Buckling and postbuckling behavior of delaminated sandwich beams

An investigation was performed to study the buckling and postbuckling behavior of sandwich beams containing lengthwise and depthwise through-the-width delaminations. An analytical beam model was developed to predict the buckling load of the beam and to describe its postbuckling response for arbitrarily situated delaminations and various combinations of boundary conditions. Griffith's energy release rate model was employed to predict the stability of delamination propagation under external loading and to determine the direction of delamination growth.

Parametric studies over a wide range of beam geometries, damage sizes and locations, composite facings and beam boundary conditions were carried out to study their effects on the overall behavior of the sandwich structure, as well as its damage tolerance. The results demonstrated that a sandwich construction is very ‘sensitive’ to the presence of delaminations situated at the core-faceplate interface. Premature buckling failure occurs at external loads which are significantly lower than the buckling load for a ‘perfect’ sandwich beam; in ‘imperfect’ beams with composite faceplates, the layup sequence affects significantly the load-carrying capacity of the beam; varying either the boundary conditions in a sandwich beam or the lengthwise location of a delamination has a small effect on the postbuckling behavior of the beam. Delaminations located within composite faceplates have less pronounced influence, and as the defect is moved outwards the limit load may reach the buckling load corresponding to that of the ‘perfect’ beam.

The proposed model is capable of analyzing the postbuckling behavior of both sandwich and composite laminated beams for arbitrary locations of the delamination, and various combinations of boundary conditions.     

Influence of predetermined delaminations on buckling and postbuckling behavior of composite sandwich beams

An investigation was performed to obtain the behavior of composite sandwich beams in the presence of predetermined delaminations, due to disbonding between the faceplate and the less rigid core. An analytical model for predicting buckling and describing the postbuckling behavior of the beam was developed. Griffith's fracture energy release rate model was introduced to predict the stability of the delamination propagation under external loading.

Parametric studies over a wide range of damage sizes, and composite facings were carried out to study the effects of these parameters on the overall behavior of the beams, as well as its damage tolerance. The results demonstrate that sandwich construction is very ‘sensitive’ to the presence of predetermined delaminatoins: premature buckling failure occurs at external loads, which are significantly lower than those corresponding to a ‘perfect’ sandwich beam. The limit load is obtained before delamination propagation takes place. In ‘imperfect’ beams with composite faceplates, the layup sequence affects significantly the load carrying capacity of the beam. It was also shown that the proposed model can be used to study the influences of predetermined delaminations in composite beams.     

Failure analysis of multiple delaminated composite plates due to bending and impact

The present work aims at the first ply failure analysis of laminated composite plates with arbitrarily located multiple delaminations subjected to transverse static load as well as impact. The theoretical formulation is based on a simple multiple delamination model. Conventional first order shear deformation is assumed using eight-noded isoparametric quadratic elements to develop the finite element analysis procedure. Composite plates are assumed to contain both single and multiple delaminations. For the case of impact, Newmark time integration algorithm is employed for solving the time dependent multiple equations of the plate and the impactor. Tsai-Wu failure criterion is used to check for failure of the laminate for both the cases. To investigate the first ply failure, parametric studies are made for different cases by varying the size and number of delaminations as well as the stacking sequences and boundary conditions.     

Vibration of beams with two overlapping delaminations in prebuckled states

An analytical solution for the free vibrations of beams with two overlapping delaminations in prebuckled states is presented. The delaminated beam is analyzed as seven interconnected Euler–Bernoulli beams. The continuity and boundary conditions are satisfied between adjoining beams. Both the ‘free mode’ and the ‘constrained mode’ assumption in delamination buckling and vibration are used. A parametric study is performed to investigate the influence of the axial compressive load on the natural frequency and the mode shape of the delaminated beam. A monotonic relation between the natural frequency and the compressive load is observed. Comparisons with the analytical results reported for delamination buckling and vibration verify the validity of the present solution.     

Vibrations of multiple delaminated beams

The free vibrations of beams with two enveloping delaminations have been solved analytically without resorting to numerical approximation. The multiple delaminated beam is analyzed as several interconnected Euler–Bernoulli beams. The differential stretching and the bending–extension coupling are considered in the formulation. The influence of the sizes and locations of the delaminations on the primary and secondary frequencies and mode shapes of a beam are investigated. For clamped–clamped beams, the primary frequency shows a high sensitivity for the long delamination but a low sensitivity for the second short delamination, while for the secondary frequency, the sensitivity is high for both delaminations. For cantilever beams, the primary and secondary frequencies show a high sensitivity for the long delamination but low sensitivity for the second short delamination. Results are compared with the analytical and experimental data reported in the literature to verify the validity of the present model.     

Failure of delaminated carbon/epoxy composite beams under cyclic compression

Experimental study of the response of laminated [(45/90/ — 45/0)₆]_s carbon/ epoxy virgin and pre-cracked composite beams to compressive cyclic loading is reported. The development of failure, in the form of delaminations, recorded continuously on video tape during the tests, revealed formation of delaminations close to the external faces of the beam. Some of the delaminations developed instantly and some propagated along the beam in jumps. Total failure occurred when the stress in the central ‘undamaged’ section of the beam reached a critical value. Calculation of the buckling load of unsymmetric laminated beams supports the experimental finding that a pre-crack close to the center of the specimen has no effect on the fatigue behavior of the beam. Prediction of time to first delamination crack, based on previous results, agree with the present experimental observation.     

复合材料梁结构应力波传播特性研究

基于铁木辛柯梁理论,研究含半无限大分层复合材料梁结构中波的反射与透射。考虑表面无接触压力(张开分层)及表面完全接触(闭合分层)两种极端分层条件,对单向复合材料梁建模导出反射与透射矩阵,计算能量反射与透射系数。数值结果表明,能量反射与透射系数同随波频率及分层位置变化,能量传输遵循守恒定律。研究各模态能量分配,描述前两阶弯曲波及第一阶膨胀波间模态转换关系;通过有限元仿真验证该理论分析的正确性。     

埋入光纤Mach-Zehnder干涉仪检测复合材料梁的分层

将光纤Mach-Zehnder干涉仪的传感臂埋入到复合材料梁的中性层来检测梁的分层。不论梁是连续支撑还是简单支撑,均取得了很好的实验结果。通过用榔头连续下压梁,由光纤干涉仪可以得到一条输出曲线,从这条曲线就可以准确判断梁内部是否存在分层,以及分层的位置。     

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。     

Determination of fracture energy and tensile cohesive strength in Mode I delamination of angle-ply laminated composites

The energy release rate in delamination of angle-ply laminated double cantilever composite beam specimens was calculated using the compliance equation, and interlaminar cohesive strengths were obtained. Instead of the traditional approach of a beam on an elastic foundation, a second-order shear-thickness deformation beam theory (SSTDBT) was considered. The equilibrium equations were obtained using the principle of minimum total potential energy and the system of ordinary differential equations were solved analytically. The problem was solved for [0°]₆ , [±30°]₅, and [±45°]₅ laminates with mid-plane delaminations and the results were verified using experimental evidence available in the literature.     

The effect of multiple damage in composite structures: a theoretical investigation

This paper focuses on the problem of damage in composite structures and discusses the theoretical analysis of the effect of multiple damaged composite laminates subject to uniaxial and bi-axial loading. The interaction effect between two 27.5 mm diameter delaminations, with 9.5 mm diameter holes, was studied using a 3-D finite element analysis as a function of damage spacing. The compressive loads required for delamination growth were predicted using a Strain Energy Release Rate approach, viz. T^*-integral. The results indicated that, for the particular layup analysed, the damage interaction can be considerable as the distance between the damage is reduced. The interaction effect appears to substantially increase T^* i.e. reduce the compressive load required for delamination growth, if the row of multiple damage is perpendicular to the applied load. T^* also appears to increase, for all the cases considered, when bi-axial loading is applied.     

Thermal buckling analysis of functionally graded material beams

Buckling of beams made of functionally graded material under various types of thermal loading is considered. The derivation of equations is based on the Euler–Bernoulli beam theory. It is assumed that the mechanical and thermal nonhomogeneous properties of beam vary smoothly by distribution of power law across the thickness of beam. Using the nonlinear strain–displacement relations, equilibrium equations and stability equations of beam are derived. The beam is assumed under three types of thermal loading, namely; uniform temperature rise, nonlinear, and linear temperature distribution through the thickness. Various types of boundary conditions are assumed for the beam with combination of roller, clamped and simply-supported edges. In each case of boundary conditions and loading, a closed form solution for the critical buckling temperature for the beam is presented. The formulations are compared using reduction of results for the functionally graded beams to those of isotropic homogeneous beams given in the literature.     

Vibrations of beams with two overlapping delaminations

Delamination in composite laminates may arise from either imperfect fabrication processes or impact during service. The locations of the delaminations are arbitrary. In this research, an analytical solution to the free vibrations of a beam with two overlapping delaminations is presented. The delaminated beam is analyzed as seven interconnected Euler–Bernoulli beams. The influence of the sizes and the locations of the delaminations on the fundamental frequency and the mode shape of the beam are investigated. Complex vibration behaviors emerge for different sizes and locations of the delaminations. The results based on the present model agree well with the analytical data reported in the literature.     

含矩形内部分层的复合材料圆柱壳块 三维问题的片条合成能量解法

根据叠加原理将含有矩形分层的复合材料圆柱壳块在横向载荷作用下的受力状态进行分解,将分层问题归结为在分层表面受附加剪切载荷作用时附加状态的分析,并据此建立了一个仅包含分层区的力学模型。通过切取纵横切片,利用含分层层合直梁与曲梁的附加位移,构造分层区附加位移模态。最后,应用最小势能原理确定位移幅值的闭合解。     

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.     

Charpy impact damage behaviour of single and multi-delaminated hybrid composite beam structures

The ply delamination which is known as a principle mode of failure of layered composites due to separation along the interfaces of the layers is one of the main concerns in designing of composite material structures. In this regard, the effect of hybrid laminate lay-up with different delamination positions in composite beam was investigated. The Charpy impact test was chosen to study the energy absorbing capability of delaminated composite beam. Hybrid composite beams were fabricated from combination of glass/epoxy and carbon/epoxy composites. It was shown that composite beams with closer position of delamination to impacted surface are able to absorb more energy in comparison with other delamination positions in hybrid and non-hybrid ones. The Charpy impact test of delaminated composite beams was also simulated by finite element software LS-DYNA and the results were verified with the relevant experimental results.     

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。     

多分层对复合材料层合板自振特性的影响

基于Mindlin一阶剪切理论分项等参插值的有限元法, 建立了含多个分层损伤复合材料层合板自由振动分析的有限元模型和分析方法, 并采用线性接触模型模拟分层区域上、 下子板的相互作用。通过典型数值算例, 讨论了分层位置、 数目及板的边界条件诸参数对其振动特性的影响。结果表明: 分层位置沿板长方向变化时, 中间分层的频率变化范围较大, 表面分层变化较小, 但变化趋势基本相同; 沿层合板厚度方向, 多分层中最长分层的位置越靠近层合板中面, 则其对振动特性的影响越大; 多个分层位置较靠近层合板表面, 且板边界条件约束较弱时, 多分层与单分层对振动特性影响的差别不大, 此时, 可将多分层损伤层合板简化为单分层损伤层合板来进行振动分析。      

有任意脱层复合材料梁的非线性动力稳定性

基于弹性理论建立了有脱层复合材料梁的基本方程式，研究了有任意脱层的考虑横向剪切变形的复合材料梁的非线性动力稳定性，对脱层梁进行分区处理，方便地描述了脱层长度，脱层位置，利用振型函数作为位移函数的形函数，采用增量谐波平衡法对基本方程式进行求解，考虑了不同脱层位置和不同脱层长度对脱层梁的非线性动力稳定性的影响，得出了各种情况下的动力不稳定性区域。