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.     

A material model for the finite element analysis of metal matrix composites

A finite element based procedure is presented which accounts for micromechanical nonlinear behavior of the matrix material in continuous fiber reinforced composites. The micromechanical model is a periodic hexagonal array of elastic fibers embedded in an elastic-plastic matrix material. This model is used to calculate the overall instantaneous material matrix at material points of a macromechanical finite element model of the structure being analyzed. The procedure is applied to a number of metal matrix composite systems subjected to thermomechanical loads.     

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。      

Cohesive fracture modeling of crack growth in thick-section composites

This paper presents a combined method for modeling the mode-I and II crack growth behavior in thick-section fiber reinforced polymeric composites having a nonlinear material response. The experimental part of this study includes crack growth tests of a thick composite material system manufactured using the pultrusion process. It consists of alternating layers of E-glass unidirectional roving and continuous filament mats in a polymeric matrix. Integrated micromechanical and cohesive finite element (FE) models are used to simulate the crack growth response in eccentrically loaded single-edge-notch, (tension), ESE(T) and notched butterfly specimens. Micromechanical constitutive models for the mat and the roving layers are used to generate the effective nonlinear material behavior from the in situ fiber and matrix responses. The validity of the numerical modeling approach before the onset of crack growth is investigated using an infrared thermal method. Cohesive FE models are calibrated and used to simulate the complete crack growth behavior for different crack configurations. The proposed integrated framework of multi-scale material models with cohesive fracture models is shown to be an effective method for predicting the structural and material responses including failure load and crack growth in thick-section fiber reinforced polymeric composites.     

A micromechanics based analysis of hollow fiber composites using DQEM

In this study, a generalized plane strain micromechanical model is presented to obtain micro-stress/strain fields within the unidirectional (UD) hollow fiber reinforced composites. In addition, the thermally induced residual stresses during cooling down process, overall elastic properties and energy absorption capability of hollow reinforced composite are studied. The representative volume element (RVE) of the composite consists of a quarter of the fiber surrounded by matrix to represent the real composite with repeating square array of fibers. Fully bonded fiber–matrix interface condition is considered and the displacement continuity and traction reciprocity are properly imposed to the interface. The cubic serendipity shape functions are used to convert the solution domain to a proper rectangular domain. A Least-squares based differential quadrature element method (DQEM) is used to obtain solutions for the governing partial differential equations of the problem. Results of the presented method for various stress and displacement components and thermal residual stresses show excellent agreement with finite element analysis. Furthermore, predicted overall properties also show good agreement with other available analytical and finite element results. Moreover, results also revealed that the presented model can provide highly accurate predictions with a few number of elements and grid points within each element.     

基于细观力学的纤维沥青混凝土有效松弛模量

为了研究纤维沥青混凝土的本构模型,将其视为以沥青混合料为粘弹性基体,纤维为弹性夹杂的两相复合材料。对基于复合材料细观力学理论建立的有效模量表达式进行了修正,提出了纤维沥青混凝土的割线有效松弛模量。以聚酯纤维沥青混凝土为例进行了有效松弛模量的解析分析和模拟蠕变实验的有限元分析,分析结果与试验数据的比较表明,该文提出的割线有效松弛模量模型对于纤维沥青混凝土粘弹性力学行为具有很好的预测能力。应用该模型对路面弯沉变形进行了有限元分析,结果表明:纤维的加入有效的改善了沥青混凝土路面的粘弹性性能。     

Machining of UD-GFRP composites chip formation mechanism

The chip formation mechanism in orthogonal machining of unidirectional glass fiber reinforced polymer (UD-GFRP) composites is simulated using quasi-static analysis. Dynamic explicit finite element method with mass scaling is used for analysis to speed up the solution. A two-dimensional, two-phase micromechanical model with elastic fiber, elasto-plastic matrix and a cohesive zone is used to simulate the debonding interface between the fiber and the matrix. The elements of the fiber are failed once the maximum principal stress reaches the tensile strength and the matrix elastic modulus is degraded once the ultimate strength is reached. The effect of fiber orientation, tool parameters and operating conditions on fiber and matrix failure and chip size is also investigated. The degradation of the matrix adjacent to the fiber occurs first, followed by failure of the fiber at its rear side. The extent of sub-surface damage due to matrix cracking and interfacial debonding is also determined.     

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.     

BEM analysis of crack onset and propagation along fiber–matrix interface under transverse tension using a linear elastic–brittle interface model

The behavior of the fiber–matrix interface under transverse tension is studied by means of a new linear elastic–brittle interface model. Similar models, also called weak or imperfect interface models, are frequently applied to describe the behavior of adhesively bonded joints. The interface is modeled by a continuous distribution of linear-elastic springs which simulates the presence of a thin adhesive layer (interphase). In the present work a new linear elastic–brittle constitutive law for the continuous distribution of springs is introduced. In this law the normal and tangential stresses across the undamaged interface are, respectively, proportional to the relative normal and tangential displacements. This model not only allows for the study of crack growth but also for the study of crack onset. An important feature of this law is that it takes into account the variation of the fracture toughness with the fracture mode mixity of a crack growing along the interface between bonded solids, in agreement with previous experimental results. The present linear elastic–brittle interface model is implemented in a 2D boundary element method (BEM) code to carry out micromechanical analysis of the fiber–matrix interface failure in fiber-reinforced composite materials. It is considered that the behavior of the fiber–matrix interphase can be modeled by the present model although, strictly speaking, there is usually no intermediate material between fiber and matrix. A linear-elastic isotropic behavior of both fiber and matrix is assumed, the fiber being stiffer than the matrix. The failure mechanism of an isolated fiber under transverse tension, i.e., the onset and growth of the fiber–matrix interface crack, is studied. The present model shows that failure along the interface initiates with an abrupt onset of a partial debonding between the fiber and the matrix, caused by presence of the maximum radial stress at the interface, and this debonding further develops as a crack growing along the interface.     

复合材料非线性本构关系的机算机模拟

本文对单向连续纤维增强复合材料的弹塑性本构关系进行了数值模拟。首先提出了基于统一弹粘塑性本构理论的有限无法,然后利用微观力学模型研究了弹性纤维增强弹粘塑性基体的复合材料应力——应变关系。      

碳纤维增强聚合物复合材料车身T型接头静态性能与失效机制

通过解析预测、有限元分析和试验手段对热塑性碳纤维增强聚合物复合材料（CFRP）T型接头的面外弯曲和弯扭耦合力学性能进行研究,分析了T型接头的结构失效形式与力-位移曲线的关系,并将解析模型、有限元仿真与试验结果进行对比。在弯曲刚度方面,解析模型、有限元分析结果相对试验结果的刚度误差分别为4.7%和0.5%。在弯扭耦合刚度方面,解析模型及有限元仿真的结果相对试验结果的弯扭耦合刚度误差分别为6.9%和9.6%。试验结果表明,CFRP层合板的渐进失效引起T型接头弯曲刚度的衰减,当力达到2 047 N时接头开始发生失效,失效形式包括纤维的断裂、缠绕、树脂的压碎及纤维和树脂的分层等。      

Effective properties of three-phase electro-magneto-elastic composites

Coupling between the electric field, magnetic field, and strain of composite materials is achieved when electro-elastic (piezoelectric) and magneto-elastic (piezomagnetic) particles are joined by an elastic matrix. Although the matrix is neither piezoelectric nor piezomagnetic, the strain field in the matrix couples the electric field of the piezoelectric phase to the magnetic field of the piezomagnetic phase. This three-phase electro-magneto-elastic composite should have greater ductility and formability than a two-phase composite in which the electric field and the magnetic field are coupled by directly bonding two brittle materials. A finite element analysis (FEA) and micromechanics based averaging of a representative volume element (RVE) are performed in this work to determine the effective dielectric, magnetic, mechanical, and coupled-field properties of an elastic matrix reinforced with piezoelectric and piezomagnetic fibers as functions of the phase volume fractions, the fiber arrangements in the RVE, and the fiber material properties with special emphasis on the poling directions of the piezoelectric and piezomagnetic fibers. The effective magneto-electric moduli of this three-phase composite are found to be less than the effective magneto-electric moduli of a two-phase piezoelectric/piezomagnetic composite, because the elastic matrix is not stiff enough to transfer significant strains between the piezomagnetic and piezoelectric fibers.     

Micromechanical analysis of nanocomposites using 3D voxel based material model

A computational study on the effect of nanocomposite structures on the elastic properties is carried out with the use of the 3D voxel based model of materials and the combined Voigt–Reuss method. A hierarchical voxel based model of a material reinforced by an array of exfoliated and intercalated nanoclay platelets surrounded by interphase layers is developed. With this model, the elastic properties of the interphase layer are estimated using the inverse analysis. The effects of aspect ratio, intercalation and orientation of nanoparticles on the elastic properties of the nanocomposites are analyzed. For modeling the damage in nanocomposites with intercalated structures, “four phase” model is suggested, in which the strength of “intrastack interphase” is lower than that of “outer” interphase around the nanoplatelets. Analyzing the effect of nanoreinforcement in the matrix on the failure probability of glass fibers in hybrid (hierarchical) composites, using the micromechanical voxel-based model of nanocomposites, it was observed that the nanoreinforcement in the matrix leads to slightly lower fiber failure probability.     

Nonlinear Viscoelastic Response of Unidirectional Polymeric Laminated Composite Plates Under Bending Loads

Nonlinear bending analysis of polymeric laminated composite plate is examined considering material nonlinearity for viscoelastic matrix material through a Micro–macro approach. The micromechanical Simplified Unit Cell Method (SUCM) in three-dimensional closed-form solution is used for the overall behavior of the unidirectional composite in any combination of loading conditions. The elastic fibers are transversely isotropic where Schapery single integral equation in multiaxial stress state describes the matrix material by recursive-iterative formulation. The finite difference Dynamic Relaxation (DR) method is utilized to study the bending behavior of Mindlin annular sector plate including geometric nonlinearity under uniform lateral pressure with clamped and hinged edge constraints. The unsymmetrical laminated plate deflection is predicted for different thicknesses and also various pressures in different time steps and they are compared with elastic finite element results. As a main objective, the deflection results of viscoelastic laminated sector plate are obtained for various fiber volume fractions in the composite system.     

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.     

铝基复合材料应力传递的有限元分析

本文使用大型有限元分析软件Ansys建立了短纤维增强铝基复合材料的有限元模型,模拟复合材料界面上的应力应变分布,进一步详细分析了纤维的不同参数对纤维使用效率的影响,以及不同纤维弹性模量的匹配对应力传递的影响。     

Linear analysis of mechanics of single and multiple cracks at fiber/matrix interface using axisymmetric model

It is well known that the life of material composite depends on the hardness of the interface between the fiber and the matrix. Herein, the aim of this work is the calculation by finite element method interaction effect between a crack and an interface by energy release rate approach. The first part of this work is devoted to the crack normal to the interface and the second one deals with the crack terminated at the interface. In this study, two cases are considered using a copper matrix with different fibers. An axisymmetric model has been used to evaluate the conditions for the crack deflection/penetration by the interface as well as the effects of the volume percent of fibers and the effects of the distance between the crack tip and the interface were highlighted as well as the effects of the elastic properties of two bonded materials.     

Effects of fiber orientation and anisotropy on tensile strength and elastic modulus of short fiber reinforced polymer composites

An experimental study was conducted to investigate anisotropy effects on tensile properties of two short glass fiber reinforced thermoplastics. Tensile tests were performed in various mold flow directions and with two thicknesses. A shell–core morphology resulting from orientation distribution of fibers influenced the degree of anisotropy. Tensile strength and elastic modulus nonlinearly decreased with specimen angle and Tsai–Hill criterion was found to correlate variation of these properties with the fiber orientation. Variation of tensile toughness with fiber orientation and strain rate was evaluated and mechanisms of failure were identified based on fracture surface microscopic analysis and crack propagation paths. Fiber length, diameter, and orientation distribution mathematical models were also used along with analytical approaches to predict tensile strength and elastic modulus form tensile properties of constituent materials. Laminate analogy and modified Tsai–Hill criteria provided satisfactory predictions of elastic modulus and tensile strength, respectively.     

Simulation of Acoustic Emission in Planar Carbon Fiber Reinforced Plastic Specimens

The simulation of acoustic emission waveforms resulting from failure during mechanical loading of carbon fiber reinforced plastic structures is investigated using a finite element simulation approach. For this investigation we focus on the dominant failure mechanisms in fiber reinforced structures consisting of matrix cracking, fiber breakage and fiber-matrix interface failure. To simulate the failure process accurately, we present a new acoustic emission source model that is based on the microscopic source geometry and micromechanical properties of fiber and resin. We demonstrate that based on this microscopic source model these failure mechanisms result in excitation of macroscopic plate waves. The propagation of these plate waves is described using a macroscopic three-dimensional model geometry which includes contributions of reflections from the specimen boundaries. We further present a model of the acoustic emission sensors used in experiments to simulate the influence of aperture effects. To enhance the understanding of correlation between macroscopically detectable acoustic emission signals and microscopic failure mechanisms we simulate the response to different source excitation times, crack surface displacements and displacement directions. The results obtained show good agreement with fundamental assumptions about the crack process reported by various other authors. The simulated acoustic emission signals obtained are compared to experimentally measured waveforms during four-point bending experiments of carbon fiber reinforced plastic structures. The simulated signals of fiber-breakage, matrix-cracking and fiber-matrix interface failure show systematic agreement with the respective experimental signals.