Stress analysis of adhesively bonded sandwich pipe joints subjected to torsional loading

Composite pipes are becoming popular in the offshore oil and gas industry. These pipes are connected to one-another by various configurations of joints. The joints are usually the weakest link in the system. In this investigation we examine the response of various joint configurations subjected to torsion, one of the most common loading conditions in piping systems. Specifically, the theoretical analysis used to evaluate the stress field in the adhesive layers of tubular and socket type bonded sandwich lap joints is presented here. The two adherends of the joints may have different thickness and materials, and the adhesive layer may be flexible or brittle. The analysis is based on the general composite shell theory. The stress concentrations at and near the end of the joints as functions of various parameters, such as the overlap length, and thickness of the adhesive layer are studied. The effects of different adherend thickness ratios, adhesive thickness and overlap length are also studied. Results obtained from the proposed analytical solutions agree well with the results obtained from finite element analysis and those obtained by other workers.     

Bonded lap joints of composite laminates with tapered edges

This study presents a semi-analytical solution method to analyze the geometrically nonlinear response of bonded composite lap joints with tapered and/or non tapered adherend edges under uniaxial tension. The solution method provides the transverse shear and normal stresses in the adhesives and in-plane stress resultants and bending moments in the adherends. The method utilizes the principle of virtual work in conjunction with von Karman’s nonlinear plate theory to model the adherends and the shear lag model to represent the kinematics of the thin adhesive layers between the adherends. Furthermore, the method accounts for the bilinear elastic material behavior of the adhesive while maintaining a linear stress–strain relationship in the adherends. In order to account for the stiffness changes due to thickness variation of the adherends along the tapered edges, the in-plane and bending stiffness matrices of the adherents are varied as a function of thickness along the tapered region. The combination of these complexities results in a system of nonlinear governing equilibrium equations. This approach represents a computationally efficient alternative to finite element method. The numerical results present the effects of taper angle, adherend overlap length, and the bilinear adhesive material on the stress fields in the adherends, as well as the adhesives of a single- and double-lap joint.     

A three-parameter elastic foundation model for interface stresses in curved beams externally strengthened by a thin FRP plate

Externally bonding of fiber reinforced polymer (FRP) plates or sheets has become a popular method for strengthening reinforced concrete structures. Stresses along the FRP–concrete interface are of great importance to the effectiveness of this type of strengthening because high stress concentration along the FRP–concrete interface can lead to the FRP debonding from the concrete beam. In this study, we develop an analytical solution of interface stresses in a curved structural beam bonded with a thin plate. A novel three-parameter elastic foundation model is used to describe the behavior of the adhesive layer. This adhesive layer model is an extension of the two-parameter elastic foundation commonly used in existing studies. It assumes that the shear stress in the adhesive layer is constant through the thickness, and the interface normal stresses along two concrete/adhesive and adhesive/FRP interfaces are different. Closed-form solutions are obtained for these two interfacial normal stresses, shear stress within the adhesive layer, and beam forces. The validation of these solutions is confirmed by finite element analysis.     

Hamiltonian parametric element and semi-analytical solution for smart laminated plates

Based on the Hellinger-Reissner (H-R) mixed variational principle for piezoelectric material, a unified 4-node Hamiltonian isoparametric element of anisotropy piezoelectric material is established. A new semi-analytical solution for the natural vibration of smart laminated plates and the transient response of the laminated cantilever with piezoelectric patch is presented. The major steps of mathematical model are as follows: the piezoelectric layer and host layer of laminated plate are considered as unattached three-dimensional bodies and discretized by the Hamiltonian isoparametric elements. The control equation of whole structure is derived by considering the compatibility of generalized displacements and generalized stresses on the interface between layers. There is no restriction for the side-face geometrical boundaries, the thickness and the number of layers of plate by the use of the present isoparametric element. Present method has wide application area.     

An investigation into the stresses in double-lap adhesive joints with laminated composite adherends

The mechanics of double-lap joints with unidirectional ([0₁₆]) and quasi-isotropic ([0/90/?45/45]_2S) composite adherends under tensile loading are investigated experimentally using moiré interferometry, numerically with a finite element method and analytically through a one-dimensional closed-form solution. Full-field moiré interferometry was employed to determine in-plane deformations of the edge surface of the joint overlaps. A linear-elastic two-dimensional finite element model was developed for comparison with the experimental results and to provide deformation and stress distributions for the joints. Shear-lag solutions, with and without the inclusion of shear deformations of the adherend, were applied to the prediction of the adhesive shear stress distributions. These stress distributions and mechanics of the joints are discussed in detail using the results obtained from experimental, numerical and theoretical analyses.     

On flaw size and distribution in lap joints

By using adhesive as the bonding substance between metals or polymeric materials, simple structural joints can be made to bear relatively high loads. Applications have increasingly been made in substituting adhesive joints for conventional mechanical fastenings, especially in the aircraft and aerospace industries where weight is a predominant factor. In order to design a most effective adhesive-bonded joint, an understanding of the stress distribution along the joint is as important as the physical properties of the bonding agent. One of the most common and widely used adhesive joints is the single lap joint.Recent investigations using various analytical models have revealed that the cause of failure in an idealized ‘defect free’ lap joint is primarily due to the localized effect of high stress concentration at the lap ends. With the presence of flaw like defects in the adhesive layer, the load transfer from adherend to adhesive is expected to be different from the idealized joint. In addition, localized stress concentrations induced by irregular adhesive defects that may be found in practical engineering applications can further reduce fracture strength of such an imperfect joint.This paper is intended to describe an investigation into the effect of internal adhesive flaw size and distribution on the fracture behaviour of adhesive-bonded lap joints. The finite element method is used to gain a quantitative understanding of the localized shear stress distributions due to the presence of the internal flaws along the bonding layer. It is observed that the reduction in the fracture strength is relatively small when a flaw is located in the central portion of the bonding length. However, a flaw located near the lap ends of the adhesive joint can cause marked reduction in the fracture strength, due to its interaction with the high stress concentration at the lap ends.     

Energy release rate and phase angle of delamination in sandwich beams and symmetric adhesively bonded joints

Delamination in sandwich structures along the interface between the face sheet and the core, or along the adherend/adhesive interface in adhesively bonded joints, is one of the most common failure modes of this type of tri-layer structure. This delamination is usually modeled as an interface crack problem, for which the energy release rate and phase angle can be calculated using interface fracture mechanics solutions. Existing interface fracture mechanics solutions, however, ignore the effect of transverse shear deformation, which can be significant for short crack. In an effort to overcome this shortcoming, this study presents new analytical solutions for the energy release rate and for the phase angle of the interface crack in sandwich structures or adhesively bonded joints. Since the new solutions incorporate relative rotation at the tip of the delamination, transverse shear effects are taken into account in this study. Typical delaminated sandwich and adhesively bonded joint specimens are analyzed by using the new solutions, as well as by the existing solutions. The energy release rate predicted by the present model agrees very well with that predicted by FEA, and furthermore it is considerably more accurate relative to existing models. As the existing model neglects the transverse shear force, it underestimates the total energy release rate. A stress field analysis is also conducted in this study in order to clarify some misunderstandings in the literature on the determination of the phase angle of adhesively bonded joints using an interface stress-based method.     

Finite Fracture Mechanics model for mixed mode fracture in adhesive joints

Up to now the failure load assessment of bonded joints is still not fully understood. This work provides a new approach for assessing the crack initiation load of bonded joints. A failure model for single lap joints is proposed that is based on Finite Fracture Mechanics. Only two basic fracture parameters are required: the tensile strength and the fracture toughness of the adhesive. A coupled stress and energy criterion proposed in 2002 by Leguillon is used to model crack initiation in the adhesive layer. The theory of this criterion is outlined in detail, its relationship to other failure criteria is discussed and an overview of applications found in literature is given. An enhanced weak interface model that predicts a linear variation of the shear stresses in the adhesive layer is utilized to model the single lap joint. To compare joint designs and to reveal the limitations of the given approach a dimensionless brittleness number for mixed-mode loading is proposed. Along with a detailed discussion of the results for exemplary joint designs a comparison to experimental results from literature is performed. The two necessary fracture parameters are each taken from standard test results published in literature. A good agreement of the failure load predictions with the experimental results is observed. A remarkable outcome is that the presented failure model renders the adhesive thickness effect correctly. The paper concludes with a discussion of the limitations of the approach and the effect of material parameters.     

胶接体系的胶接强度、粘结能及损伤破坏研究

胶接是指一种用粘合剂实现连接和固持的方法,胶接形式的金属薄板在汽车工业,建筑业以及航空航天领域有着广泛的应用.论文采用有限元模拟方法,研究了该胶接体系在受载状态下的滑剪破坏行为,重点关注了胶层粘结能,搭接长度,胶层厚度对胶接接头承载能力的影响,同时初步探讨了胶层的界面损伤情况.胶层粘结能的提高能够显著提高接头的承载能力.此承载能力受搭接长度和胶层粘结能的共同影响,较大的粘结能情况下,提高搭接长度能够显著提高接头的承载能力.胶层厚度对接头的承载能力也存在影响,在论文考虑的厚度范围内,提高厚度能够增强接头的承载能力.最后初步考虑了接头在达到载荷峰值时刻的胶层损伤情况.     

基于Layerwise离散层理论的复合材料夹层板屈曲分析

复合材料夹层结构由于面板和芯层力学特性差异较大,屈曲分析时要分层考虑各层的剪切变形。基于Reddy的Layerwise离散层理论,假设每一层变形服从一阶剪切变形理论,在统一的位移场描述下,推导建立了一种用于复合材料夹层结构屈曲分析的四节点四边形板单元,并采用混合插值方法对单元的剪切锁定进行了修正。分别对三种典型的夹层板结构进行线性屈曲有限元分析,并将计算结果与文献中已有结果进行了对比。结果表明：本文的分析方法能离散考虑各层的力学特性,将结构离散为多层时,计算结果与三维弹性理论或高阶板理论吻合;将结构等效为单层时,计算结果与基于一阶剪切变形理论的文献结构吻合,验证了单元的有效性。     

The strain energy release rates in adhesively bonded balanced and unbalanced specimens and lap joints

An analytical model is developed to determine the strain energy release rate in adhesive joints of various configurations such as the double-cantilever beam and single-lap joints. The model is based on asymptotic analysis of adhesive layer stresses and Irwin’s crack closure integral. Closed-form solutions are presented for balanced and unbalanced joints under mode I, II and mixed-mode I/II that take into account the influence of the shear force on the adhesive stresses, and its influence on the strain energy release rate. The accuracy of the model is tested against the classical beam theory expressions for double-cantilever beam and end-notch flexure specimens. In fact, classical beam theory’s expressions are found to be the lower bound of the proposed model solutions, and the two methods converge as the adhesive layer thickness decreases. Analysis of single-lap joints reveals the influence of edge shear forces on the total strain energy release rate, and more importantly on the ratio between modes I and II. Results from the proposed analytical model are in good agreement with finite element results and with analytical models found in the literature.     

Peeling experiments of ductile thin films along ceramic substrates – Critical assessment of analytical models

Two types of peeling experiments are performed in the present research. One is for the Al film/Al₂O₃ substrate system with an adhesive layer between the film and the substrate. The other one is for the Cu film/Al₂O₃ substrate system without adhesive layer between the film and the substrate, and the Cu films are electroplated onto the Al₂O₃ substrates. For the case with adhesive layer, two kinds of adhesives are selected, which are all the mixtures of epoxy and polyimide with mass ratios 1:1.5 and 1:1, respectively. The relationships between energy release rate, the film thickness and the adhesive layer thickness are measured during the steady-state peeling process. The effects of the adhesive layer on the energy release rate are analyzed. Using the experimental results, several analytical criteria for the steady-state peeling based on the bending model and on the two-dimensional finite element analysis model are critically assessed. Through assessment of analytical models, we find that the cohesive zone criterion based on the beam bend model is suitable for a weak interface strength case and it describes a macroscale fracture process zone case, while the two-dimensional finite element model is effective to both the strong interface and weak interface, and it describes a small-scale fracture process zone case.     

基于高斯过程回归的有限元应力解的改善研究

本文应用高斯过程回归方法对有限元应力解进行了改善研究．考题是一简化为平面应力问题的各向同性且受均布载荷的等截面悬臂深梁，应力考察量取Mises 应力，高斯积分点为样本点，单元角结点为改善点．4结点单元有限元模型和8 结点单元有限元模型的计算结果表明：(1)改善点的总体误差比样本点的总体误差都小，且4 结点明显、8 结点不明显；(2)边界结点的改善效果均较传统整体应力修匀的效果显著；(3)改善点应力具有置信区间；(4)较传统分片应力修匀方法，高斯过程回归方法可将所选取区域内的所有角结点的应力同时给予改善，且边界角结点改善效果好．     

组合杂交法与ANSYS软件计算精度比较研究

为探索8节点六面体组合杂交元方法(CHH(0-1))的计算效率和精度, 并正确认识ANSYS 软件计算结果的可靠性, 本文以板弯曲模型为例, 分别用CHH(0-1)元、ANSYS软件中的8节 点brick元、20节点brick元对该模型进行求解．经过对位移及应力计算结果的比较分析, 得知ANSYS软件中的8节点brick元实际是Wilson brick元, 当网格规则时位移计算结果可靠, 但应力计算结果精度差, 20节点brick元计算 非常耗时, 应力计算精度也不高, 而CHH(0-1)元用较少的计算量便可得到高精度的位移、应 力计算结果．     

Analytical solutions for adhesive composite joints considering large deflection and transverse shear deformation in adherends

This paper presents a novel formulation and analytical solutions for adhesively bonded composite single lap joints by taking into account the transverse shear deformation and large deflection in adherends. On the basis of geometrically nonlinear analysis for infinitesimal elements of adherends and adhesive, the equilibrium equations of adherends are formulated. By using the Timoshenko beam theory, the governing differential equations are expressed in terms of the adherend displacements and then analytically solved for the force boundary conditions prescribed at both overlap ends. The obtained solutions are applied to single lap joints, whose adherends can be isotropic adherends or composite laminates with symmetrical lay-ups. A new formula for adhesive peel stress is obtained, and it can accurately predict peel stress in the bondline. The closed-form analytical solutions are then simplified for the purpose of practical applications, and a new simple expression for the edge moment factor is developed. The numerical results predicted by the present full and simplified solutions are compared with those calculated by geometrically nonlinear finite element analysis using MSC/NASTRAN. The agreement noted validates the present novel formulation and solutions for adhesively bonded composite joints. The simplified shear and peel stresses at the overlap ends are used to derive energy release rates. The present predictions for the failure load of single lap joints are compared with those available in the literature.     

FRP加固梁的FRP-混凝土界面脱胶分析

为了研究纤维增强聚合物(fiber reinforced polymer, FRP) 加固梁的FRP-混凝土界面脱胶破坏过程,本文将混凝土梁和FRP 板均视为线弹性的欧拉-伯努利梁(Euler-Bernoulli beams), 且两者通过粘结层胶结在一起. 对于FRP-混凝土结构,有两种形式的脱胶破坏：板端脱胶破坏和跨中裂缝导致的脱胶破坏.对于FRP-混凝土梁,利用合理的粘结模型按第2 种脱胶失效形式,详细讨论了FRP-混凝土界面的脱胶过程,得到了不同阶段的胶结滑移、界面剪应力和FRP 轴向力的解析解. 实验研究验证了理论分析的结果,参数研究进一步探讨了胶结长度和粘结层厚度对于FRP-混凝土界面脱胶行为的影响.     

Triangular elements for Reissner-Mindlin plate

I-IntroductionInrecentyearsmuchresearchefforthasbeenspentonthedevel0pmentofreliableandefficientplateelementsbasedonReissner-Mindlintheory.Adifficultyisthelockingbehaviorexhibitedasl- 0(tisthethicknessoftheplate)forlowerorderc'elements.BasedonTaylorexpendi…     

轴向运动二维传输结构动力学有限元建模与仿真

基于物理中面概念和经典薄板理论,应用有限元法研究了机械工程中的二维传输结构作轴向运动时的面外自由振动特性．根据实际工程结构特点及设计要点,考虑受双向预张应力作用的传输薄板结构模型,由哈密顿原理出发严格导出了结构的有限元动力学方程,得到了体现轴向传输结构特性的陀螺矩阵．该矩阵具有反对称结构,这与加权余量法所得的陀螺矩阵结构不同．采用3 节点三角形单元离散求解域,且单元不受轴向运动影响,给出了单元密度对计算结果精度的影响．分析了传输结构预张应力和轴向速度与自由振动固有频率的关系;考察了不同结构的陀螺矩阵对数值结果的影响．将部分结果与ANSYS 软件模拟对比,显示出良好的一致性,证明了本文方法的有效性．研究结果可为典型传输带等结构的振动控制提供参考,建模方法可为ANSYS等计算软件添加轴向运动结构新模块提供理论依据．