A computational model for analysing interactive buckling and delamination growth in composite structures

In this paper, a unified method is presented: (i) to model delaminated stiffened laminated composite shells; (ii) for synthesising accurate multiple post-buckling solution paths under compressive loading; and (iii) for predicting delamination growth. A multi-domain modelling technique is used for modelling the delaminated stiffened shell structures. Error-free geometrically nonlinear element formulations — a 2-noded curved stiffener element (BEAM2) and a 3-noded shell element (SHELL3) — are used for the finite element analysis. An accurate and simple automated solution strategy based on Newton type iterations is used for predicting the general geometrically nonlinear and postbuckling behaviour of structures. A simple method derived from the 3-dimensionalJ-integral is used for computing the pointwise energy release rate at the delamination front in the plate/shell models. Finally, the influence of post-buckling structural behaviour and the delamination growth on each other has been demonstrated.     

剪切载荷下含椭圆形大开口层合板的试验研究

在面内纯剪切载荷作用下, 采用试验与有限元模拟方法研究了结构中心设置椭圆形大开口的正方形复合材料层合板的应力/应变集中现象及屈曲、 后屈曲行为, 通过测试结果对试验件失效模式进行了评估。研究结果表明: 层合板开口附近应力/应变集中程度很高; 大尺寸开口使结构稳定性显著降低, 且开口层合板具有较好的后屈曲承载能力; 由于弯曲产生高水平的层间应力, 导致局部分层损伤并伴有基纤剪切破坏; 随着横向挠度的增加, 各应力集中区域的纤维发生拉伸断裂, 导致整体结构瞬间发生脆性失效。有限元模拟结果与试验结果符合较好。     

Post-buckling failure in multi-delaminated composite wind turbine blade materials

This study models the inter-laminar damage due to low velocity impacts on hybrid composite materials typical of those used in wind turbine blade structures. The effect of z-pinning using natural flax yarn on the critical buckling load and post-buckling behaviour of multi-delaminated composite beams was investigated. Laminated composite beams were pinned through their thickness using natural flax yarns to control delamination failure during the post-buckling process. A multiple delamination with a triangular shape was inserted into each of the beams to simulate the damage caused by a low velocity impact e.g. ice, on composite wind turbine blades. For a laminate design of [C₉₀/G₉₀]₄, global collapse caused no delamination failure during the post-buckling test while delamination failure occurred for a laminate design of [C₀/G₀]₄. In this case, z-pinning can significantly increase the failure resistance within a composite structure and it can then postpone the failure process. The buckling process of a multi-delaminated composite beam was also simulated by finite element software ANSYS and the results were substantially verified by relevant experimental results.     

Prediction of post-buckling strength of stiffened laminated composite panels based on the criterion of mixed-mode stress intensity factors

An analytical investigation is conducted to predict the post-buckling strength of laminated composite stiffened panels under compressive loads. When a stiffened composite panel buckles, the skin would deform into a sinusoidal mode shape, and hence induces additional moments and forces near the skin-stiffener interface region. These induced loads would cause the existing small edge delamination cracks to propagate along the skin-stiffener interface, and this in turn would lead to the global failure of the stiffened panel. To reduce the cost of the analytical investigation, the failure of the stiffened panel under post-buckling loads is modeled in two stages: a global analysis to model the post-buckling behavior of the stiffened panel; and a local analysis to model the onset of propagation of the edge delamination crack at the skin-stiffener interface. The results from this study are compared with an experimental investigation conducted by Starnes, Knight, and Rouse (1987). It is found that for the eight different specimens that are considered in this study, the calculated critical energy release rate for the propagation of the edge delamination crack in each specimen differs substantially from those for the others; hence it may be concluded that the total energy release rate would not be a suitable fracture parameter for predicting the post-buckling strength of the stiffened panels. On the other hand, using the fracture criterion based on the critical mixed-mode stress intensity factors, the predicted post-buckling strength of the stiffened panels compares quite favorably with the experimental results and the standard deviation of the error of prediction is less than 10%. Furthermore, by applying the criterion of critical mixed-mode stress intensity factors on a simple damage model, the present analysis is able to predict the significant reduction in the post-buckling strenght of stiffened panels with a damage due to a low-speed impact at the skin-stiffener interface region.This work is supported by ONR, with Dr. Y. Rajapakse as the program official.     

Strength reduction and delamination growth in thin and thick composite plates under compressive loading

In this paper, the coupled local-global buckling behavior in laminated composite plates with elliptic delaminations and the associated mechanisms of delamination growth under compressive loads are critically examined. The J-integral technique is used for delamination growth prediction in terms of pointwise energy release rate distribution along the delamination edge. A Multi-plate model, in conjunction with a 3-noded quasi-conforming shell element, is used to model the delaminated plates. The incremental equilibrium equations are set up based on total Lagrangian formulation. The solution strategy incorporates Gauss elimination in a cycle of Newton-Raphson iterations and is augmented with automated arc-length controled load incrementation and equilibrium iterations; and with automated post-buckling path tracing based on a linearised asymptotic solution. The effects of structural parameters such as delamination thickness, size and shape, on the post-buckling behavior and on the delamination growth are critically examined.This work was supported by the FAA to the Center of Excellence for Computational Modeling of Aircraft Structures at Georgia Institute of Technology, and in part by a grant from ONR.     

Numerical analysis and experimental correlation of composite shell buckling and post-buckling

This paper deals with the buckling and post-buckling behaviour of carbon fibre reinforced plastic cylindrical shells under axial compression. The finite element analysis is used to investigate this problem and three different types of analysis are compared: eigenvalue analysis, non-linear Riks method and dynamic analysis. The effect of geometric imperfection shape and amplitude on critical loads is discussed. A numerical–experimental correlation is performed, using the results of experimental buckling tests. The geometric imperfections measured on the real specimens are accounted for in the finite element model. The results show the reliability of the method to follow the evolution of the cylinder shape from the buckling to the post-buckling field and good accuracy in reproducing the experimental post-buckling behaviour.     

Nonlinear analysis of bimodular composite plates under compression

The present work deals with the buckling and post-buckling behaviour of bimodular laminated composite plates. The fiber-governed bimodular constitutive model is adopted for the analysis and the geometrical nonlinearities are accounted for by using the consistent small strain and moderate rotation theory for a shear deformable Mindlin plate. Governing equations of the problem are developed and the finite element formulation is given using lagrangian C°-elements. Some numerical examples are developed to analyze the buckling and post-buckling behaviour of laminated bimodular plates.     

Mesh design in finite element analysis of post-buckled delamination in composite laminates

The role of mesh design in the post-buckling analysis of delamination in composite laminates is addressed in this paper. The determination of the strain energy release rate (SERR) along the crack front is central to the analysis. Frequently, theoretical analysis is limited to treatment of the problem in two dimensions, since considerable complexity is encountered in extending the analysis to three dimensions. However, many practical problems of embedded delamination in composite laminates are inherently three-dimensional in nature. Although in such cases, the finite element (FE) method can be employed, there are some issues that must be examined more closely to ensure physically realistic models. One of these issues is the effect of mesh design on the determination of the local SERR along the delamination front. There are few studies that deal with this aspect systematically. In this paper, the effect of mesh design in the calculation of SERR in two-dimensional (2D) and three-dimensional (3D) FE analyses of the post-buckling behavior of embedded delaminations is studied and some guidelines on mesh design are suggested. Two methods of calculation of the SERR are considered: the virtual crack closure technique (VCCT) and crack closure technique (CCT). The 2D analyses confirm that if the near-tip mesh is symmetric and consists of square elements, then the evaluation of the SERR is not sensitive to mesh refinement, and a reasonably coarse mesh is adequate. Despite agreement in the global post-buckling response of the delaminated part, the SERR calculated using different unsymmetrical near-tip meshes could be different. Therefore, unsymmetrical near-tip meshes should be avoided, as convergence of the SERR with mesh refinement could not be assured. While the results using VCCT and CCT for 2D analyses agree well with each other, these techniques yield different quantitative results when applied to 3D analyses. The reason may be due to the way in which the delamination growth is modeled. The CCT allows simultaneous delamination advance over finite circumferential lengths, but it is very difficult to implement and the results exhibit mesh dependency. Qualitatively, however, the two sets of results show similar distributions of Mode I and Mode II components of the SERR. This is fortunate, since the VCCT is relatively easy to implement.     

含分层损伤大层数复合材料层合板层间热效应分析

在机械载荷和热载下对含分层损伤大层数复合材料层合板采用三维有限元法分析其后屈曲行为。这种有限元的特点是每个单元可包含多个具有不同铺设角、不同组分材料的铺层。在分析中引入接触元来防止层间的闭合接触效应,并进一步分析了分层前缘的能量释放率。结果表明温度对于复合材料层合板的层间破坏有重要影响。     

柔性电子器件的应用、结构、力学及展望

调控薄膜基底结构的表面不稳定性已被成功应用于制备可延展的新型电子设备中。然而,该类电子器件在工作中需要承受外部载荷作用,致使薄膜-基底结构界面处残余应力集中,容易诱发薄膜电子器件与基底脱粘与分层。该文将从理论分析和数值仿真角度,研究压电薄膜在柔性基底表面上的失稳特性。由于压电薄膜变形具有大位移小应变的特点,该文基于非线性Euler-Bernoulli梁理论与能量最小化原理,建立压电薄膜基底结构无屈曲、褶皱、局部屈曲及全脱层屈曲模式的理论分析模型;从能量角度定量分析了薄膜-基底结构4种模式相互演变的临界条件;通过数值仿真,验证了该文解析结的有效性,定量、定性的讨论了薄膜基底结构的材料、几何参数对4种模式演变的影响。研究结果表明：改变基底弹性模量、预应变、物理场强度和界面粘附系数能够调控压电薄膜基底结构的屈曲模式;通过调控温度变化量和电压的方式,能够实现对压电薄膜基底结构的失稳特性精细化调控。该文的研究结果将为提升薄膜基底型的电子器件的稳定性及优化设计提供理论支持。

     

含分层损伤复合材料等三角形格栅加筋板的起裂和扩展过程研究

对在压缩载荷下先进复合材料等三角形格栅加筋板结构 (AGS) 后屈曲阶段的分层起裂和扩展过程进行了研究。基于一阶剪切变形理论和 Von2 Karman几何非线性关系 , 提出了 AGS结构后屈曲有限元分析模型 ;基于总能量释放率准则 , 并利用虚裂纹闭合法 (VCCT) 及自适应网格的生成和移动技术分析了分层损伤的扩展过程 , 在分析过程中考虑了分层前缘的接触效应。并通过典型算例 , 讨论了不同的初始分层尺寸、 肋骨刚度对等三角形格栅加筋板结构的分层起裂和扩展过程的影响 , 通过与具有相同几何尺度的正交格栅加筋板结构的比较 ,说明等三角形格栅加筋板结构具有较高的抗分层能力。本文方法和所得结论对 A GS结构的承载能力预测和设计将具有参考价值。      

考虑剪切效应的轴对称脱层圆板的后屈曲分析

基于Von Karman板理论,考虑横向剪切变形,建立了具脱层的轴对称层合圆板的后屈曲控制方程。应用正交配点法,将后屈曲控制方程、边界条件、以及连续条件转化为非线性方程组,然后进行迭代求解。讨论了不同脱层深度和脱层半径对层合圆板的屈曲及后屈曲特性影响,且与有关文献的结果进行了比较。     

Post-buckling analysis of composite plates containing embedded delaminations with arbitrary shape by using higher order shear deformation theory

The compressive post-buckling behavior of composite laminates containing embedded delamination with arbitrary shape is investigated analytically. For modeling the embedded delamination, the laminate is divided into three smaller regions. The higher order shear deformation theory is implemented and the formulation is based on the Rayleigh-Ritz approximation technique by the application of the simple/complete polynomial series for each region. The nonlinear equilibrium equations, which are achieved through the application of the principle of Minimum Potential Energy, are solved by employing the Newton-Raphson iterative procedure. Some interesting results are obtained and compared with those achieved by the finite element method of analysis using ANSYS commercial software. A good agreement is seen to exist between the results. This is while for a given level of accuracy in the results, ANSYS requires a markedly larger number of degrees of freedom compared to that needed by the developed method. Moreover, a considerable reduction in the load carrying capacity of laminate is noticed due to the presence of delamination.     

On a model of elastic-plastic structure optimized for post-buckling behaviour

The post-critical analysis performed for a structure optimized only for buckling constraints shows in many cases that the behaviour of the designed element after buckling is unstable. That should be considered as a drawback of the standard design since the applicability of such an unstable optimal structure may be questionable. Recently the new concept of structural optimization against instability has been proposed. The post-buckling analysis is included directly in the optimization problem and the modified design is formulated. As a result, the modified optimal structure with stable behaviour after buckling is created. Many modified design problems for structures exposed to elastic instability have been already formulated and solved. This paper gives some proposals of extending that approach for the design of elastic-plastic structures.     

Post-buckling behaviour of structures using a finite element–nonlinear eigenvalue technique

A series of finite element algorithms for the calculation of the post-buckling behaviour of structures are proposed. The algorithms represent a finite element implementation of a variational principle for nonlinear eigenvalue problems. Incremental amplitude solution schemes are defined. Numerical results are presented for the post-buckling behaviour of specific structures with linear and nonlinear pre-buckling states.     

复合材料整体加筋板轴压后屈曲失效评估方法

在飞机结构设计中,为高效完成复合材料加筋板结构设计,亟需一种快速有效的复合材料整体加筋板后屈曲失效评估方法。采用商业有限元软件ABAQUS建立了加筋板有限元模型,研究了复合材料整体加筋板的轴压后屈曲失效评估方法,即“整体-局部”法。通过对单筋条壁板后屈曲的失效分析发现,“整体-局部”法可得到初始脱胶时的位移和载荷值以及较准确的破坏载荷值,是一种能有效确定加筋板后屈曲失效情况的快速评估方法,对提高结构设计效率和减轻飞机结构质量具有重要的工程意义。     

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。     

An experimental investigation into the buckling and post-buckling of CFRP shells under combined axial and torsion loading

The results of an experimental study of the buckling and post-buckling behaviour of four unstiffened thin-walled CFRP cylindrical shells are presented. The test equipment allows axial and torsion loading, applied separately and in combination, using a position control mode, and includes a laser scanning system for the measurement in situ of the geometric imperfection as well as of the progressive change in deformations. The results identify the effect of laminate orientation, show that the buckling loads are essentially independent of load sequence and demonstrate that the shells are able to sustain load in the post-buckling field without any damage. The measured data are fundamental for the development and validation of analytical and numerical models and contribute to the definition of applicable strength design criteria of composite cylindrical shells in the post-buckling field, with the final aim of a larger structure weight saving.     

Straight-sided, buckling-driven delamination of thin films at high stress levels

The fracture mechanics of a straight-sided, thin film delamination at stress levels, which are high compared to the stress required to initiate the delamination is investigated. Buckling at a bifurcation point of the delaminated region, resulting from incompletely relieved stresses in this region, is analysed by a semi- analytical approach for delaminations of infinite extent. The results are compared to numerical predictions based on finite element calculations for finite sized delaminations. The finite element calculations are carried out in the post-buckling regime showing that parts of the crack front will close as a result of bifurcation buckling, while other parts will experience enhanced energy release rate and mode I stress intensity factor. The mode III stress intensity factor is shown to be negligible at the stress levels analysed.     

Delamination buckling and growth of flat, cross-ply laminates

A one-dimensional model is presented in order to predict (a) delamination buckling loads of an across the width delaminated and axially loaded laminated plate and (b) the ultimate load-carrying capability of the above geometry, when delamination growth can take place. In order to study the possibility of spreading of the damaged (delaminated) area to the undamaged area, the post-buckling solution is employed.

The energy release rate has been used to determine whether the delamination growth is stable or unstable. The results reveal that for a relatively small delamination length the buckling loads serve as a measure of the load-carrying capacity of the damaged plate, while for a relatively large delamination length, the plate could carry larger loads depending on the fracture toughness of the plate material.

Moreover, the present model can be used to study the effect of the presence of coupling between bending and stretching on delamination growth. Note that for such geometries the possibility of bifurcational buckling does not exist, regardless of the level of the applied load.