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.     

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。     

含分层损伤缝合复合材料层板的剩余压缩强度

基于渐进损伤方法,研究了含单脱层缝合复合材料层板在压缩载荷下的剩余强度。通过商用软件ABAQUS建立了含单脱层缝合复合材料层板剩余压缩强度计算模型,考虑了子层屈曲和分层扩展对剩余强度的影响。通过UMAT子程序实现了层板失效、层间失效和缝线失效的模拟。通过嵌入式杆单元结构模拟了缝线桥联作用及失效。采用Hashin准则及刚度折减法对纤维拉压、基体拉压失效进行了模拟。通过渐进损伤分析,揭示了缝合情况下含单脱层复合材料层板的失效机理,讨论了缝合参数对剩余压缩强度的影响。所预测的破坏模式和剩余强度结果与实验能较好地吻合。分析表明缝合可以明显提高含分层损伤复合材料层板的子层屈曲载荷,抑制分层扩展,并提高层板的剩余压缩强度。     

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。      

GLARE层板挤压渐进损伤分析

对GLARE36/5层板进行挤压性能试验研究,采用超声C扫描、断口微距拍摄和扫描电子显微镜等方法观测GLARE层板挤压渐进损伤过程和最终破坏模式。结果表明:GLARE层板挤压起始损伤为铝合金塑性变形;损伤扩展阶段,0°纤维主要承受挤压正应力,铝合金塑性变形增大,铺层间分层起始并扩展;0°纤维屈曲折断后层内纤维基体损伤和分层损伤急剧扩展,层板最终发生挤压破坏。将GLARE层板挤压失效分为层内失效和层间失效,采用应变描述的Hashin准则和界面单元方法并引入金属塑性建立GLARE层板挤压渐进损伤数值模型,数值模型对层板损伤起始位置、分层产生位置、损伤演化过程、最终破坏模式及破坏载荷进行了预测,计算结果与试验结果吻合较好,说明该计算方法能够有效模拟GLARE层板挤压渐进损伤性能。      

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。     

Progressive damage and failure modeling in notched laminated fiber reinforced composites

A novel progressive damage and failure model for fiber reinforced laminated composites is presented in this work. The model uses the thermodynamically based Schapery Theory (ST) to model progressive microdamage in the matrix phase. Matrix failure is not governed with a matrix failure criterion, but rather matrix failure occurs naturally through the evolution of microdamage. A maximum strain criterion is used to dictate tensile failure in the fiber direction, while compressive failure is automatically accounted for by allowing local fiber rotations and tracking the evolution of rotation. The results of this model are compared to a previously developed model that used ST at the lamina level to calculate matrix microdamage, but used the Generalized Method of Cells to resolve the lamina level strains into constituent level stresses and strains and determines constituent failure by evaluating failure criteria at the micro, fiber/matrix level. Results for global load versus displacement and local strain from both models are compared to experimental data for notched laminates loaded in uniaxial tension. The results show remarkable agreement qualitatively, and in many cases the quantitative agreement is good. Accurate damage contours and failure paths are predicted.     

基于实体-壳耦合模型的复合材料层压板冲击损伤阻抗优化

为优化复合材料层压板的冲击损伤阻抗, 提出了基于实体-壳耦合模型的优化方法。模型以实体单元模拟冲击点区域, 以壳单元模拟周围区域, 采用耦合约束连接实体与壳, 引用渐进损伤材料本构, 提出了冲击下与纤维方向种数相关的损伤变量, 优化过程利用遗传算法。通过算例对冲击阻抗的优化方法进行了验证, 并对复合材料盒段壁板进行了铺层优化。结果表明: 基于实体-壳耦合模型的遗传优化方法, 计算效率高, 收敛速度快, 提高了层压板的抗冲击性能。     

Numerical implementation of a multiple-ISV thermodynamically-based work potential theory for modeling progressive damage and failure in fiber-reinforced laminates

A thermodynamically-based work potential theory for modeling progressive damage and failure in fiber-reinforced laminates is presented. The current, multiple-internal state variable (ISV) formulation, referred to as enhanced Schapery theory, utilizes separate ISVs for modeling the effects of damage and failure. Damage is considered to be the effect of any structural changes in a material that manifest as pre-peak non-linearity in the stress versus strain response. Conversely, failure is taken to be the effect of the evolution of any mechanisms that results in post-peak strain softening, resulting in a negative tangent stiffness. It is assumed that matrix microdamage is the dominant damage mechanism in continuous fiber-reinforced polymer matrix laminates, and its evolution is controlled with a single ISV. Three additional ISVs are introduced to account for failure due to mode I transverse cracking, mode II transverse cracking, and mode I axial failure. Typically, failure evolution (i.e., post-peak strain softening characterized through a negative tangent stiffness) results in pathologically mesh dependent solutions within a finite element (FE) framework. Therefore, consistent characteristic lengths are introduced into the formulation to govern the evolution of the three failure ISVs. Using the stationarity of the total work potential with respect to each ISV, a set of thermodynamically consistent evolution equations for the ISVs are derived. The theory is implemented in association with the commercial FE software, Abaqus. Objectivity of total energy dissipated during the failure process, with regards to refinements in the FE mesh, is demonstrated. The model is also verified against experimental results from two laminated, T800/3900-2 panels containing a central notch and different fiber-orientation stacking sequences. Global load versus displacement, global load versus local strain gage data, and macroscopic failure paths obtained from the models are compared against the experimental results.     

复合材料层板静压入破坏机制

建立一个有效的计算模型, 以分析复合材料层板在静压入过程中发生分层、 纤维断裂的现象。该计算模型基于有限元程序的三维逐渐损伤理论对层板的静压入全过程进行模拟, 对逐层逐个单元的损伤进行判断, 可以模拟任意角度、 铺层厚度的层板在递增载荷下的逐渐损伤破坏过程。对炭纤维增强环氧树脂基复合材料层板在静压入过程中发生的分层和纤维断裂现象进行预测,并与实验结果进行比较; 对炭纤维增强双马来酰亚胺树脂基复合材料层板在静压入过程中的分层损伤和最终破坏接触力的大小进行预测,并与低速冲击下的结果进行比较。数值仿真与实验结果吻合较好, 表明静压入分析方法是复合材料层板在低速冲击下产生损伤的可替换分析方法。      

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.     

缝合复合材料层板低速冲击损伤数值模拟

建立了缝合复合材料层板在低速冲击载荷下的渐进损伤分析模型。模型中采用空间杆单元模拟缝线的作用;采用三维实体单元模拟缝合层板,通过基于应变描述的Hashin准则,结合相应的材料性能退化方案模拟层板的损伤和演化;采用界面单元模拟层间界面,结合传统的应力失效判据和断裂力学中的应变能释放率准则判断分层的起始和扩展规律。通过对碳800环氧树脂复合材料（T800/5228）层板的数值仿真结果和试验结果相比较,验证了模型的正确性,同时讨论了不同冲击能量下缝合层板的损伤规律。研究结果表明：缝线能够有效地抑制层板的分层损伤扩展;相同冲击能量下缝合与未缝合层板的基体损伤和纤维损伤在厚度分布上相似,缝合层板的损伤都要小于未缝合层板。     

Micromechanical Modeling of Impact Damage Mechanisms in Unidirectional Composite Laminates

Composite laminates are susceptible to the transverse impact loads resulting in significant damage such as matrix cracking, fiber breakage and delamination. In this paper, a micromechanical model is developed to predict the impact damage of composite laminates based on microstructure and various failure models of laminates. The fiber and matrix are represented by the isotropic and elastic-plastic solid, and their impact failure behaviors are modeled based on shear damage model. The delaminaton failure is modeling by the interface element controlled by cohesive damage model. Impact damage mechanisms of laminate are analyzed by using the micromechanical model proposed. In addition, the effects of impact energy and laminated type on impact damage behavior of laminates are investigated. Due to the damage of the surrounding matrix near the impact point caused by the fiber deformation, the surface damage area of laminate is larger than the area of ??impact projectile. The shape of the damage area is roughly rectangle or elliptical with the major axis extending parallel to the fiber direction in the surface layer of laminate. The alternating laminated type with two fiber directions is more propitious to improve the impact resistance of laminates.     

一种改进的内聚力损伤模型在复合材料层合板低速冲击损伤模拟中的应用

针对传统内聚力损伤模型(CZM)无法考虑层内裂纹对界面分层影响的缺点,提出了一种改进的适用于复合材料层合板低速冲击损伤模拟的CZM。通过对界面单元内聚力本构模型中的损伤起始准则进行修正,考虑了界面层相邻铺层内基体、纤维的损伤状态及应力分布对层间强度和分层扩展的影响。基于ABAQUS用户子程序VUMAT,结合本文模型及层合板失效判据,建立了模拟复合材料层合板在低速冲击作用下的渐进损伤过程的有限元模型,计算了不同铺层角度和材料属性的层合板在低速冲击作用下的损伤状态。通过数值模拟与试验结果的对比,验证了本文方法的精度及合理性。     

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.     

Modelling of fatigue damage progression and life of CFRP laminates

A progressive fatigue damage model has been developed for predicting damage accumulation and life of carbon fibre‐reinforced plastics (CFRP) laminates with arbitrary geometry and stacking sequence subjected to constant amplitude cyclic loading. The model comprises the components of stress analysis, fatigue failure analysis and fatigue material property degradation. Stress analysis of the composite laminate was performed by creating a three‐dimensional finite element model in the ANSYS FE code. Fatigue failure analysis was performed by using a set of Hashin‐type failure criteria and the Ye‐delamination criterion. Two types of material property degradations on the basis of element stiffness and strength were applied: a sudden degradation because of sudden failure detected by the fatigue failure criteria and a gradual degradation because of the nature of cyclic loading, which is driven by the increased number of cycles. The gradual degradation of the composite material was modelled by using functions relating the residual stiffness and residual strength of the laminate to the number of cycles. All model components have been programmed in the ANSYS FE code in order to create a user‐friendly macro‐routine. The model has been applied in two different quasi‐isotropic CFRP laminates subjected to tension–compression (T–C) fatigue and the predictions of fatigue life and damage accumulation as a function of the number of cycles were compared with experimental data available in the literature. A very good agreement was obtained.     

碳纤维编织复合材料层合板抗侵彻性能研究

通过弹道冲击实验开展了碳纤维编织复合材料层合板的抗侵彻性能研究,进行了动态响应分析和损伤模式分析。建立了基于Hashin失效和Yeh分层失效准则的渐进损伤模型,运用ABAQUS有限元软件模拟了碳纤维编织复合材料层合板的侵彻失效过程,采用Lambert-Jonas公式拟合了柱状弹侵彻层合板弹道极限曲线,对比分析了碳纤维编织复合材料层合板侵彻实验与数值模拟的弹道极限速度及损伤形貌。结果表明,层合板侵彻损伤模式主要为分层、纤维断裂和基体开裂失效,弹道极限速度数值模拟结果与实验结果吻合较好。     

Numerical simulation of impact tests on GFRP composite laminates

The design of advanced composite structures or components subjected to dynamic loadings requires a deep understanding of the damage and degradation mechanisms occurring within the composite material. The present paper deals with the numerical simulation of low-velocity impact tests on glass fabric/epoxy laminates through the LS-DYNA Finite Element (FE) code. Two laminates of different thickness were subjected to transverse impact at different energy levels and modeled by FE. Solid finite elements combined with orthotropic failure criteria were used to model the composite failure and stress based contact failure between plies were adopted to model the delamination mechanism. The final simulation results showed a good correlation with experimental data in terms of both force–displacement curves and material damage.     

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.     

Progressive damage and nonlinear analysis of pultruded composite structures

This study combines a simple damage modeling approach with micromechanical models for the progressive damage analysis of pultruded composite materials and structures. Two micromodels are used to generate the nonlinear effective response of a pultruded composite system made up from two alternating layers reinforced with roving and continuous filaments mat (CFM). The layers have E-glass fiber and vinylester matrix constituents. The proposed constitutive and damage framework is integrated within a finite element (FE) code for a general nonlinear analysis of pultruded composite structures using layered shell or plate elements. The micromechanical models are implemented at the through-thickness Gaussian integration points of the pultruded cross-section. A layer-wise damage analysis approach is proposed. The Tsai–Wu failure criterion is calibrated separately for the CFM and roving layers using ultimate stress values from off-axis pultruded coupons under uniaxial loading. Once a failure is detected in one of the layers, the micromodel of that layer is no longer used. Instead, an elastic degrading material model is activated for the failed layer to simulate the post-ultimate response. Damage variables for in-plane modes of failure are considered in the effective anisotropic strain energy density of the layer. The degraded secant stiffness is used in the FE analysis. Examples of progressive damage analysis are carried out for notched plates under compression and tension, and a single-bolted connection under tension. Good agreement is shown when comparing the experimental results and the FE models that incorporate the combined micromechanical and damage models.