含脱层纤维增强复合材料层合板在湿热环境下的屈曲分析

依据复合材料细观力学研究了含脱层的正交各向异性复合材料层合板的力学性能与温度和湿度的关系,在宏-细观力学模型框架下建立了考虑湿热效应的屈曲控制方程,利用空间上分离变量的方法求解了控制方程,得到满足连续性条件和边界条件的控制方程的解。通过含脱层的复合材料层合板的屈曲数值算例,综合讨论了几何参数、材料参数和湿热环境等多方面的参数变化对含脱层的正交对称铺设复合材料层合板的临界屈曲载荷的 影响。     

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。     

剪切载荷作用下复合材料挖补修理层合板试验及有限元分析

为了确定剪切载荷作用下含非穿透损伤复合材料挖补修理层合板的破坏模式和抗剪切能力,进行了复合材料挖补修理层合板的剪切试验,并与未损伤复合材料层合板进行对比。试验结果表明,复合材料挖补修理后的层合板具有较高的强度恢复率,且不影响层合板的后屈曲承载能力。同时,建立了剪切载荷作用下复合材料挖补修理层合板的有限元分析（FEA）模型,复合材料母板和补片采用了三维Hashin准则来判定材料失效,母板层与层之间采用零厚度界面单元以有效模拟剪切载荷作用下复合材料母板上、下子板之间的分层。该模型得到的破坏模式与试验结果基本相符。由于挖补修理的设计与工艺复杂性,理论模拟的破坏载荷与试验结果虽不能完全吻合,但其最大15%左右的差异能够满足修理设计的需要。以上结果说明,该模型对剪切载荷作用下复合材料挖补修理层合板的破坏模式和破坏载荷能够进行工程适用的预测。     

非对称复合材料层板在面内载荷作用下的非线性横向变形或屈曲

本文利用广义富里叶级数法对非对称复合材料层板在面内载荷作用下的非线性横向变形或屈曲问题进行了分析。文中主要研究了四边简支边界条件下,非对称层板的铺层方式和面内载荷形式对横向变形的影响。通过求解非线性控制方程得到了层板的载荷—挠度曲线或特殊情况下的后屈曲平衡曲线。计算结果表明,对于大多数非对称复合材料层板在面内载荷作用下所产生的是横向变形问题,而不是分叉屈曲问题。     

面内线性变化载荷作用复合材料层合板的振动与屈曲优化

采用广义微分求积（GDQ）法开展了不同边界条件下承受面内线性变化载荷作用复合材料层合板振动与屈曲的分析与优化。针对GDQ法求解面内线性变化载荷工况复合材料层合板屈曲问题存在计算振荡、不收敛现象,提出载荷扰动策略实现了GDQ法对复合材料层合板屈曲问题的稳定高效求解。基于基础圆频率和临界屈曲载荷系数的归一化指标,分析了铺层角度对复合材料层合板综合性能的影响,并结合直接搜索模拟退火算法开展了复合材料层合板的铺层顺序优化。结果表明:铺层角度变化对屈曲性能的影响明显强于频率特性;面内线性变化载荷中,以弯曲载荷作用下复合材料层合板的优化综合性能受边界条件变化的影响最小,而优化铺层角度受边界条件变化的影响最大。研究结果为复杂载荷作用下复合材料层合板的设计提供了参考。      

复合材料层板开孔压缩损伤分析

针对纤维增强复合材料层板开孔压缩, 将复合材料层板的失效分为层内失效和层间失效, 建立了复合材料层板开孔压缩损伤分析模型。该模型基于逐渐损伤分析, 对不同复合材料开孔层板进行了失效预测, 并与文献中试验结果进行了对比, 破坏强度和失效模式均与文献试验结果非常吻合。结果表明, 本文中所建立的层板开孔压缩损伤分析模型能够模拟含孔层合板压缩过程中的损伤起始、损伤扩展和最终破坏, 并最终预测含孔层合板压缩失效模式和破坏强度。     

复合材料层板开孔拉伸损伤分析

针对纤维增强复合材料层板开孔拉伸, 将复合材料层板的失效分为层内失效和层间失效, 建立了复合材料层板开孔拉伸损伤分析模型。该模型基于逐渐损伤分析, 对不同复合材料开孔层板进行了失效预测, 并与文献试验结果进行了对比, 破坏强度和失效模式均与文献试验结果非常吻合。结果表明本文中所建立的层板开孔拉伸损伤分析模型能够模拟含孔层合板拉伸过程中的损伤起始、 损伤扩展和最终破坏模式, 并最终预测含孔层合板拉伸失效模式和破坏强度。      

复合材料层合板剪切稳定性试验及强度预测

对无损伤及含冲击损伤的复合材料层合板进行了剪切稳定性试验,基于数字图像相关方法 (Digital image correlation,DIC)对层合板屈曲后屈曲行为进行了实时测量。试验结果表明：引入冲击损伤后,复合材料层合板剪切屈曲波形、屈曲载荷无明显变化,失效模式转变,承载能力下降了9.69%。随后,基于断裂面失效理论,建立了考虑剪切非线性效应的复合材料渐进损伤失效模型,并对复合材料层合板剪切失效过程进行了模拟。模型采用软化夹杂法将冲击损伤等效简化,直接将损伤区的几何边界信息写入材料模型中,不需要对冲击损伤区进行切割,从而保证了整体网格质量。与试验结果对比发现：模型考虑剪切非线性对屈曲载荷预测无明显影响,对后屈曲承载能力的预测精度影响较大,不考虑剪切非线性效应时的误差可达20%以上;软化夹杂法可以有效地模拟冲击损伤,预测的含冲击损伤的复合材料层合板的屈曲载荷、破坏载荷误差分别为-3.17%、-1.27%。     

含脱层单向铺设层合梁非线性后屈曲分析

采用四分区模型,将含脱层单向铺设复合材料层合板梁分为4个子梁,根据复合材料层合理论,考虑后屈曲路径上位于脱层界面上、下子梁之间的局部受力与变形机制,建立了子梁之间接触力与变形之间的非线性定量关系。在此基础上,结合可伸长梁的几何非线性理论,推导出了计及接触效应的各子梁的非线性后屈曲控制方程。设定简支板梁的边界条件以及脱层前沿处各子梁之间力和位移的连续性条件,通过对控制方程和定解条件归一化,采用小参数摄动法求解,并根据梁的平衡微分方程的特点,解析其通解与特解的构造,获得了含脱层单向铺设层合梁受轴向压力作用的临界屈曲荷载及后屈曲平衡路径的理论解。通过对含脱层单向铺设的复合材料层合梁进行数值分析,综合讨论了脱层长度和深度等对层合板梁的临界屈曲载荷及接触性能的影响,并将所得的理论解与ABAQUS有限元分析得到的结果进行对比,结果表明二者高度吻合。研究发现梁的屈曲模态包含宏观的整体失效模态和界面的微观屈曲模态。梁的屈曲荷载和接触性能都是其固有属性,前者受梁的几何参数和材料参数的影响较显著,而后者则主要受脱层的位置和大小影响。     

具有局部分层的对称铺设层合板在非保守力作用下的屈曲分析

利用弹性非保守系统自激振动的拟固有频率变分原理,推导出复合材料矩形板受非保守随从力作用的变分方程,进而导出复合材料层合板含分层损伤的有限元基本方程及求解临界荷载力和固有频率的特征方程。用载荷增量法计算了不同边长比的复合材料矩形板在面内受随从力作用且含有分层的临界载荷,分析了不同角铺设方向对临界载荷的影响。分析表明,分层对临界载荷有一定影响,复合材料层合板的角铺设方向对临界载荷有较大影响。     

Buckling analysis of a plate with built-in rectangular delamination by strip distributed transfer function method

Summary. Delamination may reduce the buckling of the laminated plate. In this paper, a semi-analytical, semi-exact method, namely the strip transfer function method based on Mindlins first-order shear deformation theory is developed to investigate the buckling of a delaminated plate. First, a composite plate with bulit-in rectangular delamination is divided into two kinds of rectangular super-units, one with a delamination and one without. The variational principle is used to obtain equilibrium equations and boundary conditions. Then, by displacement continuity and force balance of nodes that connect two super-units, the characteristic equation for the buckling analysis of the delaminated plate is derived. Consequently, buckling load and mode are computed. By comparing the results of the plate with through-the–width delamination to the analytic solutions of a beam and the results of the finite element method, the validity of this method is tested. Furthermore, the influence of length, depth and position of the delamination, the boundary condition and the plying angle of the material on the buckling load is analyzed.     

Delamination buckling of laminated plates

The subject of this paper is the buckling of laminated plates, with a pre-existing delamination, subjected to in-plane loading. Each laminate is modelled as an orthotropic Mindlin plate. The analysis is carried out by a combination of the finite element and asymptotic expansion methods. By applying the finite element method, plates with general delamination regions can be studied. The asymptotic expansion method reduces the number of unknown variables of the eigenvalue equation to that of the equation for a single Kirchhoff plate. Numerical results for the critical buckling load are presented for several examples. The effects of the shape, size and position of the delamination on the buckling load are studied through these examples.     

含椭圆分层损伤复合材料层合板分层前缘接触效应研究

采用基于Mindlin 一阶剪切理论的四节点板单元, 分析了分层前缘闭合接触效应对含椭圆分层复合材料层合板前后屈曲行为的影响。通过在分层区域内引入虚杆单元来防止上、下子板发生相互重叠, 并假设接触区内没有摩擦。结果表明, 分层前缘的闭合接触效应受分层几何形状的影响很大, 当椭圆分层子板的长轴与压缩载荷方向一致时, 闭合接触效应对含分层层合板前后屈曲行为最大。      

基于弯曲刚度最大分层临界载荷的层压板局部屈曲预测

提出了一种预测含特定分层损伤层压板发生局部屈曲时整体应变的方法。认为含分层子板的局部屈曲载荷由其弯曲刚度最大的分层决定, 因而含有相同最大弯曲刚度分层的不同子板具有相同的屈曲载荷。在已知弯曲刚度最大分层的屈曲载荷的情况下, 根据层压板的轴向刚度公式, 计算出发生局部屈曲时弯曲刚度最大的分层与完好的基板分别承受的载荷, 即得到总载荷, 进而得到层压板的整体应变。用ABAQUS有限元分析软件建立含分层损伤的层压板模型, 使用准静态加载进行了多种分层深度和分层位置下的局部屈曲仿真, 所得局部屈曲载荷符合上述推论。用所提方法预测发生局部屈曲时的整体应变, 结果与有限元结果吻合较好, 此方法可用于建立分层参数识别的参照样本库。     

Local Buckling Delamination of a Rectangular Sandwich Plate Containing Interface Embedded Rectangular Cracks and Made From Elastic and Viscoelastic Materials

A three-dimensional buckling delamination problem for a rectangular sandwich plate made from elastic and viscoelastic materials is studied. It is supposed that the plate contains interface embedded rectangular cracks and that the edge-surfaces of these cracks have initial infinitesimal imperfections. The evolution of these initial imperfections with an external bi-axial compressed force (for the case where the materials of the layers of the plate are elastic) or with duration of time (for the case where the materials of the layers of the plate are viscoelastic) is investigated. The corresponding boundary value problem is formulated within the framework of the piecewise homogeneous body model with the use of three-dimensional geometrically nonlinear field equations of the theory of viscoelastic bodies. This problem is solved by employing boundary form perturbation techniques, Laplace transform and FEM. According to the initial imperfection criterion, the values of the critical parameters are determined. Numerical results on the critical force and critical time are presented and discussed. In particular, it is established that the values of the critical forces obtained for the buckling delamination around the rectangular embedded interface cracks are significantly greater than those obtained for the corresponding edge and band cracks.     

层板具有椭圆形、矩形和三角形分层屈曲破坏的实验研究

本文对层板具有表面二维的椭圆形、矩形和三角形分层屈曲破坏的机制,进行了实验研究。探讨了在压缩和拉伸作用下,分层屈曲应变ε₀与母层板和子层板各种参数的关系及分层扩展方向。      

Determining buckling strain energy release rate through indentation-induced delamination

An oscillating indentation load was applied to delaminate a diamond-like-carbon film from a silicon substrate. After delamination occurred, a two-stage behavior was exhibited in the load-depth results; then, a three-stage behavior was exhibited after buckling occurred due to a long enough delamination length. After removing the indentation load, the debonding film was single-buckled and suspended over the substrate; thus, the delamination length was obtained via the residual profile. Through analysis of the deflection of the buckled film, the buckling strain energy release rate was evaluated.     

带脱层的复合材料层板的屈曲分析

用基于Mindlin 板理论的有限元方法进行了带脱层损伤的复合材料层板的屈曲载荷分析。为了获得物理上可能的屈曲模态, 即避免上下脱层的相互贯穿, 在接触区域引入一些假想弹簧, 并给出了这些假想弹簧刚度系数的计算公式和接触计算的迭代格式, 通过这些弹簧对原始刚度矩阵进行修正可以有效地求解屈曲载荷特征值分析中的接触问题。数值计算结果表明了本算法的有效性和引入接触分析对这类屈曲分析的重要性。同时, 还对脱层的大小、形状、位置和脱层的纤维铺层方向对屈曲载荷的影响进行了研究。      

Buckling analysis of delaminated laminates with consideration of contact in buckling mode

This paper concerns the buckling load analysis of laminates with a pre‐existing delamination, using the finite element method based on the Mindlin plate theory. To deal with the contact problem in the buckling mode, an effective algorithm is presented. In this method, an iterative updating process based on the first‐order sensitivity analysis and the quadratic programming technique is proposed to compute the fictitious forces in contacting areas at first. These fictitious forces are then transferred into the stiffness parameters of some artificial springs. The original stiffness matrix of system can be modified, using these artificial springs. Finally, the penetration between two delaminated layers in the buckling mode can be prevented effectively. Numerical examples show that this method is very efficient to solve the contact problem in eigenvalue analysis from the viewpoint of its accuracy, stability and convergence speed. The effects of contact and delamination size on the buckling load analysis are also investigated. Copyright © 1999 John Wiley & Sons, Ltd.