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.     

Improving adhesion performance of polyethylene surfaces by cold plasma treatment

In this paper, the effects of low pressure plasma treatment on surface energy of polyethylene samples and on shear properties of adhesive bonded joints based on these substrates have been investigated. In particular, the optimization of two plasma process parameters, exposure time and power input, was studied performing contact angle evaluation and lap-shear tests. The plasma treatment was also compared with a conventional primer treatment, for which it is a clean and effective alternative. As a measure of the durability of both treatments, the bond shear strength immediately after bonding was compared with that after a storage period in the laboratory environment. The experimental results show that the optimized plasma process may remarkably increase wettability properties of polyethylene surfaces and shear strength of bonded joints, even higher than those treated with primer and that these good properties remain quite unchanged even after some days of storage in a laboratory.     

直角结合异材界面端应力强度系数的经验公式

由不同材料结合而成的材料(简称异材或双材料)的力学性能及其可靠性评价是工程中亟待解决的问题。表征界面端奇异应力场大小的应力强度系数是结合异材强度评价的依据，本文针对工程中最常见的直角结合异材，通过对大量不同材料组合的异材的边界元数值分析，提出了界面端应力强度系数的近似计算公式，无量纲化后的应力强度系数的值只与异材Dundurs参数a，卢有关，该公式具有较高的精度，可以作为一般工程上的应力强度系数的计算以及异材结构设计的依据。     

Mixed-mode interface toughness of wafer-level Cu-Cu bonds using asymmetric chevron test

Characterization of interfacial adhesion is critical for the development of wafer bonding processes to manufacture microsystems with high yield and reliability. It is imperative that the test method used in such adhesion studies corresponds to the loading conditions present during processing and operation of the devices. In most applications in which wafers and die are bonded, the interface experiences a combination of shear and normal loading (i.e. mixed-mode loading) with the relative magnitude of the Mode I and II components varying in different scenarios. In the current work, the toughness of Cu-Cu thermocompression bonds, which are of interest for the fabrication of three-dimensional integrated circuits, is analyzed using a bonded chevron specimen with layers of different thickness that allows for the application of interfacial loading with variable mode mixity. The phase angle (a function of the degree of mode mixity at the interface) is varied from 0° to 24° by changing the layer thickness ratio from 1 to 0.48. The Cu-Cu bond toughness increases from 2.68 to 10.1 J/m², as the loading is changed from Mode I (pure tension) to a loading with a phase angle of 24°. The energy of plastic dissipation increases with increasing mode mixity, resulting in the enhanced interface toughness. The Mode I toughness of Cu-Cu bonds is minimally affected by plasticity, and therefore, provides the closest estimate of the interfacial work of fracture under the bonding conditions employed.     

云纹干涉法现场测量技术及其在微电子封装中的应用

本文研制了多功能微观云纹干涉仪系统.该系统可以现场测量电子封装组件热疲劳、热湿耦合、热载荷引起的变形,被应用于电子封装组件的可靠性分析中.由现场云纹干涉技术测得的疲劳寿命与加速热循环实验的结果相吻合.本系统还被应用于铜焊点的断裂行为分析中.实验证明本系统可以测量多层结构材料的应力强度因子、应变能释放率以及位相角.     

The analysis of thermal residual stresses near the apex in bonded dissimilar materials

By employing the complex variable method and constructing the particular solution sequences in the form of complex functions, all the cases of the thermal residual stress field near the apex in dissimilar materials bonded with two arbitrary angles are researched theoretically, and the corresponding classical solutions are obtained. Moreover, the primary paradox, the secondary paradox and even the triple paradox are discovered in the classical solutions and also resolved here, thereby it is confirmed that thermal residual stresses near the apex in bonded dissimilar materials probably possess the singularities of lnr (when the primary paradox occurs) , ln²r (when the secondary paradox occurs) and even ln³r (when the triple paradox occurs) . In addition, the systematic method to solve multiple paradox problems is put forward. © 1999 Elsevier Science Ltd. All rights reserved.     

Analysis of fracture initiation angle in some cracked ceramics using the generalized maximum tangential stress criterion

Brittle fracture in ceramics sometimes occurs under combined opening-sliding (or mixed mode I/II) crack deformation. In this paper, a generalized maximum tangential stress criterion is employed for predicting the fracture initiation angle under mixed mode I/II loading in some brittle ceramics including alumina, zirconia, soda lime glass and three silicon based ceramics. The experimental results reported for the fracture angles in these ceramics have been obtained from fracture tests on the centrally cracked circular disc (often called the Brazilian disc). Very good agreement is shown to exist between the experimental results and the theoretical predictions. According to the fracture model, the mixed mode fracture angle is strongly dependent on the elastic T-stress in the tested ceramics. The negative T-stress that exists in the Brazilian disc specimen can be the main influencing parameter for decreasing the fracture initiation angle in the investigated ceramics.     

FRP-混凝土界面粘结行为的参数影响研究

FRP-混凝土界面的粘结性能对FRP加固混凝土结构力学行为和破坏模式有着重要影响。本文对表征FRP-混凝土界面粘结性能的三个重要参数(界面初始刚度、最大剪应力、界面破坏能)开展研究,通过13个单剪试件的试验考察了混凝土强度、胶层厚度和粘结长度等因素对界面粘结行为的影响,根据试验结果拟合了界面破坏能、最大剪切应力与胶层剪切刚度、混凝土强度之间的函数关系。在试验研究基础上,构建了外贴FRP-混凝土界面粘结的有限元模型。通过有限元分析考察了界面破坏能等三个参数不变的前提下,不同的局部粘结滑移本构关系对界面粘结行为的影响;进而研究了其中一个参数变化时引起的界面粘结性能改变。研究结果表明:界面粘结承载力随着胶层厚度增加而逐渐提高;胶层厚度与界面破坏能成正比,与峰值剪应力成反比;当界面破坏能等三个参数保持不变时,局部粘结滑移本构关系对FRP-混凝土界面粘结性能的影响较小;三个参数中的一个增大时将延缓界面破坏的过程。     

Interaction between stress waves and a growing crack

An experimental investigation is made of interaction between longitudinal and Rayleigh waves and a growing crack. It is shown that stress waves can be used effectively to change the direction of a growing crack and to slow it down. The change in the trajectory of the growth of the crack is due to changes in the state of stress at its apex. The angle of deviation of the crack depends on the angle of attack of the wave and on the state of stress at the apex. An expression is given for determining the angle of deviation of a crack.     

CFRP-混凝土界面粘结的疲劳性能试验研究

外贴FRP是重要的混凝土结构加固技术,但目前对外贴FRP加固混凝土结构的疲劳性能研究尚不充分,尤其对FRP-混凝土粘结界面的疲劳退化规律和破坏模式的研究更为缺乏。本文采用双面剪切试件,通过2个静载试件和4个疲劳试件的试验研究,考察了粘结长度和胶层厚度等因素对FRP-混凝土界面粘结疲劳性能的影响。通过分析沿粘结长度的FRP应变分布在疲劳循环过程中和疲劳后静载过程中的变化情况,讨论了不同粘结长度和粘结胶层厚度条件下的粘结界面疲劳退化规律和疲劳后静载性能。试验结果表明:胶层树脂-混凝土粘结界面是发生疲劳剥离破坏的薄弱环节;胶层厚度增大时,由于疲劳引起的界面损伤累积发展显著减小,疲劳后静载中胶层厚度较大试件的粘结承载力也更大;粘结长度增大时,界面粘结呈现更为明显的损伤退化,但由于试验粘结长度小于有效粘结长度,疲劳后的静粘结承载力仍更大。     

极松软煤层工作面片帮力学机制分析与煤体加固实验研究

针对极松软煤层工作面煤壁片帮控制难题,三维有限差分数值计算表明,极松软煤层开挖后在煤壁底角产生剪应力集中,破坏位置由此沿渐变剪应力带牵引至煤壁顶部,产生卸载松弛浅层坍滑片帮。室内实验结果表明,极松软煤天然含水率极低,自身保水能力严重不足,极易失水。含水率由1.46%提高到3.39%,应变量增高154.32%;含水率4.49%,粘土含量10.00%。与无粘土极松软煤相比,抗压强度提高55.02%,应变提高574.26%。含水率在0~4.03%内,抗剪强度与含水率正相关;含水率在4.03%~12.70%区间,随着含水率的增高,抗剪强度迅速降低。且黏聚力对水的敏感度远大于内摩擦角对含水率的敏感程度,存在某一特定含水率,此时抗剪强度最大。极松软煤层可采用施工扰动方法,使煤层在工作面前方壳基支承压力作用下发生团化固结,达到有效应力增加、孔隙比减小、抗剪强度提高的目的。     

3D printed,bio-inspired prototypes and analytical models for structured suture interfaces with geometrically-tuned deformation and failure behavior

Geometrically structured interfaces in nature possess enhanced, and often surprising, mechanical properties, and provide inspiration for materials design. This paper investigates the mechanics of deformation and failure mechanisms of suture interface designs through analytical models and experiments on 3D printed polymer physical prototypes. Suture waveforms with generalized trapezoidal geometries (trapezoidal, rectangular, anti-trapezoidal, and triangular) are studied and characterized by several important geometric parameters: the presence or absence of a bonded tip region, the tip angle, and the geometry. It is shown that a wide range (in some cases as great as an order of magnitude) in stiffness, strength, and toughness is achievable dependent on tip bonding, tip angle, and geometry. Suture interfaces with a bonded tip region exhibit a higher initial stiffness due to the greater load bearing by the skeletal teeth, a double peak in the stress–strain curve corresponding to the failure of the bonded tip and the failure of the slanted interface region or tooth, respectively, and an additional failure and toughening mechanism due to the failure of the bonded tip. Anti-trapezoidal geometries promote the greatest amplification of properties for suture interfaces with a bonded tip due the large tip interface area. The tip angle and geometry govern the stress distributions in the teeth and the ratio of normal to shear stresses in the interfacial layers, which together determine the failure mechanism of the interface and/or the teeth. Rectangular suture interfaces fail by simple shearing of the interfaces. Trapezoidal and triangular suture interfaces fail by a combination of shear and tensile normal stresses in the interface, leading to plastic deformation, cavitation events, and subsequent stretching of interface ligaments with mostly elastic deformation in the teeth. Anti-trapezoidal suture interfaces with small tip angles have high stress concentrations in the teeth and fail catastrophically by tooth failure, whereas larger tip angles exhibit a shear failure of the interfaces. Therefore, larger tip angles and trapezoidal or triangular geometries promote graceful failure, and smaller tip angles and anti-trapezoidal geometries promote more brittle-like failure. This dependence is reminiscent of biological systems, which exhibit a range of failure behaviors with limited materials and varied geometry. Triangular geometries uniquely exhibit uniform stress distributions in its teeth and promote the greatest amplification of mechanical properties. In both the bonded and unbonded cases, the predictions from the presented analytical models and experimental results on 3D printed prototypes show excellent agreement. This validates the analytical models and allows for the models to be used as a tool for the design of new materials and interfaces with tailored mechanical behavior.     

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.     

Stress-function variational method for interfacial stress analysis of adhesively bonded joints

High interfacial stresses at the free edges of adherends are responsible for the debonding failure of adhesively bonded joints (ABJs). In this paper, a general stress-function variational method is formulated to determinate the interfacial shear and normal (peeling) stresses in ABJs in high accuracy. By extending authors’ prior work in stress analysis of bonded joints (Wu and Jenson, 2011), all the planar stress components in the adherends and adhesive layer of an ABJ are expressed in terms of four unknown interfacial stress functions, which are introduced at the upper and lower surfaces of the adhesive layer. A set of governing ordinary differential equations (ODEs) of the four interfacial stress functions is obtained via minimizing the complimentary strain energy of the ABJ, which is further solved by using eigenfunctions. The obtained semi-analytic stress field can satisfy all the traction boundary conditions (BCs) of the ABJ, especially the stress continuity across the bonding lines and the shear-free condition at the ends of adherends and adhesive layer. As an example, the stress field in an adhesively single-sided strap joint is determined by the present method, whose numerical accuracy and reliability are validated by finite element method (FEM) and compared to existing models in the literature. Parameter studies are performed to examine the dependencies of the interfacial stresses of the exemplified ABJ upon the geometries, moduli and temperature change of the adherends and adhesive layer, respectively. The present method is applicable for scaling analysis of joint strength, optimal design of ABJs, etc.     

A simple continuum damage model for adhesively bonded butt joints

The present work is concerned with the study of the damage behavior of adhesive joints consisting of an epoxy adhesive layer bonding aluminium alloy substrates. A model for butt joints, developed within the framework of Continuum Damage Mechanics, that accounts for the effect of the thickness of the adhesive layer on the strength of the system is proposed and analyzed. The predicted values of rupture stress for different values of the thickness of the adhesive layer are compared with experimental data, showing a good agreement.     

Effects of adhesive thickness on global and local Mode-I interfacial fracture of bonded joints

The interfacial fracture of adhesively bonded structures is a critical issue for the extensive applications to a variety of modern industries. In the recent two decades, cohesive zone models (CZMs) have been receiving intensive attentions for fracture problems of adhesively bonded joints. Numerous global tests have been conducted to measure the interfacial toughness of adhesive joints. Limited local tests have also been conducted to determine the interface traction-separation laws in adhesive joints. However, very few studies focused on the local test of effects of adhesive thickness on the interfacial traction-separation laws. Interfacial toughness and interfacial strength, as two critical parameters in an interfacial traction-separation law, have important effect on the fracture behaviors of bonded joints. In this work, the global and local tests are employed to investigate the effect of adhesive thickness on interfacial energy release rate, interfacial strength, and shapes of the interfacial traction-separation laws. Basically, the measured laws in this work reflect the equivalent and lumped interfacial fracture behaviors which include the cohesive fracture, damage and plasticity. The experimentally determined interfacial traction-separation laws may provide valuable baseline data for the parameter calibrations in numerical models. The current experimental results may also facilitate the understanding of adhesive thickness-dependent interface fracture of bonded joints.     

Singular stress field near the edge of interface of bonded dissimilar materials with an interlayer

For bonded dissimilar materials, the free-edge stress singularity usually prevails near the intersection of the free-surface and the interface. When two materials are bonded by using an adhesive, an interlayer develops between the two bonded materials. When a ceramic and a metal are bonded, the residual stress develops because of difference in the coefficient of thermal expansion. An interlayer may be inserted between the two materials to defuse the residual stress. Stress field near the intersection of the interface and free-surface in the presence of the interlayer is then very important for evaluating the strength of bonded dissimilar materials.In this study, stress distributions on the interface of bonded dissimilar materials with an interlayer were calculated by using the boundary element method to investigate the effect of the interlayer on the stress distribution. The relation between the free-edge singular stress fields of bonded dissimilar materials with and without an interlayer was investigated numerically. It was found that the influence of the interlayer on the stress distributions was confined within a small area of the order of interlayer thickness around the intersection of the interface and the free-surface when the interlayer was very thin. The stress distribution near the intersection of the interface and the free-surface was controlled by the free-edge stress singularity of the bonded dissimilar materials without the interlayer. In this case, the interlayer can be called free-edge singularity-controlled interlayer. If a stress distribution on the interface is known for one thickness of an interlayer h, stress distributions on the interface for other values of h can be estimated.     

Water discharge over a dam

A solution is given for a problem of plane steady motion of a heavy ideal incompressible liquid which is partially bounded from below by two planes positioned at an angle of ±30° to the horizontal. The problem may be interpreted as water discharge over a dam in the form of a wedge with apex angle 120°. The so-called fixed-weir rockfill dams have a profile similar to the one considered here [1]. The flow discharge coefficient, which is very close to the experimental value, is calculated for the dam in question.     

长杆弹撞击装甲陶瓷界面击溃/侵彻特性

界面击溃/驻留效应可以有效提高装甲陶瓷的抗侵彻能力。为研究长杆弹撞击装甲陶瓷界面击溃及侵彻特性,开展了长杆弹撞击装甲陶瓷实验研究。同时,基于裂纹扩展理论建立了考虑界面击溃/驻留效应的长杆弹侵彻装甲陶瓷计算模型,以定量描述界面击溃/驻留效应对装甲陶瓷抗侵彻性能的影响。不同弹靶条件下的界面击溃/侵彻转变速度、界面驻留时间、侵彻速度与侵彻深度的理论计算值与实验结果具有较好的一致性,表明计算模型可靠。在此基础上,分析了弹体及陶瓷材料对界面击溃/驻留及侵彻过程的影响规律。研究结果表明:随着弹体撞击速度的提高,陶瓷表面由界面击溃向侵彻转变。考虑界面击溃/驻留效应的长杆弹侵彻装甲陶瓷理论模型,可以较好地反映不同弹体撞击速度对应的弹靶作用模式。弹体材料的屈服强度和密度越高,界面驻留时间越短,弹体侵彻靶体的能力越强;陶瓷的屈服强度越高,界面击溃/驻留效应越显著,靶体的抗侵彻能力越强。考虑界面击溃/驻留效应的长杆弹侵彻装甲陶瓷理论模型揭示了部分界面击溃作用机理,可为陶瓷复合靶的设计提供参考。     

复合材料胶接结构有限元分析方法研究进展

胶接结构的强度分析方法可以分为解析法和数值法两类,数值法主要是有限元方法.本文综述了复合材料胶接结构的有限元分析方法,按照胶接结构有限元模型建立的物理机理,将胶接结构力学分析模型分为基于有限元应力分析模型、基于断裂力学模型和基于损伤力学模型3类.详细介绍了这3类模型中的主要有限元建模分析方法:三维应力分析方法、虚拟裂纹闭合技术方法和内聚力模型方法,介绍了每种方法的基本思想、适用范围、优缺点、改进和扩展、有限元建模的实施步骤,以及有限元分析中应用该方法所取得的成果.第五部分从适用范围、应力奇异和破坏判据3个方面对这几种分析模型进行了对比分析.最后,对该领域发展趋势进行了展望.