基于虚拟裂纹闭合技术的应变能释放率分析

基于虚拟裂纹闭合技术(VCCT),建立了复合材料层合板层间裂纹尖端的应变能释放率(SERR)三维有限元计算模型。该模型考虑了裂纹尖端大转动和离散单元形状变化对应变能释放率计算的影响,修正了裂纹尖端应变能释放率的计算方法。利用该模型计算了裂纹长度为15 mm和35 mm时纯Ⅰ型和纯Ⅱ型的应变能释放率,纯Ⅰ型应变能释放率分别为 207 J/m2和 253 J/m2;纯Ⅱ型应变能释放率分别为 758 J / m 2和 1040 J / m2;计算值与试验值吻合得很好。同时,该模型计算了混合型不同比值 R=(G_Ⅱ/G_Ⅰ+G_Ⅱ)的长裂纹层合板层间断裂过程的应变能释放率,其中Ⅰ型和Ⅱ型应变能释放率计算值与试验平均值的最大误差为 11.4%,最小误差为 0.4%。该模型能有效计算裂纹尖端的应变能释放率。     

裂纹闭合与疲劳裂纹扩展力的测试方法

介绍了一种在近十年里发展的裂纹扩展力测量方法，这种方法将裂纹扩展的门槛值行为与直流电位法结合起来，可以测量某一载荷下裂纹开始扩展的应力强度因子Ｋｐｒ，并由此计算有效应力强度因子范围ΔＫｅｆｆ＝Ｋｍａｘ－Ｋｐｒ。     

基于小波内聚力模型的界面裂纹扩展

利用区间B样条小波良好的局部化性能,将内聚力模型（CZM）引入小波有限元法（WFEM）数值分析中,以区间B样条小波尺度函数作为插值函数,构造小波内聚力界面单元,推导了小波内聚力界面单元刚度矩阵,基于虚拟裂纹闭合技术（VCCT）计算界面裂纹应变能释放率（SERR）,采用β-Κ断裂准则,实现界面裂纹扩展准静态分析。将WFEM和传统有限元法（CFEM） 的SERR数值分析结果与理论解进行比较,结果表明:采用WFEM和CFEM计算的SERR分别为96.60 J/m2 和 101.43 J/m2,2种方法的SERR数值解与理论解相对误差分别为1.85%和3.06%,这明确表明WFEM在计算界面裂纹扩展方面能用较少单元和节点数获得较高的计算精度和效率。在此基础上,探讨了界面裂纹初始长度和双材料弹性模量比对界面裂纹扩展的影响,分析结果表明:界面裂纹尖端等效应力随界面裂纹初始长度的增加而增加;双材料弹性模量比相差越大,界面裂纹越易于扩展,且裂纹扩展长度也越大,因此可通过调节双材料弹性模量比来延缓界面裂纹扩展。      

压缩载荷下闭合斜裂纹的分支裂纹渐近扩展分析

采用滑动裂纹模型并结合现有张开斜裂纹的I 型分支裂纹扩展特性的研究成果,研究了闭合斜裂纹的I型分支裂纹的渐近扩展特点,结果表明：1) 闭合斜裂纹的I 型分支裂纹路径的渐近线为平行于最大主应力的一条直线,并得出了渐近线方程;和张开斜裂纹的翼型裂纹不同,闭合斜裂纹的翼型裂纹路径的渐近线不一定过初始裂纹中心点,该渐近线位置与初始裂纹面的摩擦系数、初始裂纹长度及初始裂纹角有关;2) 闭合斜裂纹的I 型分支裂纹的扩展路径可以近似采用双曲线描述,并得出了描述I 型分支裂纹扩展路径的方程.采用ABAQUS 二次开发对闭合斜裂纹的分支裂纹的扩展过程进行了数值模拟,并采用数值模拟和现有试验相结合的方法验证了以上结论的正确性.     

压缩载荷下闭合裂纹的曲线分支裂纹模型研究

目前远场压应力作用下分支裂纹扩展过程中,其应力强度因子的计算模型中,经常将曲线分支裂纹简化为直线分支裂纹处理,忽略了分支裂纹扩展路径的曲线效应。基于这个考虑,在远场压应力作用下曲线分支裂纹扩展路径数学描述的基础上,建立了曲线分支裂纹模型,该模型可以考虑分支裂纹扩展过程中的曲线效应,进而计算出了曲线分支裂纹扩展过程中应力强度因子。基于ABQUS二次开发实现了对裂纹扩展过程的数值模拟,并将数值计算得出的应力强度因子与所建立的曲线分支裂纹模型解进行对比分析,验证了该模型的可行性,同时将曲线分支裂纹模型解与原有的直线分支裂纹模型解进行了对比,表明了建立曲线分支裂纹模型的必要性。     

橡胶夹层／复合材料粘接界面疲劳裂纹扩展行为的研究

用Ⅰ型加载下的双悬臂夹层梁试样,以应变能释放率为裂纹扩展参量,研究橡胶夹层／复合材料粘接界面疲劳裂纹的扩展行为。结果表明,循环载荷下的裂纹扩展速率对试验频率、载荷比、温度及橡胶夹层厚度反映较敏感。     

复合材料层合板分层损伤数值模拟方法研究现状

复合材料层合板在航空航天等领域受到广泛应用,分层损伤作为复合材料层合板主要的损伤形式,对复合材料结构的强度和刚度有显著的影响,是限制其重大工程应用的热点问题之一.通过实验的方法对复合材料结构进行研究,往往需要耗费大量的时间和成本,成熟的有限元数值模拟技术可以较低成本实现复合材料结构的分层行为模拟,成为分层损伤研究的重要...     

水环境对热塑性复合材料层合板分层疲劳裂纹扩展的影响

本文研究了水环境对ICIAPC-2热塑性预浸料(AS4/PEEK)制成的单向复合材料层合板分层疲劳裂纹扩展的影响.用双悬臂梁试件进行了I型张开位移加载试验.试验环境为23℃水中和50℃水中.水环境未引起很大的不利影响.用电子显微镜和机理分析讨论了水环境对CF/PEEK和CF/环氧两种层合板的差异.     

水环境对热塑性复合材料层合板分层疲劳裂纹扩展的影响

本文研究了水环境对ICIAPC-2热塑性预浸料(AS4/PEEK)制成的单向复合材料层合板分层疲劳裂纹扩展的影响.用双悬臂梁试件进行了I型张开位移加载试验.试验环境为23℃水中和50℃水中.水环境未引起很大的不利影响.用电子显微镜和机理分析讨论了水环境对CF/PEEK和CF/环氧两种层合板的差异.      

微观组织与裂纹闭合效应对40CrNiMo钢疲劳短裂纹扩展的影响

对具有粗、细晶粒组织的40CrNiMo 钢进行了疲劳短裂纹扩展试验研究。试验和分析结果表明,短裂纹扩展的偏折强烈,裂纹闭合效应较小。粗晶组织比细晶组织的裂纹偏折更大,粗糙度诱发闭合效应更强,因而裂纹扩展较幔。微观组织通过对闭合效应的作用进而影响了疲劳短裂纹的扩展行为。     

复合材料疲劳分层的界面单元模型

提出一种三维黏聚力界面损伤模型,可以描述单调和交变载荷下层合复合材料混合型的分层损伤。损伤用界面所经历过的最大位移间断来定义,交变荷载下一个周期的加、卸载过程均考虑有损伤积累,模型还考虑了单调和疲劳损伤的门槛效应和交变载荷下裂纹的闭合效应。建立了包含该界面损伤模型的初始无厚度八节点等参界面单元,并引入加速损伤的算法,用一次计算循环代替若干次实际循环,提高计算效率。用该单元模型对某复合材料动部件疲劳分层裂纹的形成和扩展进行了模拟,得到了分层裂纹前沿界面局部损伤和结构疲劳分层的发展规律,模型预测的裂纹长度-荷载循环次数对数(a-log N)曲线和结构剩余刚度与试验数据吻合。     

Finite element analysis of postbuckling and delamination of composite laminates using virtual crack closure technique

The two-dimensional and three-dimensional parametric finite element analysis (FEA) of composite flat laminates with two through-the-width delamination types: 0₄/(±θ)₆//0₄ and 0₄//(±θ)₆//0₄ (θ = 0°, 45°, and “//” denotes the delaminated interface) under compressive load are performed to explore the effects of multiple delaminations on the postbuckling properties. The virtual crack closure technique which is employed to calculate the energy release rate (ERR) for crack propagation is used to deal with the delamination growth. Three typical failure criteria: B-K law, Reeder law and Power law are comparatively studied for predicting the crack propagation. Effects of different mesh sizes and pre-existing crack length on the delamination growth and postbuckling properties of composite laminates are discussed. Interaction between the delamination growth mechanisms for multiple cracks for 0₄//(±θ)₆//0₄ composite laminates is also investigated. Numerical results using FEA are also compared with those by existing models and experiments.     

Finite element interface models for the delamination analysis of laminated composites: mechanical and computational issues

The finite element analysis of delamination in laminated composites is addressed using interface elements and an interface damage law. The principles of linear elastic fracture mechanics are indirectly used by equating, in the case of single‐mode delamination, the area underneath the traction/relative displacement curve to the critical energy release rate of the mode under examination. For mixed‐mode delamination an interaction model is used which can fulfil various fracture criteria proposed in the literature. It is then shown that the model can be recast in the framework of a more general damage mechanics theory. Numerical results are presented for the analyses of a double cantilever beam specimen and for a problem involving multiple delamination for which comparisons are made with experimental results. Issues related with the numerical solution of the non‐linear problem of the delamination are discussed, such as the influence of the interface strength on the convergence properties and the final results, the optimal choice of the iterative matrix in the predictor and the number of integration points in the interface elements. Copyright © 2001 John Wiley & Sons, Ltd.     

Mesh‐independent matrix cracking and delamination modeling in laminated composites

The initiation and evolution of transverse matrix cracks and delaminations are predicted within a mesh‐independent cracking (MIC) framework. MIC is a regularized extended finite element method (x‐FEM) that allows the insertion of cracks in directions that are independent of the mesh orientation. The Heaviside step function that is typically used to introduce a displacement discontinuity across a crack surface is replaced by a continuous function approximated by using the original displacement shape functions. Such regularization allows the preservation of the Gaussian integration schema regardless of the enrichment required to model cracking in an arbitrary direction. The interaction between plies is anchored on the integration point distribution, which remains constant through the entire simulation. Initiation and propagation of delaminations between plies as well as intra‐ply MIC opening is implemented by using a mixed‐mode cohesive formulation in a fully three‐dimensional model that includes residual thermal stresses. The validity of the proposed methodology was tested against a variety of problems ranging from simple evolution of delamination from existing transverse cracks to strength predictions of complex laminates withouttextita priori knowledge of damage location or initiation. Good agreement with conventional numerical solutions and/or experimental data was observed in all the problems considered. Published 2011. This article is a US Government work and is in the public domain in the USA.     

Evaluation of energy release rate-based approaches for predicting delamination growth in laminated composites

A variety of energy release rate-based approaches are evaluated for their accuracy in predicting delamination growth in unidirectional and multidirectional laminated composites. To this end, a large number of unidirectional and multidirectional laminates were tested in different bending and tension configurations. In all cases, the critical energy release rate was determined from the tests in the most accurate way possible, such as by compliance calibration or the area method of data reduction. The mode mix from the tests, however, was determined by a variety of different approaches. These data were then examined to determine whether any of the approaches yielded the result that toughness was a single-valued function of mode mix. That is, for an approach to have accurate predictive capabilities, different test geometries that are predicted to be at the same mode mix must display the same toughness. It was found that variously proposed singular field-based mode mix definitions, such as the =0 approach or basing energy release rate components on a finite amount of crack extension, had relatively poor predictive capabilities. Conversely, an approach that used a previously developed crack tip element analysis and which decomposed the total energy release rate into non-classical components was found to have excellent predictive capabilities. It is postulated that this approach is more appropriate for many present-day laminated composites.     

Dynamic delamination growth in laminated composite structures

The dynamic growth of a thin strip delamination in a thick base laminate under in-plane loadings has been analysed. A variational principle, coupled with a Griffith-type fracture criterion, is used to formulate the delamination growth problem. Two approximate solutions, including one mode and two modes, respectively, are calculated in this paper. The resulting equations of motion and the dynamic local growth condition at the crack tip turn out to be two and three coupled ordinary differential equations for one-mode and two-mode solutions. A fourth-order Runge-Kutta method is then used to obtain the numerical solutions. The results show that delamination growth will approach a state of arrest for materials with high fracture toughness, and continue all the way without a limit for low fracture toughness materials. The inertial effect is important and should not be ignored in calculation of the arrested delamination length for high fracture toughness materials. For materials with low fracture toughness, the inertial effect is significant and high admissible modes are noticeable. A comparison between the present results and the previously known quasi-dynamic solution is also given.     

A concise interface constitutive law for analysis of delamination and splitting in composite materials and its application to scaled notched tensile specimens

A concise constitutive law for cohesive interfaces is proposed in this paper. A new state variable is introduced to track the extent of damage accumulated at the interface. The constitutive equations not only account for mixed‐mode delamination propagation in composite materials, but also satisfactorily deal with mode ratio change during the debonding process. The interface model is implemented in the LS‐DYNA explicit finite element code. The model has been applied to scaled open hole tension tests on laminated composite material. Comparison between numerical results and experiments shows good correlation for failure modes and strengths for a range of different specimen sizes. Copyright © 2006 John Wiley & Sons, Ltd.     

Matrix cracking and delamination in laminated composites. Part II: Evolution of crack density and delamination

This paper presents a model to predict the propagation of transverse cracks in polymer matrix composite laminates. Different possibilities for the crack pattern are analyzed and the different stress-strain response are compared. Taking into account that matrix cracking promotes delamination between the plies, the propagation of delamination is also simulated. The model predictions are compared with experimental data obtained in composite laminates that accumulate transverse cracks and delaminations before failing catastrophically. The possibility and limitations of a general constitutive law applied at ply level, as a mesomodel, is analyzed and the bounds of applicability of the model are explained.     

Mode I delamination toughness of laminated composites with through-thickness reinforcement

Through-thickness reinforcement is an effective way to suppress delamination in laminated composites. Micromechanics based models are developed to study the effect of through-thickness reinforcement (stitching) in improving the Mode I delamination crack growth resistance of laminated composites. In the development of these models, two types of stitch geometries are considered. In the first case, the stitches are assumed disconnected as in many cases the top and the bottom surfaces of the stitched laminates are ground off to remove surface in-plane waviness caused by stitching loops. The force in the stitches in this case is estimated from frictional bonding between stitches and the matrix. In the second case, interconnected stitches are considered and the force carried by the stitches is modelled as Winkler elastic foundation type of stress-separation relation. The effect of stitches is expressed in terms of a single stitching parameter Gl or Gb and closed form analytical expressions for the crack-growth resistance (K _R (a)) are obtained. The effects of the stitching parameter and various geometric and material properties are examined.On leave at the Department of Mechanical Engineering, Hong Kong University of Science & Technology, Clear Water Bay, Kowloon, Hong Kong.     

Hybrid equilibrium element with interelement interface for the analysis of delamination and crack propagation problems

This article proposes a formulation for the analysis of delamination and fracture propagation problems at the interelement interface, with perfect adhesion at the pre-failure condition and with linear softening at the post-failure regime. The proposed formulation is based on the hybrid equilibrium element (HEE) model, with stress fields which strongly verify the homogeneous equilibrium equations and interelement equilibrium equations. The HEE can easily model high-order stress fields and can implicitly model the initially rigid behavior of an extrinsic interface at the element sides. The interface model is defined as a function of the same degrees of freedom of the HEE (generalized stresses) and the pre- and post-failure behavior of the interface can be modeled without any additional degree of freedom. The proposed formulation is developed for a nine-node triangular HEE with quadratic stress fields. This article also proposes an extrinsic cohesive model, rigorously developed in the damage mechanics framework.