基于剪切非线性三维损伤本构模型的复合材料层合板失效强度预测

基于连续损伤力学,建立了同时考虑复合材料剪切非线性效应和损伤累积导致材料属性退化的三维损伤本构模型。模型能够区分纤维损伤、基体损伤和分层损伤不同的失效模式,并定义了相应损伤模式的损伤变量。复合材料层合板层内纤维初始损伤采用最大应力准则判定,基体初始损伤采用三维Puck准则中的基体失效准则判定,分层初始损伤采用三维Hou准则中的分层破坏准则判定,为了计算Puck失效理论中的基体失效断裂面角度,本文提出了分区抛物线法,通过Matlab软件编写计算程序并进行分析。结果表明,与Puck遍历法和分区黄金分割法对比,本文提出的分区抛物线法有效地降低了求解断裂面角度的计算次数,提高了计算效率和计算精度。推导了本构模型的应变驱动显式积分算法以更新应力和解答相关的状态变量,开发了包含数值积分算法的用户自定义子程序VUMAT,并嵌于有限元程序Abaqus v6.14中。通过对力学行为展现显著非线性效应的AS4碳纤维/3501-6环氧树脂复合材料层合板进行渐进失效分析,验证了本文提出的材料本构模型的有效性。结果显示,已提出的模型能够较准确地预测此类复合材料层合板的力学行为及其失效强度,为复合材料构件及其结构设计提供一种有效的分析方法。      

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.     

Recent developments on damage modeling and finite element analysis for composite laminates: A review

Under complex environments such as continuous or cyclic loads, the stiffness degradation for the laminated composites such as the carbon fiber reinforced polymer matrix composites is an important physical and mechanical response to the damage and failure evolution. It is essential to simulate the initial and subsequent evolution process of this kind of damage phenomenon accurately in order to explore the mechanical properties of composite laminates. This paper gives a comprehensive review on the general methodologies on the damage constitutive modeling by continuum damage mechanics (CDM), the various failure criteria, the damage evolution law simulating the stiffness degradation, and the finite element implementation of progressive failure analysis in terms of the mechanical response for the variable-stiffness composite laminates arising from the continuous failure. The damage constitutive modeling is discussed by describing the evolvement of damage tensors and conjugate forces in the CDM theory. The failure criteria which interpret the failure modes and their interaction are compared and some advanced methods such as the cohesive theory which are used to predict the damage evolution properties of composites are also discussed. In addition, the solution algorithm using finite element analysis which implements progressive failure analysis is summarized and several applicable methods which deal with the numerical convergence problem due to singular finite element stiffness matrices are also compared in order to explore the whole failure process and ultimate load-bearing ability of composite laminates. Finally, the multiscale progressive failure analysis as a popular topic which associates the macroscopic with microscopic damage and failure mechanisms is discussed and the extended finite element method as a new finite element technique is expected to accelerate its practical application to the progressive failure analysis of composite laminates.     

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     

Simulating Initial and Progressive Failure of Open-Hole Composite Laminates under Tension

A finite element (FE) model is developed for the progressive failure analysis of fiber reinforced polymer laminates. The failure criterion for fiber and matrix failure is implemented in the FE code Abaqus using user-defined material subroutine UMAT. The gradual degradation of the material properties is controlled by the individual fracture energies of fiber and matrix. The failure and damage in composite laminates containing a central hole subjected to uniaxial tension are simulated. The numerical results show that the damage model can be used to accurately predicte the progressive failure behaviour both qualitatively and quantitatively.     

Failure analysis of fiber-reinforced composite laminates subjected to biaxial loads

A nonlinear constitutive model for a single lamina is proposed for the failure analysis of composite laminates. In the material model, both fiber and matrix are assumed to behave as elastic-plastic and the in-plane shear is assumed to behave nonlinearly with a variable shear parameter. The damage onset for individual lamina is detected by a mixed failure criterion, composed of the Tsai-Wu criterion and the maximum stress criterion. After damage takes place within the lamina, the fiber and in-plane shear are assumed to exhibit brittle behavior, and the matrix is assumed to exhibit degrading behavior. The proposed nonlinear constitutive model is tested against experimental data and good agreement is obtained. Then, numerical analyses are carried out to study the failure behavior of symmetric angle-ply composite laminates and symmetric cross-ply composite laminates subjected to biaxial loads. Finally, the conclusions obtained from the numerical analysis are given.     

单向纤维增强聚合物复合材料压缩渐进破坏单向纤维增强聚合物复合材料压缩渐进破坏

复合材料结构在承压时破坏如何演化,是其强度破坏分析的基础和核心任务。本文提出了基于连续介质损伤力学（CDM）的单向纤维增强聚合物复合材料压缩破坏渐进损伤分析（PDA）模型。建模中考虑了材料非线性行为、失效判断及损伤演化中材料性能退化等基本问题,分别对应于拉压不对称弹塑性本构关系、Puck准则、LaRC05准则及考虑破坏面方向的刚度退化方法。该模型通过用户材料子程序接口VUMAT引入到有限元软件ABAQUS中实现了有限元求解。对文献中提供的纵向、横向及偏轴压缩案例进行了数值计算并与试验数据对比。数值分析结果与试验数据吻合较好,证明了该方法的合理性和有效性,对开展多向层合板压缩破坏分析富有参考价值。      

复合材料层合板多尺度交互渐进损伤分析

纤维增强复合材料强度的准确表征是复合材料力学性能研究的核心问题之一。该文以碳纤维增强树脂基复合材料层合板为研究对象,基于宏观-细观多尺度分析方法,根据复合材料的物理失效模式分别给出了基体和纤维的细观失效准则,同时考虑基体失效对复合材料层合板纤维轴向力学性能的影响。提出了新的刚度退化方式,可准确表征复合材料层合板的损伤演化过程,开展了复合材料层合板四点弯模型的多尺度交互渐进损伤分析和试验验证。结果表明:基于多尺度方法的复合材料层合板宏-细观交互渐进损伤分析结果与试验结果吻合较好,新的刚度退化方式可以准确模拟层合板的失效过程。     

拉压异性纤维增强树脂基复合材料弹塑性问题的有限元分析

为了对复杂的非线性问题进行便捷求解,首先提出了考虑拉压异性的纤维增强树脂基复合材料统一非线性本构模型;然后,在此基础上进一步导出了本构模型的三维表现形式,以适用于非线性有限元分析工具的开发;随后,利用有限元软件ABAQUS提供的用户自定义子程序UMAT,自编了在二维和三维情况下的弹塑性应力分析程序;最后,应用程序对复合材料单向板和复合材料斜交板在偏轴拉伸/压缩下应力-应变曲线的预测与测试结果进行了比较,探讨了复合材料悬臂梁的弹塑性问题,并分析和比较了有无考虑拉压异性情况下应力分布和挠度响应的差异。结果表明:运用所提出的本构模型对考虑拉压不对称问题的弹塑性变形分析十分有效,这一本构模型有望成为实用数值分析工具,进而指导工程实践。     

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.     

基于单胞解析模型的复合材料层合板渐进损伤数值分析

基于单胞解析模型,建立一种从复合材料细观组分到宏观层合板的渐进损伤分析模型。根据连续介质力学和均匀化方法构建细-宏观关联矩阵,通过该矩阵将细观组分材料的弹性和损伤性能传递到宏观复合材料中。该模型只需给出纤维和基体的材料属性及纤维体积含量无需层合板的弹性和强度参数,通过组分材料的损伤失效判据确定其是否损伤,如果发生损伤则用损伤因子折算成相应的刚度衰减。通过用户材料子程序UMAT 及VUMAT将单胞解析模型以及损伤理论嵌入到有限元软件ABAQUS 中,对开孔复合材料层合板的渐进损伤过程进行模拟,预测了层合板强度。结果表明:预报的强度与试验值吻合较好,验证了该方法的有效性。     

不同形状弹体高速冲击下复合材料层板损伤分析

根据纤维增强复合材料宏细观结构,基于纤维的线弹性假设和基体的粘弹性假设,推导了单向复合材料粘弹性损伤本构关系。在此基础上,结合Hashin失效准则进行单层板面内损伤识别,通过界面单元模拟层间分层损伤,采用非线性有限元方法,建立了复合材料层板高速冲击损伤有限元分析模型。利用该模型,深入研究了不同形状弹体高速冲击下复合材料层板的弹道性能和损伤特性,探讨了相关参数对冲击损伤的影响规律,获得了一些有价值的结论。     

Characterization of polyurethane composites manufactured using vacuum assisted resin transfer molding

Glass fiber-reinforced polymer composites have promising applications in infrastructure, marine, and automotive industries due to their low cost, high specific stiffness/strength, durability, and corrosion resistance. Polyurethane (PU) resin system is widely used as matrix material in glass fiber-reinforced composites due to their superior mechanical behavior and higher impact strength. Glass fiber-reinforced PU composites are often manufactured using pultrusion process, due to shorter pot life of PU resin system. In this study, E-glass/PU composites are manufactured using a low-cost vacuum-assisted resin transfer molding process. A novel, one-part PU thermoset resin system with a longer pot life is adopted in this study. Tensile, flexure, and impact tests are conducted on both the thermoset PU neat resin system and E-glass/PU composites. A three-dimensional finite element model is developed in a commercial finite element code to simulate the impact behavior of E-glass/PU composite for three different energy levels. Finite element model is validated by comparing it with experimental results.     

形状记忆合金-玻璃纤维/环氧树脂复合材料在振动边界条件下的低速冲击数值模拟

采用有限元方法（FEM）研究了振动边界条件对形状记忆合金（SMA）-玻璃纤维/环氧树脂复合材料的抗低速冲击性能的影响。在数值模拟过程中,将改进的三维Hashin失效准则和Brinson模型分别应用于玻璃纤维/环氧树脂复合材料层合板和SMA,以表征其本构关系。首先通过与固定边界条件下的SMA-玻璃纤维/环氧树脂复合材料板低速冲击实验进行比较,验证了数值模拟过程中所用模型及材料参数的准确性。其次,在模拟过程中,应用了包含不同振幅的一系列振动边界条件,对其进行模拟,揭示了振动边界条件对其抗低速冲击性能的影响。数值模拟结果表明,在大振幅条件下,无SMA复合材料的抗冲击性能比小振幅条件下弱;在相同振动边界条件下,SMA-玻璃纤维/环氧树脂复合材料与无SMA复合材料相比,其抗低速冲击性能提高。      

A damage mechanics model of crack-weakened,chopped fiber composites under impact loading

A micromechanical approach recently proposed by Lee and Simunovic [Compos. Part B: Engng. 31 (2000) 77] is introduced to develop analytical and numerical models that efficiently predict the behavior of chopped fiber based composites containing microcracks under impact loading. Based on the ensemble-volume averaging process and the first-order effects of eigenstrains due to the existence of chopped fibers and microcracks, an effective yield criterion of the composites is derived. Microcracks in the matrix are considered by employing the Eshelby's equivalence principle and their influence on the stress–strain relations of the composites is investigated. Further, the Weibull's probabilistic function is used to model the varying probability of progressive partial fiber debonding. The developed micromechanical constitutive model is then implemented into the finite element code DYNA3D to perform impact simulation of the composites. Finally, numerical simulations for cantilever beam test and composite contact test are carried out to validate the finite element implementation and predict the impact behavior of composite structures.     

不同孔隙率CFRP层合板静态力学性能研究

为了研究孔隙率对织物碳纤维/环氧树脂复合材料层合板静态力学性能的影响规律,分别测量了孔隙率为0.33%至1.50%的CFRP层合板的弯曲强度和层间剪切强度,并进行有限元模拟.在适用于复合材料单向板的改进Hashin失效准则基础上,建立了适用于织物纤维增强复合材料静态力学强度的失效准则.通过引入复合材料基本强度参数预测不同孔隙率CFRP层合板的力学性能,结合刚度突然退化模型,采用ABAQUS软件建立了有限元模型.试验结果表明,随着孔隙率的增加,复合材料层合板的弯曲强度和层间剪切强度均呈下降趋势.有限元模型较为准确地预测了不同孔隙率织物碳纤维/环氧树脂复合材料层合板的弯曲强度和层间剪切强度.     

Meso-Scale Progressive Damage Behavior Characterization of Triaxial Braided Composites under Quasi-Static Tensile Load

Based on continuum damage mechanics (CDM), a sophisticated 3D meso-scale finite element (FE) model is proposed to characterize the progressive damage behavior of 2D Triaxial Braided Composites (2DTBC) with 60° braiding angle under quasi-static tensile load. The modified Von Mises strength criterion and 3D Hashin failure criterion are used to predict the damage initiation of the pure matrix and fiber tows. A combining interface damage and friction constitutive model is applied to predict the interface damage behavior. Murakami-Ohno stiffness degradation scheme is employed to predict the damage evolution process of each constituent. Coupling with the ordinary and translational symmetry boundary conditions, the tensile elastic response including tensile strength and failure strain of 2DTBC are in good agreement with the available experiment data. The numerical results show that the main failure modes of the composites under axial tensile load are pure matrix cracking, fiber and matrix tension failure in bias fiber tows, matrix tension failure in axial fiber tows and interface debonding; the main failure modes of the composites subjected to transverse tensile load are free-edge effect, matrix tension failure in bias fiber tows and interface debonding.     

基于连续介质损伤力学的复合材料层合板低速冲击损伤模型

基于连续介质损伤力学（CDM）方法,建立了分析复合材料层合板低速冲击问题的三维数值模型。该模型考虑了层内损伤（纤维和基体损伤）、层间分层损伤和剪切非线性行为,采用最大应变失效准则预测纤维损伤的萌生,双线性损伤本构模型表征纤维损伤演化,基于物理失效机制的三维Puck准则判断基体损伤的起始,根据断裂面内等效应变建立混合模式下基体损伤扩展准则。横向基体拉伸强度和面内剪切强度采用基于断裂力学假设的就地强度（in-situ strength）。纤维和基体损伤本构关系中引入单元特征长度,有效降低模型对网格密度的依赖性。层间分层损伤情况由内聚力单元（cohesive element）预测,以二次应力准则为分层损伤的起始准则,B-K准则表征分层损伤演化。分别通过数值分析方法和试验研究方法对复合材料典型铺层层合板四级能量低速冲击下的冲击损伤和冲击响应规律进行分析,数值计算和试验测量的接触力-时间曲线、分层损伤的形状和面积较好吻合,表明该模型能够准确地预测层合板低速冲击损伤和冲击响应。     

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.