Increasing single-lap joint strength by adherend curvature-induced residual stresses

Single-lap joint (SLJ) geometry is the most widely used type of adhesive joint geometry. In this joint, peel stresses occur at the overlap ends due to load eccentricity and the presence of shear-free adhesive termination surfaces. These peel stresses, along with the transverse tensile stresses which occur along the overlap longitudinal axes, and adhesive shear stresses, ultimately cause joint failure. Obviously, reductions in these stresses should result in higher joint strength and increased load capacity. To this end, we exploited elastic spring-back capability of (steel) metal adherends by initially forming curved segments of varying arc lengths and radii at overlap ends. These adherends with curved-end sections were then bonded in single-lap configuration, simply by applying sufficient bonding pressure to elastically flatten the curved segments to result in typically flat overlap sections subsequent to adhesive cure and the removal of bonding pressure. Since the elastic adherend overlap ends tend to revert back to their initial curved form, they exert compressive residual stresses on the adhesive layer in the overlap end regions. We determined that the compressive residual stresses induced in this fashion considerably increased the load capacity of SLJs subjected to tension.     

Elastic analysis and engineering design formulae for bonded joints

The general elastic plane strain problem of adhesively bonded structures which consist of two different adherends is considered. To facilitate a truly general approach the adhesive joint is modelled as an adherend-adhesive sandwich with any combination of tensile, shear and moment loading being applied at the ends of both adherends. A full elastic analysis is presented which calculates the adhesive shear and tensile stresses in the overlap region, this analysis has been validated for a range of load cases using a finite element program. Basic design approaches are outlined and explicit expressions are developed which enable the simple evaluation of the stress distributions in the adhesive overlap. Simplified two parameter design formulae are also produced which accurately describe the peak stresses at the ends of the adhesive overlap in both the transverse and longitudinal shear directions. In all of the analyses the adherends are assumed to behave as linear elastic cylindrically bent plates with the adhesive forming an elastic interlayer between them. In the simplified analyses only one component of adhesive stress is considered, while in the full elastic analysis two components of stress are considered with a consequent increase in the complexity of the required solution method, but also an increase in accuracy over the simplified analyses for a wider range of joint configurations.     

Closed-form solutions for elastic stress-strain analysis in unbalanced adhesive single-lap joints considering adherend deformations and bond thickness

A theoretical model is developed for the stress analysis in adhesive-bonded single-lap joints under tension, for which the two adherends could have different thicknesses and consist of different materials. A two-dimensional (2D) elasticity theory is adopted in the analysis, which simultaneously incorporates the complete strain-displacement and the complete stress-strain relationships for the adherends and adhesive. The approach provides a unified treatment for any possible adhesive layer flexibility and capable of satisfying the stress-free condition at the ends of the bondline. An explicit closed-form analytical solution is formulated for upper and lower adherends/adhesive stresses (strains) and tensile, shear and bending loads acting on the adherends along the overlap and then simplified for practical applications, and simple design formulae for adhesive stresses are produced. The results predicted by the present full and simplified solutions were compared with the previously theoretical solution by Bigwood and Crocombe (1989) [35], and the 2D geometrically nonlinear finite element model using MSC/NASTRAN. The agreement validates the present formulation and solutions for unbalanced bonded joints. The effects of the stiffness unbalanced parameters on the adhesive stress distributions were also discussed.     

On the von Mises elastic stress evaluations in the bi-adhesive single-lap joint: a numerical and analytical study

Bi-adhesive joints are an alternative stress-reduction technique for adhesively bonded joints. The joints have two types of adhesives in the overlap region. The stiff adhesive should be located in the middle and the flexible adhesive at the ends. This study is the extension of our previous paper to the von Mises stress evaluation and discusses the values and importance of the von Mises stresses in the bi-adhesive single-lap joint. Both analytical and numerical analyses were performed using three different bi-adhesive bondline configurations. The Zhao’s closed form (analytic) solution used includes the bending moment effect. In the finite element models, overlap surfaces of the adherends and the adhesives were modeled using surface-to-surface contact elements. The contribution levels of the peel and shear stresses for producing a peak von Mises stress are also studied. It is concluded that the contribution level of the shear stress at where von Mises stress becomes peak is more than that of the peel stress. Joint strength analyses were performed based on the peak elastic von Mises stresses. It is seen that joint strength can be increased using bi-adhesive bondline. The analytical and numerical results show that the appropriate bond-length ratio must be used to obtain high joint strength.     

Strength Improvement of Adhesively-Bonded Joints Using a Reverse-Bent Geometry

Adhesive bonding of components has become more efficient in recent years due to the developments in adhesive technology, which has resulted in higher peel and shear strengths, and also in allowable ductility up to failure. As a result, fastening and riveting methods are being progressively replaced by adhesive bonding, allowing a big step towards stronger and lighter unions. However, single-lap bonded joints still generate substantial peel and shear stress concentrations at the overlap edges that can be harmful to the structure, especially when using brittle adhesives that do not allow plasticization in these regions. In this work, a numerical and experimental study is performed to evaluate the feasibility of bending the adherends at the ends of the overlap for the strength improvement of single-lap aluminium joints bonded with a brittle and a ductile adhesive. Different combinations of joint eccentricity were tested, including absence of eccentricity, allowing the optimization of the joint. A Finite Element stress and failure analysis in ABAQUS^® was also carried out to provide a better understanding of the bent configuration. Results showed a major advantage of using the proposed modification for the brittle adhesive, but the joints with the ductile adhesive were not much affected by the bending technique.     

Stress Distribution in Single Lap Joints with a Cracked Composite Adherend—Part II: Laminated Adherends

The effect of a crack in the overlap region of an adhesive single lap joint is studied on the shear stress distribution in adhesive layer. Each adherend is considered to be a laminated composite material with unidirectional fibers aligned in the direction of the applied load. Crack location is selected to be in the top adherend laminate, in the form of cut fibers and matrix bays. The crack can occur in any layer. The shear-lag model is used to derive the equilibrium equations which are then solved by means of eigenvector expansion. The effects of adhesive thickness, crack size, and location in the adherend, total number of layers in each adherends, volume fraction of fibers, and type of fibers are investigated on the shear distribution in the adhesive as well as load distribution in the intact fiber at the crack tip located in the top adherend. The effect of dissimilar laminated adherends is also investigated on the adhesive shear stress distribution. According to the results, in the presence of a crack, the peak shear stress in the adhesive layer and load concentration in the fibers are very susceptible to the adhesive thickness and number of layers in laminated adherends.     

Yield in Adhesive Joints and Design of Zones with Constant Elastic Shear Stresses

Yield in adhesive joints has been investigated by several scientists among whom L. J. Hart-Smith¹ especially is to be mentioned.

In the following, a method is demonstrated which is based on a simple elastic-plastic model. It shows the distribution of stresses in the adhesive and gives a total picture of the development of the length of the yield zones and their strain as a function of load.

Methods are given for the design of adhesive joints with constant elastic shear stresses at their ends or throughout their whole length. These stresses are obtained by varying the thickness of the adherends, the adhesive, or a combination of both. The constant elastic shear stress zones can be designed to take into consideration all known factors as temperature and hardening stresses, moments, etc. The characteristic yield properties as well as internal stresses after yield and unloading are determined together with the modified stress distribution for a new load.     

A Comparison of Numerous Lap Joint Theories for Adhesively Bonded Joints

Numerous authors have investigated the state of stress in the adhesive of adhesively bonded joints. They have made various assumptions concerning the behavior of the adhesive and adherends to yield tractable differential equations which remove the stress singularities which occur at the edges of the bi-material interfaces. By examining several test problems, this paper investigates the effect of these assumptions on predicted adhesive stress. It was found that predicted maximum adhesive shear stress is insensitive to underlying assumptions and that maximum adhesive peel stress is relatively unaffected by most assumptions except that neglecting shear deformation of the adherends can affect results by as much as 30%. Peel stresses from the well known theory of Goland and Reissner which neglects shear deformation of the adherends and makes several inconsistent assumptions vary as much as 30% from stresses from a consistent lap joint theory which considers shear deformation of the adherends. However, in most cases the effects of the inconsistencies cancel the effects of neglecting the shear deformation of the adherends and the variation is less than 15%. This paper points out that finite element analyses of bonded joints where one layer of 4 node isoparametric elements are used to model the adhesive give results very close to those from consistent lap joint theories.     

Single and dual adhesive bond strength analysis of single lap joint between dissimilar adherends

The emerging trends for joining of aircraft structural parts made up of different materials are essential for structural optimization. Adhesively bonded joints are widely used in the aircraft structural constructions for joining of the similar and dissimilar materials. The bond strength mainly depends on the type of adhesive and its properties. Dual adhesive bonded single lap joint concept is preferred where there is large difference in properties of the two dissimilar adherends and demanding environmental conditions. In this work, Araldite-2015 ductile and AV138 brittle adhesives have been used separately between the dissimilar adherends such as, CFRP and aluminium adherends. In the dual adhesive case, the ductile adhesive Araldite-2015 has been used at the ends of the overlap because of high shear and peel strength, whereas in the middle of the bonded region the brittle adhesive AV138 has been used at different dimensions. The bond strength and corresponding failure patterns have been evaluated. The Digital Image Correlation (DIC) method has been used to monitor the relative displacements between the dissimilar adherends. Finite element analysis (FEA) has been carried-out using ABAQUS software. The variation of peel and shear stresses along the single and dual adhesive bond length have been captured. Comparison of experimental and numerical studies have been carried-out and the results of numerical values are closely matching with the experimental values. From the studies it is found that, the use of dual adhesive helps in increasing the bond strength.     

Shear and peel stress analysis of an adhesively bonded scarf joint

The shear and peel stress distributions in a scarf joint made of two isotropic adherends with blunt adherend tips are analysed using a linear elastic analysis. The limits of the analysis with respect to adherend tip thickness have been investigated. A finite difference method is used to solve the differential equations for the shear and peel stress distributions over the joint. The boundary conditions used limit the analysis to the two adherends having the same thicknesses, lengths, and material properties. The adherends are modelled as plates with extensional and bending stiffnesses bonded together with an elastic interlayer. The stresses across the adhesive layer are assumed to be constant. The current analysis applied to cases known from the literature shows good agreement with the shear stresses but the peel stresses are overestimated.     

Analytical solutions for nonlinear analysis of composite single-lap adhesive joints

This paper presents analytical nonlinear solutions for composite single-lap adhesive joints. The ply layups of each composite adherend can be arbitrary, but in the overlap region the ply layups of the upper and lower adherends are assumed to be symmetrical about the adhesive layer. In the present formulation, equilibrium equations of the overlap are derived on the basis of geometrical nonlinear analysis. The governing equations are presented in terms of adherend displacements by taking into account large deflections of the overlap adherends and adhesive shear and peel stresses simultaneously. Closed-form nonlinear solutions for adherend displacements, an edge moment factor and adhesive stresses are formulated and then simplified for practical applications. To verify the present analytical solutions for nonlinear analysis of composite single-lap joints, the geometrically nonlinear 2D finite element analysis is conducted using commercial package MSC/NASTRAN. The numerical results of the edge moment factor, deflections and adhesive stresses predicted by the present solutions correlate well with those of the geometrically nonlinear finite element analysis. This indicates that the present analytical solutions capture key features of geometrical nonlinearity of composite single-lap adhesive joints.     

Through-the-width delamination damage propagation characteristics in single-lap laminated FRP composite joints

Three-dimensional non-linear finite element analyses have been carried out to study the effects of through-the-width delaminations on delamination damage propagation characteristics in adhesively bonded single-lap laminated FRP composite joints. The delaminations have been presumed either to pre-exist or to get evolved due to coupled stress failure criteria in the laminated FRP composite adherends near the overlap ends beneath the ply adjacent to the overlap region. The out-of-plane stresses in the adhesive layer, the interlaminar stress distributions along the delamination fronts and the strain energy release rates (SERRs) corresponding to the three individual modes have been evaluated for varying positions of the delaminations pre-embedded in either of the adherends. A good matching between the present 3D results and experimental and analytical solution of the literature has been established for the undamaged and a damaged model. A significant difference in the interlaminar stresses and the SERR values has been observed and is largely dependent on the adherends (bottom or top) possessing the through-the-width delamination damages. Also, the interlaminar stresses and SERR values along the two corresponding delamination fronts are different. Accordingly, it can be concluded that the positions of the through-the-width delaminations significantly influence the delamination damage propagation behaviour vis-a-vis the performance of the composite joint.     

On the thermomechanical behavior of two-dimensional foam/metal joints with shear-deformable adherends: Model validation with FE analysis

The stress distributions in metal/adhesive/foam planar joints subjected to biaxial tensile load and thermal load was investigated through a semi-analytical model. The shear deformation of adherends was accounted for according to a linear law in order to obtain closed-form solutions. For the model validation, a comparative study with a finite element (FE) simulation was carried out. A 2D behavior of stress fields is observed due especially to the Poisson's ratio effects and the biaxial nature of loads. The through thickness shear stresses are comparable to normal stresses; therefore, the adherend shear deformation must be accounted for correct failure prediction. According to the comparison with FE results, the normal stress distributions at any location in the foam and the shear stresses in the foam regions close to the adhesive surface can be well predicted by the proposed model. The through thickness shear stresses, however, showed to vary according to a cubic law rather than a linear law.     

Effect of shear deformation on interfacial stresses in plated beams subjected to arbitrary loading

Bonding a fibre reinforced polymer (FRP) composite or metallic plate to the soffit of a reinforced concrete (RC), timber or metallic beam can significantly increase its strength and other aspects of structural performance. These hybrid beams are often found to fail due to premature debonding of the plate from the original beam in a brittle manner. This has led to the development of many analytical solutions over the last two decades to quantify the interfacial shear and normal stresses between the adherends. The adherends are subjected to axial, bending and shear deformations. However, most analytical solutions have neglected the influence of shear deformation of the adherends. For the few solutions which consider this effect in an approximate manner, their applicability is limited to one or two specific load cases. This paper presents a general analytical solution for the interfacial stresses in plated beams under an arbitrary loading with the shear deformation of the adherends duly considered. The shear stress distribution is assumed to be parabolic through the depth of the adherends in predicting the interfacial shear stress and Timoshenko's beam theory is adopted in predicting interfacial normal stress to account for the shear deformation. The solution is applicable to a beam of arbitrary prismatic cross-section bonded symmetrically or asymmetrically with a thin or thick plate, both having linear elastic material properties. The effect of shear deformation is illustrated through an example beam. The influence of material and geometric parameters of the adherends and adhesive on the interfacial stress concentrations at the plate end is discussed.     

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.     

The use of flexible interface theory for fully coupled nonlinear analysis of balanced adhesive single-lap joint

A theoretical model is presented for determining the edge moment factors, the transverse deflections and the interfacial stresses of the balanced adhesive single-lap joint (SLJ). Based on the flexible interface theory, the improved one-dimensional beam model incorporates simultaneously the effects of interfacial compliances, the overlap geometric nonlinearity and the transverse shear deformations for the adherends. On the basis of normal and tangential displacement compatibility condition for the flexible interface, two sets of fully coupled governing equations concerning rotation of transverse normal and longitudinal displacement of adherends are constructed, from which the improved solutions for the edge moment factors, the transverse deflections, and the interfacial stresses can be obtained. The applicability and accuracy of the improved one-dimensional beam model are validated by comparing the present solutions with the results of the classical model, non-linear finite element analysis, and experimental results. Finally, the effects of the interface compliances on the adhesive stresses distributions of the balanced SLJ are studied.     

The behaviour of single lap joints under bending loading

Four-point bend tests were performed on single lap joints with hard steel adherends and a structural epoxy adhesive. The effect of the overlap, the adherend thickness and the adhesive thickness was studied. It was found that the length of the overlap has no significant effect on the strength of the joints. This is because the load transfer is occurring in a very localised area around the edges of the overlap, being the failure governed by peel mechanisms. The thickness of the adherends strongly affects the strength of the joints. The thicker the adherend, the stronger is the joint. The experimental results are compared with a finite element model and reinforce the fact that the failure takes place due to local strains at the ends of the overlap in tension. An analytical model is also given to predict in a simple but effective way the joint strength and its dependence on the adherend thickness.     

Effect of protrusion at the ends of bondline in single lap joints under tension and bending

In this work, elasto-plastic stress analysis of single lap joints with and without protrusion in adhesive bondline subjected to tension and bending was carried out using 2D non-linear finite element analysis and confirmed experimentally. AA 2024-T3 aluminum adherends were bonded with SBT 9244 film adhesive. The protrusion was obtained by extending the adhesive film by 2?mm from the overlap length at both overlap ends. Three different adherend thicknesses and overlap lengths for each loading and bondline type were used. The joints with and without protrusion, for comparison, were loaded with the same load for each adherend thickness and overlap length. Finally, it was observed that the protrusion reduces the strength in the joint under tension, while the protrusion increases the strength in the joint under bending.     

Analysis and design of adhesive-bonded tee joints

In this study, the stresses in adhesive-bonded tee joints, in which a right-angled plate is bonded to a rigid plate with an adhesive, have been analysed with a finite element method. It was assumed that the adhesive and adherends had linear elastic properties. The tee joint was analysed under three loading conditions, two linear and one bending moment. The stress distributions in the joint area are given by stress contours and XY plots under the three load conditions. It was found from the results that high stress concentrations occur in the inside corner of the angle plate for loading in the x-direction (P_x) and under bending moment (M), this suggesting that failure would not occur in the bonded joint. However, for loading in the y-direction (P_y), the maximum normal stresses are concentrated at the left free end of the adhesive layer in the joint, and the first failure may be expected at this edge. Since the geometry of the joints affects the analysis and design of such joints, the influences on the stress distributions of the overlap length, adhesive thickness and adherend thickness were investigated. Practical experiments were carried out and it was found that experimental results were in good agreement with those of the finite element analysis.     

复合材料/金属胶接结构研究进展及发展趋势

胶接连接应用日渐广泛,特别是在汽车和航空航天等结构领域。首先分析了复合材料/金属胶接连接方式的特点,重点介绍了接头中的次弯曲效应、异质材料间刚度与热膨胀系数的不匹配特性以及载荷传递特性。然后总结了提高胶接接头强度的研究进展,主要包括增大胶接长度和宽度、选择胶黏剂、表面处理、增加胶瘤和被粘合物形状的设计等方面。最后对胶接接头的发展趋势进行了展望。