weakly dependent on fiber’s shape. In sum, the sensitivity of cross-link relations to the fiber’s shape depends on the extent of anisotropic behavior of fiber composites. Such cross-link relations can be potentially applied for predicting the difficult-to-measure elastic modulus from the measured thermal conductivities.     

An RVE-based micromechanical analysis of fiber-reinforced composites considering fiber size dependency

An RVE-based micromechanical elastic damage model considering fiber size dependency is presented to predict the effective elastic moduli and interfacial damage evolution in fiber-reinforced composites. To assess the validity of the present model, the predictions based on the proposed micromechanical elastic model are compared with Hashin’s theoretical bounds [Hashin Z. Analysis of properties of fiber composites with anisotropic constituents. J Appl Mech: Trans ASME 1979;46:543–50]. The proposed micromechanical elastic damage model is then exercised under uniaxial loading conditions to show the overall elastic damage behavior of the proposed micromechanical framework and to illustrate fiber size effect on the behavior of the composites. Moreover, comparisons between the present prediction and experimental data are made to further illustrate the capability of the proposed micromechanical framework for predicting the elastic damage behavior of fiber-reinforced composites.     

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.     

Micromechanical analysis of layered systems of MMCs subjected to bending––effects of thermal residual stresses

A three-dimensional finite element micromechanical model is presented to study the effects of manufacturing process thermal residual stresses on the mechanical behavior of layered systems of metal matrix composites subjected to four point bending. The presented model contains layered systems, consisting of layers of monolithic titanium alloy (IMI834) and unidirectional fiber reinforced titanium metal matrix composite (SiC/Ti). A representative volume element (RVE) was defined and appropriate boundary conditions were imposed to apply bending and temperature change simultaneously on the model. In an agreement with experimental data, the model is able to predict asymmetric behavior of the composite in tension and compression on the bottom and top surfaces of the beam. This is due to the existence of a high level of thermal residual stresses arising from cool-down from manufacturing temperature. As a result of this asymmetric behavior, the neutral axis of the beam during bending moves from the mid-surface through the compressive part of the beam.     

双斜接修补复合材料层合板的拉伸行为及影响因素双斜接修补复合材料层合板的拉伸行为及影响因素

基于试验和有限元数值方法对双斜接修补碳纤维增强聚合物（CFRP）复合材料层合板在拉伸载荷作用下的力学行为开展研究。通过试验分析了两种不同厚度的双斜接修补复合材料结构的承载能力和失效形式。结果表明,对于不同厚度的双斜接修补复合材料结构,失效强度接近,主要破坏形式均以胶层内聚破坏为主,伴随局部的90°基体开裂。利用连续介质损伤力学模型和内聚力模型分别对复合材料和胶层失效进行描述,通过数值方法开展双斜接修补结构的强度预测和损伤演化分析。数值结果与试验吻合较好,并且指出复合材料基体开裂起始早于胶层失效。通过有限元模型讨论了附加层、双斜接内部尖端所处位置和修补胶层参数对修补性能的影响。      

智能材料电-磁-热-弹耦合性能的细观力学模型

基于变分渐近均匀化方法建立能预测智能材料电-磁-热-弹全耦合性能的细观力学模型。从智能材料电-磁-热-弹耦合本构方程中推导能量泛函变分表达式出发,利用单胞细观尺度与宏观尺度比作为小参数将材料的能量泛函渐近扩展为系列近似泛函,通过最小化近似泛函求解场变量的波动函数,从而建立逼近物理和工程真实性的细观力学模型,并通过有限元数值实现。通过BaTiO₃-CoFe₂O₄纤维/环氧树脂复合材料算例表明:构建的细观力学模型可准确预测电-磁-热-弹耦合性能和重构多物理场局部分布。      

Determination of fracture stress and strain of highly oriented short fibre-reinforced composites using a fracture mechanics-based iterative finite-element method

For a tensile test specimen made of a short fibre-reinforced composite with the fibres oriented in the direction of force, a model was developed to describe the onset and propagation of microcracks, which finally lead to macroscopic failure of the specimen. The crack propagation theory used is based on a standard fracture mechanics method and was applied to the microstructure of the specimen by the finite element method. The results appear qualitatively correct. The micromechanical method applied gives a deeper insight into the fracture processes within short fibre-reinforced composites.     

A computational approach for prediction of the damage evolution and crushing behavior of chopped random fiber composites

A computational model is developed, by implementing the damage models previously proposed by authors into a finite element code, for simulating the damage evolution and crushing behavior of chopped random fiber composites. Material damages induced by fiber debonding and crack nucleation and growth are considered. Systematic computational algorithms are developed to combine the damage models into the constitutive relation. Based on the implemented computational model, a range of simulations are carried out to probe the behavior of the composites and to validate the proposed methodology. Numerical examples show that the present computational model is capable of modeling progressive deterioration of effective stiffness and softening behavior after the peak load. Crushing behavior of composite tube is also simulated, which shows the applicability of the proposed computational model for crashworthiness simulations.     

Micromechanical modeling and experimental characterization on viscoelastic behavior of 1–3 active composites

A study on the temperature-dependent viscoelastic behavior of (1–3 active composites) 1–3 piezocomposites and bulk piezoceramic subjected to electromechanical loading is carried out. The temperature-dependent effective properties are obtained experimentally using resonance based measurement technique. Experiments are also preformed for various fiber volume fractions of 1–3 piezocomposites subjected to constant compressive prestress and cyclic electric field at elevated temperature to understand the time-dependent behavior. Based on the measurements it is observed that the viscoelastic behavior has a significant influence on the electromechanical responses of 1–3 piezocomposites. Hence a viscoelastic based numerical model (unit cell approach) is proposed to predict the time-dependent effective properties of 1–3 piezocomposites. The evaluated effective properties are incorporated in a finite element based 3-D micromechanical model to predict the time-dependent thermo-electro-mechanical behavior of 1–3 piezocomposites and compared with the experimental observations.     

On the capability of micromechanics models to capture the auxetic behavior of fibers/particles reinforced composite materials

This work investigates the possibility to predict the auxetic behavior of composites consisting of non-auxetic phases by means of micromechanical models based on Eshelby’s inclusion concept. Two specific microstructures have been considered: (i) the three-layered hollow-cored fibers-reinforced composite and (ii) a microstructure imitating the re-entrant honeycomb micro-architecture. The micromechanical analysis is based on kinematic integral equations as a formal solution of the inhomogeneous material problem. The interaction tensors between the inhomogeneities are computed thanks to the Fourier’s transform. The material anisotropy due to the morphological and topological textures of the inhomogeneities was taken into account thanks to the multi-site approximation of these tensors. In both cases, the numerical results show that auxetic behavior cannot be captured by such models at least in the case of elastic and isotropic phases. This conclusion is supported by corresponding finite element investigations of the second microstructure that indicate that auxetic behavior can be recovered by introducing joints between inclusions. Otherwise, favorable issues are only expected with auxetic components.     

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.