A stress singularity approach to failure initiation in a bonded joint with varying bondline thickness

The stress singularity at the theoretical point of maximum stress in an uncracked single lap joint is analysed by a finite element method. By treating the interface corner of a bonded joint (between adherend and adhesive) as a perfectly bonded wedge and using a fracture mechanics method, considerable advantages over other continuum mechanics approaches for investigating the bondline thickness effect on joint strength are shown. This study has essentially two aims: (i) determination of the strength of the singularity by finite element analysis and comparison with the analytical prediction of Bogy for varying bondline thickness; and (ii) determination of stress intensity factors for varying bondline thickness. Good agreement is shown between the numerically-calculated strength of the singularity with the analytical value obtained from Bogy. The calculated stress intensity, after an initial decrease in the low bondline thickness range, is found to increase with increasing bondline thickness. This agrees well with the trends predicted by experiments.     

Evaluation of Fatigue Damage in Adhesive Bonding: Part 2: Single Lap Joint

The damage parameters for crack initiation in a single lap joint (SLJ) are determined by combining continuous damage mechanics, finite element analysis (FEA) and experimental fatigue data. Even though a SLJ has a simple configuration, the stresses in the adhesive region are quite complex and exhibit multi-axial states. Such a condition leads to the need to introduce a general value for the triaxiality function in the damage evolution law rather than using a triaxiality function which equals unity, as in the case of a uni-axial stress state, e.g., the bulk adhesive test specimen presented in Part 1 of this paper. The effect of stress singularity, due to the presence of corners at edges, also contributes to the complex state of stress and to the variability of the triaxiality function along the adhesive layer in a SLJ. The damage parameters A and β determined in Part 1 for bulk adhesive are now extended to take into account the multi-axial stress state in the adhesive layer, as calculated from FEA.     

Extension of a one-dimensional finite element model program for analysing elastic-plastic stresses and progressive failure of adhesive bonded joints

A program for stress analysis of adhesive bonded joints within an elastic range was extended to consider the elastic-plastic stress state in an adhesive layer and its progressive failure. The program is based on the one dimensional finite element method. The von Mises yield criterion and the Mohr-Coulomb failure criterion are used in the program. Numerical analysis of a single lap joint subjected to four-point bending load was conducted and its result was compared with the experimental result. Good agreements were obtained between both results except for the final failure load. The present extension has some advantages. The stress singularity in the adhesive layer at the lap end or crack tip can be avoided due to the simple assumption for adhesive strains. Shorter computing time by the present method than by other general two- or three-dimensional finite element model programs should be much emphasized as one of the advantages.     

Finite-element and boundary-element analysis of craze micromechanics

The two numerical methods are used to estimate craze surface displacements and stresses for both isolated crazes and crazes at crack tips. The results are compared with the predictions of craze micromechanics models. The investigation includes the computation of the craze surface stress profile required to maintain a given craze opening displacement profile. The boundary element program requires less computer time than the finite element one, and similar results are obtained. The analysis also considers the craze surface displacement profile corresponding to an assumed craze surface stress distribution. The element methods produce results which are approximately the same as those obtained using the model of Verheulpen-Heymans and Bauwens.     

Single Lap Joints with Rounded Adherend Corners: Stress and Strain Analysis

One of the major difficulties in designing adhesive lap joints is the stress singularity present at the adherend corners at the ends of the overlap. One way to overcome this problem is to assume that the corners have a certain degree of rounding. The objective of the present study was to better understand the effect of the change in the geometry of the adherend corners on the stress distribution and, therefore, on the joint strength. Various degrees of rounding were studied and two different types of adhesives were used, one very brittle and another which could sustain a large plastic deformation. The study gives a detailed stress and strain distribution around the rounded adherends using the finite element method. The major finding is that the stresses or strains in the adhesive layer of a joint with rounded adherend corners are finite. In real joints, adherends generally have small rounded corners. Consequently, the model with small radius corners may be used to represent real adherends.     

A two-dimensional stress analysis of single-lap adhesive joints subjected to external bending moments

The stress distributions in single-lap adhesive joints of similar adherends subjected to external bending moments have been analyzed as a three-body contact problem using a two-dimensional theory of elasticity (plain strain state). In the analysis, both adherends and the adhesive were replaced by finite strips. In the numerical calculations, the effects of the ratio of Young's moduli of the adherends to that of the adhesive and the adhesive thickness on the stress distribution at the interfaces were examined. It was found that the stress singularity occurs at the edges of the interfaces and that the peel stress at the edges of the interfaces increases with decreasing Young's modulus of the adherends. It was noticed that the singular stress decreases at the edges of the interfaces as the adherend thickness increases. In addition, photoelastic experiments and FEM (finite element method) calculations were carried out and fairly good agreement was found between the analytical and the experimental results.     

Effects of imperfect adhesion on thermal micro-residual stresses in polymer matrix composites

This paper investigates the influences of imperfect bonding between the fiber and matrix on thermal micro-residual stress fields in polymer matrix composites. For this purpose, a representative volume element consisting of a three-phase composite material subjected to a uniform temperature change is considered. Based on the energy method, a three-dimensional closed-form solution for micro-residual stresses is obtained. Besides, a finite element model is developed and the results are compared with the analytical solution. Both the energy method and finite element analysis show similar trend for thermal stress distribution along the fiber length, while due to the stress singularity, the interfacial shear stress from the finite element solution cannot satisfy the stress-free condition at the fiber end. The analysis shows that the magnitude of thermal stresses and their distribution mainly depend on the bonding efficiency parameter. An increase in thermal and elastic properties bonding efficiencies leads to a considerable decrease in composite axial and shear residual stresses, while the Poisson's ratio bonding efficiency does not affect the thermal stress fields. The interfacial radial residual stress distribution is approximately independent of the bonding conditions. Inefficient bonding may result in higher residual stresses in comparison with the perfect bonding condition. It means that in cases of low bonding efficiency conditions, the ability of composites to sustain and transmit load decreases drastically. Thermal stress concentration occurs at the vicinity of the fiber ends, although peak values depend on the bonding efficiency value.     

Finite element analysis of mass transport through a viscous fluid with reaction

A finite element analysis is developed for transport of a chemical species through a viscous fluid with reaction at a solid boundary. In particular, we examine the relative effect of diffusion, convection and reaction on the quantity of mass transported through the fluid and reacting at the boundary. Numerical comparison studies with a global collocation approximation for a convection-dominated transport problem are given and mesh refinement studies performed to assess the effect of an entry singularity. A quantitative measure of the effectiveness of the reaction is derived using the asymptotic downstream solution. Finally, we consider the influence of a non-uniform fluid-solid interface on the transport process, examining the enhancement or depression of the reaction rate at corners.     

On the use of fracture mechanics in designing a single lap adhesive joint

The design of adhesively bonded joints is a quite difficult task, due to the stress singularity that arises at the edges of the adhesive adjacent to the loaded substrate. This stress singularity makes any design approach based on elastic stress analysis inconvenient. A more convenient design tool for an adhesive joint should be based on its mode of failure. Most of the adhesive joints fail at the adhesive/adherend interface or very close to it in the adhesive layer. Therefore, a fracture theory such as linear elastic fracture mechanics (LEFM) can be used to analyse the failure of an adhesive joint. In this paper, the design of a single lap joint using a fracture mechanics parameter, i.e. the strain energy release rate (SERR), is discussed. The SERR is extracted from a finite element model using Irwin's virtual crack closure integral. A design equation relating the lap length to the adherend thickness through some design parameters is derived.     

A Two-dimensional Stress Analysis and Strength of Single-lap Adhesive Joints of Dissimilar Adherends Subjected to External Bending Moments

The stress distributions of single-lap adhesive joints of dissimilar adherends subjected to external bending moments are analyzed as a three-body contact problem by using a two-dimensional theory of elasticity (plane strain). In the analysis, dissimilar adherends and an adhesive are replaced by finite strips. In the numerical calculations, the effects of the ratio of Young's moduli of adherends, the adherend thickness ratio and the adherend length ratio between dissimilar adherends on the stress distributions at the interfaces are examined. The results show that the stress singularity occurs at the ends of the interfaces, and its intensity is greater at the interface of the adherend with smaller Young's modulus. It is also noted that the singular stress is greater at the interface of the thinner adherend. It is found that the effect of the adherend length ratio on the stress singularity at the interfaces is very small. Joint strength is predicted by using the interface stress and it was measured by experiments. From the analysis and the experiments, it is found that the joint strength increases as Young's modulus of adherends and the adherend thickness increase while the effect of the adherend lengths on the joint strength is small. For verification of the analysis, a finite element analysis (FEA) is carried out. A fairly good agreement of the interface stress distribution is seen between the analytical and the FEA results.     

Experimental Study of Fracture of Glass:I, The Fracture Process

A concept of fracture is developed from experimental data. Fractures are found to originate at flaws or cracks of finite size, most of which are at the surface. The mechanism is one of crack propagation which begins when the local stress at the crack exceeds a minimum value. The rate of propagation increases with crack growth until a critical stress is reached at the crack tip which coincides with a limiting crack velocity. This limiting condition is identified with the boundary of the mirror surface of the fracture. From calculations to be presented in Part 11, the critical stress is estimated to be several million pounds per square inch.     

Numerical Fracture Analysis of Chevron-Notched Specimens: I, Shear Correction Factor, k

Numerical analyses are developed in both short bar and 4-point bend bar cases to estimate the interlaminar shear correction factor k of chevron-notched specimens with various kinds of geometry. The values of k were calculated by comparing the specimen compliances of Bluhm's slice models with those of finite element models. We elucidated the effect of surface boundary on k and modified the Bluhm's assumption. The modification has a slight influence on compliance, but is substantial when considering the stress intensity factor and elastic stored energy at fracture load. The present results give a basis for further consideration of the fracture behavior of chevron-notched specimens. Part II is a discussion of the stability condition for crack growth of chevron-notched specimens using the present results.     

喷嘴洗涤器弯头开孔结构有限元分析及强度评定

由于弯头开孔结构无法按常规设计方法进行开孔补强计算,故对弯头接管开孔区域建立了三维有限元力学分析模型。利用三维实体模型,真实地模拟了特殊结构的形状、载荷分布、边界条件,计算出最接近真实状况的应力分布情况;根据有限元分析结果,按JB4732-1995《钢制压力容器——分析设计标准》进行了应力强度评定,为详细工程设计提供了弯头开孔补强计算方法。     

A two-dimensional stress analysis of single-lap adhesive joints of dissimilar adherends subjected to tensile loads

Single-lap adhesive joints of dissimilar adherends subjected to tensile loads are analyzed as a three-body contact problem using the two-dimensional theory of elasticity. In the numerical calculations, the effects of Young's modulus ratio between different adherends, the ratio of the adherend thicknesses, the ratio of the adherend lengths, and the adhesive thickness on the contact stress distributions at the interfaces are examined. As a result, it is found that (1) the stress singularity occurs near the edges of the interfaces and it increases at the edge of the interface of an adherend with smaller Young's modulus; (2) the stress singularity increases at the edge of the interface of an adherend with thinner thickness; (3) the singular stresses increase at the edges of the two interfaces as the ratio of the upper adherend length to the lower one decreases; and (4) the singular stresses increase at the edges of the two interfaces as the adhesive thickness decreases when the adhesive is thin enough, and they also increase as the adhesive thickness increases when the adhesive is thick enough. In addition, the singular stresses obtained from the present analysis are compared with those obtained by Bogy. Fairly good agreement is seen between the present analysis and the results from Bogy. Strain measurement and finite element analysis (FEA) were carried out. The analytical results are in fairly good agreement with the measured and the FEA results.     

A Stress Singularity Approach for the Prediction of Fatigue Crack Initiation in Adhesive Bonds. Part 1: Theory

Since crack initiation in adhesive bonds tends to occur near the interface corners where the stress fields are singular, we define a fatigue initiation criterion using stress singularity parameter, Q (a generalized stress intensity factor) and the singular eigenvalue, λ.

Hattori et al., successfully used a generalized stress intensity factor to characterize the static strength of bimaterial interfaces. We show that this criterion is only appropriate for situations in which the adhesive contact angle is no larger than 90° and the modulus ratio (adhesive to adherend) is smaller than 0.1. Fortunately, these conditions are often met in real joints, permitting the use of a single eigenvalue approach. We then extend this criterion to the case of fatigue arising from mechanical, thermal, or hygroscopic cycling.

In preparation for Part 2 (experimental), the special case of an epoxy wedge on a flat aluminum substrate is considered. The singularity is analyzed both analytically and numerically. The scale of the region dominated by the singularity is found to be of the order of 100 μm. The size of the plastically yielded zone near the apex is found to decrease extremely rapidly as the stress intensity factor goes down, thereby increasing the applicability of the method at the low stress levels often encountered in fatigue.     

An experimental and numerical investigation of adhesive bonding strengths of polymer materials

We employed the Iosipescu shear specimens and butt-joint specimens to measure the shear and tensile strengths of five types of adhesive bonds for brittle poly(methyl methacrylate) and Homalite polymers. In order to examine the possible stress singularities due to property mismatch between the adhesives and polymers, and ensure uniform stress distributions along the bonded interfaces, two optical techniques, photoelasticity and coherent gradient sensing, were employed to record full field, in situ fringe patterns until specimens failed. Direct comparison of finite element analysis and experimental stress analysis of Iosipescu shear specimens showed that along the polymer/adhesive/polymer interface, only a very weak stress singularity existed. Consequently, the stress distributions were quite uniform. Butt-joint tensile experiments verified negligible stress singularities and uniform stress distributions along the interface. However, for some shear specimens with strong bonds, the final failure occurred in a tensile mode at the upper edge, rather than a shear failure mode in the gauge section. Hence, only the lower limits of the shear strength rather than the actual magnitude could be measured.     

Analysis and design of adhesively bonded tee joints with a single support plus angled reinforcement

In this study, stress and stiffness analyses of adhesively bonded tee joints with a single support plus angled reinforcement were carried out using the finite element method. It was assumed that the adhesive had linear elastic properties. In actual bonded joints, some amount of adhesive, called the spew fillet, accumulated at the free ends of the adhesive layer; therefore, the presence of the adhesive fillet at the adhesive free ends was taken into account. The tee joints were analysed for two boundary conditions: a rigid base and a flexible base. In addition, each boundary condition was analysed for four loading conditions: tensile, compressive, and two side loadings. The stress analysis showed that both side loading conditions resulted in higher stress levels in the joint region in which the vertical plate and supports are bonded to each other, as well as in the adhesive layer in this region for both rigid and flexible base boundary conditions. In adhesively bonded joints, the joint failure is expected to initiate in the adhesive regions subjected to high stress concentrations; therefore, the peak adhesive stresses were evaluated in these critical regions. In the case of the rigid base, the peak adhesive stresses occurred at the corner of the vertical plate, which was bent at right angles, for the tensile and compressive loading conditions, and in the adhesive fillet at the upper free end of the vertical adhesive layer-vertical support interface for both the left and the right side loading conditions. However, in case of the flexible base, the peak adhesive stresses occurred in the adhesive fillet at the right free end of the horizontal adhesive layer-horizontal support interface for the tensile, compressive, and the right side loading conditions, and in the vertical adhesive fillet at the upper free end of the vertical adhesive layer-vertical support interface for the left side loading condition. Furthermore, the adhesive stresses showed a nonlinear variation in the direction of the adhesive thickness for all boundary and loading conditions. The left side loading condition, among the present loading conditions, which results in the highest adhesive stresses is the most critical loading condition for both boundary conditions. The effects of horizontal and vertical support lengths on the peak adhesive stresses and on the joint stiffness were also investigated and the appropriate support dimensions relative to the plate thickness were determined based on the stress and stiffness analyses.     

带大孔径接管锥壳变径段应力的数值计算和强度分析

针对带有大孔径接管锥壳变径段结构不连续应力和局部应力的计算与强度分析问题,根据其结构特点,选择研究对象,处理边界条件;应用有限元理论和方法,建立数值计算模型;采用ANSYS程序,进行网格划分和数值计算,获得变径段部位详尽的位移场和应力场;在应力分析的基础上,根据分析设计的思想对应力进行分类和强度评定。应力计算结果表明,变径段上多个部位产生了较高的局部应力,强度评价结果表明,锥壳变径段的强度满足要求。     

窗口材料热力耦合模拟

当飞行器以超声速在大气中飞行时,飞行器表面将受到强烈的气动力和气动热的影响,从而使飞行器表面温度升高,外部边界层厚度增加,这对窗口材料提出了严格的要求。为了给窗口材料的气动力和气动热的研究提供理论依据,本文采用有限元分析方法,分别计算了三种窗口材料在超声速飞行时的温度场和应力场分布。通过计算和对比,结果表明,在恒定热通量为1×10⁶ W·m^-2时,多光谱ZnS和蓝宝石窗口材料的最大应力小于材料的许用应力,满足设计要求。     

Stress Distributions in Al2O3 Bicrystal Tensile Specimens

Stress distributions in Al₂O₃ bicrystals were analyzed for certain misorientations across the grain boundary in straight-sided tensile specimens with the grain boundary normal to the tensile axis. Stresses were found using the numerical analysis technique of direct stiffness calculations or by finite element analysis. When the anisotropy in elastic constants of the bicrystals was considered, misorientation of principal axes yielded stress concentrations at the boundary as high as 1.50. The assumption of uniform stress states in bicrystal mechanical response studies, therefore, is not generally accurate.