Ultimate strength of composite laminates with free-edge delamination

The present paper deals with the free edge effect of composite laminates by using a generalized quasi-three dimensional analysis and experimental verification of an analysis performed for laminates with Teflon inserted on interfaces to simulate initial free-edge delamination. We performed tensile tests for laminates [30₂/?30₂/90]_s carbon-epoxy laminates with free-edge delamination under uniaxial tension. The experiment reveals that extensional stiffness of the laminate decreases by the initiation of the delamination, and that strength of the laminate without delamination is smaller than that of the laminates with delamination. Generalized quasi-three dimensional finite element technique, which employs energy release rate and maximum stress criteria, is developed to estimate behavior of the laminate after initial delamination. The numerical result by use of this technique predicts the ultimate strength of the laminates with sufficient accuracy according as the comparison with an experimental stress-strain curve. In the experiment conducted both for the laminate with initial delamination and the laminate without initial delamination, an unexpected results were obtained that is the ultimate load of the laminate without initial delamination was lower than that of the laminate with initial delamination. We presented clear explanation on the phenomenon occurred and developed the method to predict the nonlinear behavior of the laminate with or without initial delamination.     

A simple method to calculate mode components of strain energy release rate of free-edge delaminations in composite laminates

A simple method, which calculates the mode components of the strain energy release rate of free-edge delaminations in the laminates, is proposed. The interlaminar stresses are evaluated as an interface moment and interface shear forces that are obtained from the equilibrium equations at the interface between the adjacent layers. Deformation of an edge-delaminated laminate is calculated by using a generalized quasi-three dimensional classical lamination theory developed by the author. The analysis provides closed-form expressions for the three components of the strain energy release rale. The analyses are performed on [+30/−30/90]s laminates subjected to uniaxial extension, with free-edge delaminations located symmetrically and asymmetrically with respect to the laminate midplane. Comparison of the results with a finite element solution using the virtual crack closure technique shows good agreement. The simple nature of this method makes it suitable for primary design analysis for the delaminations of composite laminates.     

复合材料层合板阻尼特性有限元数值模拟

应用耗散能原理建立了复合材料层合板的阻尼预测分析模型,对复合材料层合板进行三维有限元模态分析,求出各个模态下的应力、应变分量。根据模态分析结果,从单向复合材料的阻尼性能参数出发,利用层合板应变能、耗散能和结构模态阻尼的关系求出各个模态对应的模态阻尼损耗因子。利用该方法,分别计算了单向层合板和对称层合板的结构模态阻尼损耗因子。数值计算结果与已有的理论分析和试验结果相比吻合较好,从而验证了该方法的合理性,该方法还可以比较三维应力分量对阻尼的贡献。     

Modélisation,identification et simulations éléments finis des phénomènes de délaminage dans les structures composites stratifiées

Modelling, identification and finite element predictions of delamination in laminated composite structures. In order to forecast the delamination initiation and propagation in a finite element context, a previously defined damage meso-modelling of composite laminates is used. At the meso-level, the laminate is described as an assembly of damageable layers and interlaminar interfaces. The present work concerns the modelling, the identification and the finite element predictions of delamination phenomena in composite structures. Finite element predictions are conducted with non-linear geometric and material hypothesis. The interface modelling is implemented in the finite element code Castem 2000 developped by CEA. Classic edge delamination tension and propagation tests are conducted in order to improve the interface damage model approach in the finite elements context.     

层间增韧复合材料在静压痕力下的损伤阻抗和渐进损伤分析

在复合材料层合板层间植入韧性层是提高复合材料韧性和抗冲击能力的有效方法。为了研究层间增韧对层合板损伤阻抗的改善作用，文中通过准静态压痕试验研究层间增韧复合材料在准静态压痕力下的损伤和破坏行为，利用超声C扫描测量分层损伤面积。试验结果表明，层间增韧复合材料具有较高的分层起始载荷和分层起始能量，损伤阻抗显著提高。在相同的载荷水平下，具有较小的分层损伤面积。文中还采用有限元方法对层间增韧复合材料在静压痕力下的分层和铺层失效进行数值分析，有限元计算结果与试验结果吻合较好。     

Enriched finite element method for three-dimensional viscoelastic interface crack problems

The enriched finite element method is developed for three-dimensional problems of an interface crack between elastic and viscoelastic (including dissimilar viscoelastic) materials. According to the displacement fields of elastic interface crack, the displacement fields of viscoelastic interface crack are derived through the correspondence principle. By incorporating the displacement expressions into the displacement model of regular element, the incremental formulations of enriched element are derived. The stress intensity factors and strain energy release rates can be solved based on the enriched degree of freedoms. A 3-D through interface crack at the center of jointed dissimilar viscoelastic plate subjected to remote tension and a quarter-circular viscoelastic interface corner crack subjected to uniform thermal loading was investigated using the enriched finite element method. It is shown that the present solutions are consistent with the analytical solutions, which indicates the present method is correct and efficient.

     

橡胶纯剪试件断裂力学分析

在橡胶材料纯剪试件中,当裂纹的长度和试件的高度尺寸接近时,应变能释放率与裂纹尺寸无关,由于存在这个特点,纯剪试件经常被用来研究橡胶材料的断裂属性。文中对橡胶纯剪试件在试件中心线上分别存在中心裂纹和边缘裂纹,以及粘接界面分别存在中心裂纹和边缘裂纹的情况进行非线性有限元分析,并将有限元计算的应变能释放率与已存在的解进行比较。对于长裂纹,有限元解与已存在的解吻合较好;但是对于小裂纹,有限元解与已存在的解之间仍然存在一些差异。     

复合材料含损伤结构剩余强度分析

考虑层压结构受冲击后的“花生壳形”分层及分层损伤引起的局部不对称性和耦合效应,并考虑压缩加载过程中可能出现的多层分级屈曲,发展一种计算低能冲击层压板受压剩余强度计算方法。数值分析表明本文的预测结果与试验结果吻合良好。     

A Study on Determining Mode Components of Strain Energy Release Rate of Free-Edge Delaminations in Composite Laminates

A simplified method for determining the individual mode components of the strain energy release rate of free-edge delaminations in composite laminates is proposed. Interlaminar stresses are evaluated as an interface moment, as are interface shear forces that are obtained from equilibrium equation of stress resultants at the interface between the adjacent layers. The deformation of edge-delaminated laminate is calculated by using a generalised quasi-3D classical laminated plate theory developed by the authors. The analysis provides closed-form expressions for the Mode-I, Mode-II, and Mode-III components of the strain energy release rate by combining the deformation of the edge-delaminated laminate with the interface moment and the interface shear forces. Comparison of the results with a finite-element analysis using the virtual crack closure technique shows good agreement.     

3D finite element analysis of stress distributions and strain energy release rates for adhesive bonded flat composite lap shear joints having pre-existing delaminations

The rate of propagation of embedded delamination in the strap adherend of lap shear joint (LSJ) made of carbon/epoxy composites has been evaluated employing three-dimensional non-linear finite elements. The delamination has been presumed to pre-exist in the thin resin layer between the first and second plies of the strap adherend. The inter-laminar peel and shear stress distributions have been studied in details and are seen to be predominantly three-dimensional in nature. The components of strain energy release rate (SERR) corresponding to the opening, sliding and cross sliding modes of delamination are significantly different at the two fronts of the embedded delamination. The sequential release of multi-point constraint (MPC) finite elements in the vicinity of the delamination fronts enables to simulate the growth of the delamination at either ends. This simulation procedure can be utilized effectively for evaluation of the status of the structural integrity of the bonded joints.     

FATIGUE LIFE PREDICTION THEORY OF COMPOSITE LAMINATES AND EXPERIMENTAL VERIFICATION

According to traditional phenomenological fatigue methodology and modem continuum damage mechanics theory, dual fatigue cumulative damage rules to predict fatigue damage formation and propagation lives of the notched composite laminates are presented. A 3-dimensional damage constitutive equation of anisotropic composites is also established. Damage strain energy release rate is interpreted as a driving force of the fatigue delamination damage propagation. A new damage evolution equation and a damage propagation σa-σm-N surface (stress amplitude-mean stress-life surface) are derived. Hence, using the method above, the fatigue life of composite components can be predicted. Finally, theoretically predicted results are compared with experimental data. It is found that the deviation of theoretic prediction from experimental results is about 22%.     

盲孔法测量焊接残余应力应变释放系数的有限元分析

为探讨简单易行的盲孔法测量焊接残余应力应变释放系数A、B的标定方法，根据盲孔法测量残余应力时应变释放系数A、B试验标定原理和强度理论，建立三维有限元模型，分别对盲孔法测量92lA钢焊接残余应力应变释放系数进行有限元标定和孔边应力集中有限元塑性修正．并由此得出应变释放系数随孔深与孔径比值的关系式和应变释放系数随形状改变比能参量S变化的塑性修正公式；将有限元标定结果与试验标定结果、通孔应变释放系数理论解进行比较，结果表明，有限元标定结果与试验结果、通孔应变释放系数理论值有较好的一致性，经塑性修正，计算结果与试验测量结果的偏差大大减小，建立适当有限元模型，用有限元法标定释放系数和进行孔边塑性变形修正是可行的。     

Vibration analysis of delaminated composite beams and plates using a higher-order finite element

In order to analyze the vibration response of delaminated composite plates of moderate thickness, a FEM model based on a simple higher-order plate theory, which can satisfy the zero transverse shear strain condition on the top and bottom surfaces of plates, has been proposed in this paper. To set up a C⁰-type FEM model, two artificial variables have been introduced in the displacement field to avoid the higher-order derivatives in the higher-order plate theory. The corresponding constraint conditions from the two artificial variables have been enforced effectively through the penalty function method using the reduced integration scheme within the element area. Furthermore, the implementation of displacement continuity conditions at the delamination front has been described using the present FEM theory. Various examples studied in many previous researches have been employed to verify the justification, accuracy and efficiency of the present FEM model. The influences of delamination on the vibration characteristic of composite laminates have been investigated. Especially the variation of ‘curvature of vibration mode’ (i.e., the second-order differential of deflections in vibration mode) caused by delamination has been studied in detail to provide valuable information for the possible identification of delamination. Furthermore, two approaches have been investigated to detect a delamination in laminates by employing this information.     

基于断裂力学的O型密封圈疲劳性能研究

根据断裂力学中的应变能释放率,制定疲劳断裂参数,对得到的O型密封圈实验数据进行拟合归类处理,得到计算O型密封圈疲劳寿命模型,并计算密封圈上危险截面单元的疲劳寿命。同时,利用疲劳分析软件对密封圈进行分析,找到密封圈上疲劳断裂的危险截面,并计算出危险截面节点上的疲劳寿命。比较断裂力学计算结果、疲劳分析软件分析结果和实验结果,表明3种方法得到的危险截面出现的位置和疲劳寿命基本一致,证明了运用断裂力学计算密封圈疲劳寿命的合理性。     

工字型梁腹板中Ⅲ型裂纹应力强度因子分析

基于能量释放率研究Ⅲ型裂纹平面应变条件下的J积分能量表达式。采用有限元软件模拟了工字梁腹板受扭转时裂纹裂尖应力奇异场,通过数值模拟得出裂纹区的应力、位移分布状态,并计算应力强度因子和J积分,从而验证表达式的可行性。     

基于改进应变能密度法的电动轮自卸车车架焊缝疲劳寿命预测

针对复杂载荷作用下焊接结构应力应变响应出现非完全封闭而交叉的现象,考虑封闭环以外的塑性应变能密度,提出了一种改进的应变能密度计算方法。通过设计制作对接接头试验试件,开展了焊接接头机械性能和疲劳试验研究,获取了Ramberg|Osgood方程参量并构建了基于总应变能密度的疲劳损伤模型。建立了电动轮自卸车车架有限元模型,开展了车架焊缝多载荷步非线性有限元分析。结合新方法和数值模拟得到的应力应变响应计算危险点各应变能密度,依据拟合的疲劳损伤模型进行寿命预测,计算结果与实际失效位置和开裂时间吻合较好。     

Indentation-induced buckling of organic coatings part II: measurements with impacting particles

The impact-induced buckling and delamination of a thin coating was analysed for the purpose of predicting the amount of coating removed when a single particle was launched, at a given velocity, against a coated substrate. A novel post-buckling analysis is presented in which the coating is modelled as a clamped disk prevented from buckling at an arbitrarily set inner radius, due to the presence of the indenting particle. A method for calculating the arrest strain energy release rate and mode mix of interfacial delamination cracks, based on the coupling of the presented buckling analysis with an existing strain energy release rate analysis is then presented. A method to estimate the critical interfacial shear stress at crack initiation is also outlined. An accompanying paper compares experimental results with the results of this analysis, and shows how the results can be used in the context of blast cleaning.     

化学机械抛光中Si/Cu/Ta/low-k界面剥离和断裂特性研究

超大规模集成电路随着布线层数增加和线宽的缩小,low-k材料的介电常数进一步降低,多孔low-k材料力学性能随之降低,使得晶圆在化学机械抛光(Chemical mechanical polishing,CMP)中面临的主要问题是Cu/Ta/low-k或者超低k材料的界面剥离。针对Si/Cu/Ta/low-k在CMP过程中的承载特性,建立单层布线和多层布线体系的界面力学模型,采用断裂力学理论和有限元法研究Si/Cu/Ta/low-k界面在CMP过程中界面的应力分布规律和界面裂纹的断裂强度。采用能量释放率来描述裂纹的扩展情况,根据界面裂纹能量释放率数值计算方法对裂纹长度、材料性质及不同的布线层数对裂纹扩展时的界面断裂/剥离特性进行仿真分析,得到界面应力分布、能量释放率、相位角与裂纹长度、材料性能、布线层数之间的关系变化曲线。结果表明:随着low-k力学性能降低和布线层数增加,裂纹能量释放率升高,界面裂纹更容易扩展。     

Dynamic crack growth in TDCB specimens

Dynamic crack propagation in tapered double cantilever beam (TDCB) specimens is analysed via beam theory and the finite element method. Steady state and transient solutions of the energy release rate G are given for various load conditions. Finite element analysis is performed to obtain the dynamic G at given crack speed or the crack history for a given fracture toughness. The stress wave effects on the dynamic G are discussed. The beam solutions are compared with the finite element results and some experimental phenomena are explained.     

Fatigue damage of quasi-isotropic composite laminates under tensile loading in different directions

The purpose of this work is to investigate fatigue damage of quasi-isotropic laminates under tensile loading in different directions. Low cycle fatigue tests of [0/−60/60]_s laminates and [30/−30/90]_s laminates were carried out. Material systems used are AS4/Epoxy and AS4/PEEK. The fatigue damage of [30/−30/90]_s is very different from that of [0/−60/60]_s. The experimental results are compared with the result obtained from the method for determining strain energy release rate components proposed by the authors. The analytical results were in good agreement with the experimental results. It is proved that the failure criterion based on the strain energy release rate is an appropriate approach to predict the initiation and growth of delaminations under cyclic loading.