Progressive failure modeling of woven fabric composite materials using multicontinuum theory

Failure of composite materials often results from damage accumulation in the individual constituents (fiber and matrix) of the composite. At times, damage may even be limited to a single constituent. The ability to accurately predict not only ultimate strength values but also intermediate constituent level failures is crucial to the success of introducing composite materials into demanding structural applications.In this paper, we develop two progressive failure models for the analysis of a plain weave composite material. The formulations are based on treating the weave as consisting of separate but linked continua representing the warp fiber bundles, fill fiber bundles, and pure matrix pockets. Retaining constituent identities allows one to access constituent (phase averaged) stress fields that are used in conjunction with both a stress based and damage based failure criterion to construct a nonlinear progressive failure algorithm for the woven fabric composite material. The MCT decomposition and the nonlinear progressive failure algorithm are incorporated within the framework of a traditional finite element analysis.The constituent based progressive failure algorithm combined with both the stress based and damage based failure criteria are compared against experimental data for a plain weave, woven fabric composite under various loading conditions. The analytical results from the damage based approach show a marked improvement over the stress based predictions and are in excellent agreement with the experimental data.     

A three-constituent multicontinuum theory for woven fabric composite materials

Multicontinuum theory (MCT) refers to the use of phase averaged constituent stress/strain fields for predicting failure in composite structural analysis. Given the composite material mechanical properties as well as those of the constituents, well known closed form algebraic expressions exist to decompose the composite stress/strain fields down to the constituent level. Recent research indicates constituent based failure algorithms show a great deal of promise in predicting material failure when coupled to nonlinear finite element codes. A limitation of MCT is that the traditional constituent decomposition is only valid for materials composed of two constituents. In this paper, the MCT decomposition is generalized to handle composite materials composed of three constituents. The application of interest is a woven fabric composite material. The three constituents consist of the warp bundles, fill bundles, and pure matrix pockets. Numerical results are presented for the proposed three-constituent decomposition and are shown to be in good agreement with phase averaged stresses obtained from direct volume averaging of finite element micromechanics models.     

2-D biaxial testing and failure predictions of IM7/977-2 carbon/epoxy quasi-isotropic laminates

In previous research, a series of a thickness-tapered cruciform specimen configurations have been used to determine the biaxial (two-dimensional, in-plane) and triaxial (three-dimensional) strength of several carbon/epoxy and glass/vinyl-ester laminate configurations. Refinements to the cruciform geometry have been shown capable of producing acceptable results for cross-ply laminate configurations. However, the presence of a biaxial strengthening effect in quasi-isotropic, [(0_N/90_N/ ± 45_N)_M]_S, laminates have brought into question whether the cruciform geometry could be used to successfully generate two-dimensional strength envelopes. In the present study, a two-dimensional failure envelope for a IM7/977-2 carbon/epoxy laminate was developed at the Air Force Research Laboratory, Space Vehicles Directorate, using a triaxial test facility. The electromechanical test frame is capable of generating any combination of tensile or compressive stresses in σ₁:σ₂:σ₃ stress space and can evaluate the uniaxial (one-dimensional, in-plane), biaxial or triaxial response of composite materials. Results are promising as they indicated that failure in the majority of the IM7/977-2 specimens occurred in the gage section. This leads the authors to believe that maximum biaxial stress states were correctly generated within the test specimen. In addition to the experimental data presented, multi-continuum theory (MCT) was used to predict and analyze the onset of damage and ultimate failure of a biaxially loaded IM7/977-2 laminate. Multi-continuum theory is a micromechanics based theory and associated numerical algorithm for extracting, virtually without a time penalty, the stress and strain fields for a composites’ constituents during a routine structural finite element analysis. Damage in a composite material typically begins at the constituent level and may, in fact, be limited to only one constituent in some situations. An accurate prediction of constituent failure at sampling points throughout the laminate provides a genesis for progressively analyzing damage propagation in a composite specimen allowing identification of intermediate damage modes. A constituent-based, quadratic, stress-interactive, failure criterion was used to take advantage of the micro-scale information provided by MCT. There was reasonable correlation between analytically and experimentally developed IM7/977-2 2D failure envelope which leads us to believe that the thickness-tapered cruciform specimen can be used to determine the biaxial strength of quasi-isotropic laminates.     

翼肋支撑对复合材料加筋板轴压性能的影响

为确定翼肋支撑对复合材料加筋板轴压性能的影响,对施加翼肋支撑前后的复合材料工型加筋板和帽型加筋板进行压缩试验和数值模拟研究。轴压试验中,通过应变计和影像云纹法实时监测试验件的失稳载荷及失稳模态,通过断面观测分析结构损伤破坏机制。基于ABAQUS软件建立有限元模型模拟加筋板屈曲及后屈曲过程,通过失稳节线及反节线上的应力分布变化分析加筋板破坏机制。计算结果与试验结果相吻合,表明翼肋支撑对不同筋条加筋板失稳模态有影响但均不改变结构失稳载荷,位于节线上的翼肋支撑对工型加筋板破坏载荷影响较小,但位于反节线上的翼肋支撑使帽型加筋板的承载能力提高了26.2%。试验件失稳后应力向反节线上筋条蒙皮界面集中,过高的应力导致界面脱粘,使得结构集中在反节线上破坏。      

基于非线性本构关系的复合材料风机叶片有限元极限分析与设计

为了研究具有三维复杂构形的复合材料风机叶片的逐次破坏过程和极限承载能力, 将复合材料细观力学非线性本构理论桥联模型与有限元软件ABAQUS通过用户子程序UGENS结合起来对风力发电机叶片结构进行极限强度分析。只需提供纤维和基体的材料性能参数、 纤维体积含量以及蒙皮和增强筋的铺层数据包括铺设角、 层厚和铺层数, 就可预报出复合材料复杂叶片结构的整体承载能力以及叶片破坏所处的位置, 为正确评估和合理设计风机叶片结构提供了一种简便有效的分析方法。以一种20kW风机叶片为例, 用此方法实现了新型复合材料叶片结构的极限分析和合理设计, 提高了叶片的强度和刚度, 有效降低了叶片的重量。本文中的方法同样适用于其它复合材料复杂结构的极限分析与强度设计。      

复合材料整体化多墙盒段渐进式失效分析和试验验证

为准确预测复合材料盒段的损伤起始和破坏过程,针对复合材料整体化多墙盒段研究了考虑材料失效的渐进损伤有限元分析技术。首先基于ABAQUS软件,利用标准试验获得的材料力学性能建立了盒段渐进损伤分析模型,分别采用三维Hashin失效准则和平方应力失效准则作为复合材料层板和连接界面的失效判据;然后,基于该模型完成了复合材料整体化多墙盒段后屈曲承载能力的求解,并利用破坏试验对分析模型进行验证。结果表明:结构承载能力和应力的有限元分析结果与试验值吻合良好,预测的失效模式也与试验结果一致,屈曲载荷和承载能力误差在5%以内。所得结论表明考虑层板失效和界面脱粘的分析模型能有效模拟整体化多墙盒段的破坏过程。      

Multicontinuum Failure Analysis of Composite Structural Laminates

Damage in a composite typically begins at the constituent level and may, in fact, be limited to only one constituent in some situations. Accurate predictions of constituent damage at points in a laminate provide a genesis for progressively analyzing failure of a composite structure from start to finish. In this article we develop an efficient constituent-based failure analysis for composite structural laminates. Continuum-based (phase-averaged) constituent stress and strain fields are computed in a finite-element environment without a computational time penalty. Constituent stress-based failure criteria are developed and used to construct a progressive failure algorithm in which one constituent is allowed to fail while the other constituent remains intact, e.g., matrix cracking. The proposed failure algorithm was used to predict failure of a variety of laminates under uniaxial and biaxial loads. The results were shown to be superior to comparable single-continuum failure analyses and in good agreement with experimentally determined failure loads.     

复合材料帽型加筋壁板的失效机制分析与改进设计

为了准确预测复合材料帽型加筋壁板的后屈曲承载能力,针对压缩载荷下筋条端头斜削的复合材料帽型加筋壁板结构的失效机制及失效载荷进行了研究。首先利用物理试验,研究了端头斜削的复合材料帽型加筋壁板失效过程,然后构建了考虑蒙皮/缘条胶接界面以及复合材料层板失效的非线性损伤分析模型,详细地研究了损伤起始、扩展和失效的全过程。在此基础上,提出了包覆层对蒙皮/缘条界面进行增强的设计方案,并基于数值仿真和试验研究了包覆层对复合材料帽型壁板的破坏模式和承载能力的影响。数值分析和试验结果表明,包覆层设计能够明显提高结构的屈曲载荷和后屈曲承载能力,分析结果与试验值吻合良好,且预测的破坏模式也与试验结果一致。     

A mechanically fastened composite laminate joint and progressive failure analysis

A comprehensive procedure for a mechanically fastened composite laminate joint (ASTM D5961 Proc. A, B) is demonstrated from fixture design to analysis of test results. The ASTM tests are applied to evaluate the standard laminate properties and the composite joints. Composite laminate mechanical joints were analyzed using the finite element method (FEM), and the results were compared to test results. A progressive failure analysis (PFA) was applied to the FEM to predict the overall failure behavior of the test specimens. Three laminate failure theories – maximum stress, maximum strain, and Tsai–Wu – were applied to the PFA to predict the test failure load, displacement and strength. The PFA method was suitable to predict the initial test range of test and maximum test load except for the excessive failure area.     

Analysis of bolted joints in composite laminates: Strains and bearing stiffness predictions

A review of the investigations conducted on mechanically fastened joints is presented. A finite-element model is developed to predict the response of pin-loaded composite plates. The model takes into account contact at the pin–hole interface, progressive damage, large deformation theory, and a nonlinear shear stress–strain relationship. To predict progressive ply failure, four different analyses combining Hashin and the maximum stress failure criteria, and different associated degradation rules are conducted. The objectives of the study are to determine the influence of the failure criteria and the associated degradation rules on the predictions of the strains around the hole and the bearing stiffness. Predictions are compared with experimental results. It appears that agreement between the two depends on an appropriate selection of the failure criterion and the degradation rule. Better agreement between experimental results and numerical predictions is observed with the maximum stress criterion.     

Bending analyses for 3D engineered structural panels made from laminated paper and carbon fabric

This paper presents analysis of a 3-dimensional engineered structural panel (3DESP) having a tri-axial core structure made from phenolic impregnated laminated-paper composites with and without high-strength composite carbon-fiber fabric laminated to the outside of both faces. Both I-beam equations and finite element method were used to analyze four-point bending of the panels. Comparisons were made with experimental panels. In this study, four experimental panels were fabricated and analyzed to determine the influence of the carbon-fiber on bending performance. The materials properties for finite element analyses (FEA) and I-beam equations were obtained from either the manufacturer or in-house material tensile tests. The results of the FEA and I-beam equations were used to compare with the experimental 3DESP four-point bending tests. The maximum load, face stresses, shear stresses, and apparent modulus of elasticity were determined. For the I-beam equations, failure was based on maximum stress values. For FEA, the Tsai-Wu strength failure criterion was used to determine structural materials failure. The I-beam equations underestimated the performance of the experimental panels. The FEA-estimated load values were generally higher than the experimental panels exhibiting slightly higher panel properties and load capacity. The addition of carbon-fiber fabric to the face of the panels influenced the failure mechanism from face buckling to panel shear at the face–rib interface. FEA provided the best comparison with the experimental bending results for 3DESP.     

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.     

Large-Deformation Constitutive Theories for Structural Composites: Rate-Dependent Concepts and Effect of Microstructure

Abstract:  Polymer-based composite materials are widely used in applications subjected to a variety of loading types, including shock and impact loading in the range of hundreds of strain per second. The behaviour of composite laminates loaded at those rates is typically nonlinear and may involve rather large strains to failure. In the present study, the large-deformation characteristics and constitutive representations of structural composites were investigated as functions of strain rate and temperature. A plain-weave vinyl ester composite material was selected for the study. Tensile tests of off-axis coupon specimens were conducted over several orders of strain rates and limited change of temperatures. A three-parameter constitutive model was proposed to model the large-deformation stress–strain relationship. The constitutive model was then used to predict the material response at different strain rates. The model predictions were verified by a different set of tests. The basic concepts and methodologies involved in reducing such data to constitutive equations that can be used in commercial computational codes to enable structural analysis in the presence of large-strain progressive damage under dynamic loading is discussed.     

Multi-scale modeling, stress and failure analyses of 3-D woven composites

The very complex, multi-level hierarchical construction of textile composites and their structural components commonly manifests via significant property variation even at the macro-level. The concept of a “meso-volume” (introduced by this author in early 1990s) is consistently applied in this work to 3-D stress/strain and failure analyses of 3-D woven composites at several levels of structural hierarchy. The meso-volume is defined as homogeneous, anisotropic block of composite material with effective elastic properties determined through volumetrically averaged 3-D stress and strain fields computed at a lower (“finer”) level of structural hierarchy and application of generalized Hooke’s law to the averaged fields. The meso-volume can represent a relatively large, homogenized section of a composite structural component, a lamina in laminated composite structure, a homogenized assembly of several textile composite unit cells, a single homogenized unit cell, a resin-impregnated yarn, a single carbon fiber, even a carbon nanotube assembly. When composed together, distinct meso-volumes constitute a 3-D Mosaic model at the respective hierarchy level. A multi-scale methodology presented in this paper first illustrates 3-D stress/strain analysis of the Mosaic unidirectional composite, computation of its effective elastic properties and their further use in 3-D stress/strain analysis of the Mosaic model of 3-D woven composite Unit Cell. The obtained 3-D stress/strain fields are then volumetrically averaged within the Unit Cell, and its effective elastic properties are computed. The predicted effective elastic properties of 3-D woven composite are compared with experimental data and show very good agreement. Further, those effective elastic properties are used in 3-D simulations of three-point bending tests of 3-D woven composite; theoretical predictions for central deflection show excellent agreement with experimental data. Finally, a 3-D progressive failure analysis of generic 3-D Mosaic structure is developed using ultimate strain criterion and illustrated on the 3-D woven composite Unit Cell. The predicted strength values are compared to experimental results. The presented comparisons of theoretical and experimental results validate the adequacy and accuracy of the developed material models, mathematical algorithms, and computational tools.     

Numerical investigation of progressive damage and the effect of layup in overheight compact tension tests

This work describes a numerical investigation into progressive damage development in notched fibre-reinforced composite laminates. A finite element approach is used which explicitly models the sub-critical damage in the form of delamination and splits using interface elements, and fibre failure using a progressive statistical failure theory. Failure predictions were made for Overheight Compact Tension (OCT) test specimens using five different layups made up from IM7/8552 carbon/epoxy pre-preg. Owing to the detailed modelling of the individual damage modes, their interaction is well characterised. The numerical results obtained compare well with detailed test observations, capturing delamination, intraply splitting and fibre breakage. By including the subcritical damage that occurs at the notch tip in the model, it is able to represent the effect on the stress concentration and hence to predict ultimate specimen failure.     

RTM成型非对称复合材料T型接头的拉伸失效机制

采用树脂传递模塑(RTM)工艺制备了结构对称和非对称两种复合材料T型接头试样,并对其进行了静态拉伸力学试验,对比分析了两种结构的拉伸破坏模式、结构刚度及破坏载荷。同时基于T接头内聚力模型(CZM),研究了两种不同结构T型接头的拉伸破坏过程及失效机制,并对比分析了不同偏转角下T接头的层间应力。结果表明：不同结构T型接头的拉伸破坏模式不同,偏转角的存在使结构非对称T型接头夹角大侧圆弧受力明显高于小侧圆弧,导致接头首先在大侧夹角圆弧与三角区界面定向萌生初始裂纹,随后裂纹主要沿大侧腹板翻边与蒙皮的界面扩展,进而导致接头最终破坏,最终失效载荷较对称T型接头提高了15.3%,且结构刚度更大。有限元结果表明T型接头三角区的初始失效主要由层间正应力及剪应力引起,有限元分析的失效模式与试验一致,结构对称及非对称T型接头最终失效载荷与试验值均吻合较好;且随着偏转角的增加,腹板圆弧处层间应力逐渐减小,初始失效载荷将随之增大;初始破坏位置将转移至大侧夹角圆弧末端。     

Progressive failure analysis of 2/2 twill weave fabric composites with moulded-in circular hole

Micromechanical three-dimensional finite element models of 2/2 twill weave T300 carbon/epoxy woven fabric composite panels with moulded-in circular hole are established for stress analysis. In these models, the streamline equation is used as a shape function to simulate the fibre configuration. A progressive failure analysis together with a newly developed ‘maximum notched strength method’ are also proposed to predict the failure modes and notched strengths of the fibre dominated laminate with moulded-in hole. Perforated specimens of different hole sizes are prepared using a special procedure. Tension tests are performed to evaluate the stress–strain and failure characteristics. An increase in tensile strength with increasing hole size is observed within the experimental data range. Numerical results from progressive failure analysis provide good prediction to the failure phenomena of the fractured specimens. The notched strengths from the proposed numerical procedure are slightly higher than the experimental results.     

Failure Analysis of Adhesively Bonded Structures: From Coupon Level Data to Structural Level Predictions and Verification

This paper presents a predictive methodology and verification through experiment for the analysis and failure of adhesively bonded, hat stiffened structures using coupon level input data. The hats were made of steel and carbon fiber reinforced polymer composite, respectively, and bonded to steel adherends. A critical strain energy release rate criterion was used to predict the failure loads of the structure. To account for significant geometrical changes observed in the structural level test, an adaptive virtual crack closure technique based on an updated local coordinate system at the crack tip was developed to calculate the strain energy release rates. Input data for critical strain energy release rates as a function of mode mixity was obtained by carrying out coupon level mixed mode fracture tests using the Fernlund–Spelt (FS) test fixture. The predicted loads at failure, along with strains at different locations, were compared with those measured from the structural level tests. The predictions were found to agree well with measurements for multiple replicates of adhesively bonded hat-stiffened structures made with steel hat/adhesive/steel and composite hat/adhesive/steel, thus validating the proposed methodology for failure prediction.     

Predicting fracture from the tensile properties of a composite biomaterial

Fracture and tensile tests were conducted on a composite biomaterial consisting of polycarbonate matrix and calcium phosphate fibers. The fibers were short and randomly oriented. Test results were compared for composites with and without a surface treatment of the fibers.

A nonlinear finite element method was used to predict the maximum loads on pre-cracked panels. The method used the unnotched stress–strain behavior to predict the failure process in notched panels. A cohesive stress zone near the crack tip was used to model damage, stable crack growth, and failure. As in the experiments, the predicted loads were lower for the composite with coated fibers. For both materials, the predicted maximum loads were within the 6% of the experimental loads.     

纤维增强复合材料的基体和界面控制破坏的强度理论

本文简略地回顾了各向同性和各向异性材料的破坏准则.在文献[1]和[2]的基础上,更完整地提出了以基体和界面破坏判定复合材料在复杂应力下破坏的准则.准则方程的形式取决于基体的破坏特征;方程的系数可由组份性能、含量和界面粘接状况所确定.这就揭示了这些参数对复合材抖强度的作用和影响,对复合材料的材料和结构设计有直接的指导意义.偏轴拉伸强度的理论计算结果与试验结果很一致.