Influence of the Spew Fillet and other Parameters on the Stress Distribution in the Single Lap Joint

Even the most recent closed form analyses of single lap joints assume that the adhesive terminates in a square end. In practice a fillet of adhesive (hereafter called the spew) usually forms at the overlap ends. This spew can considerably reduce peak adhesive stresses and so strengthen the joint. An investigation has been made into the role of the spew for a wide range of joint parameters. The stress distribution across the adhesive thickness was also considered, and was found to be essentially uniform over a large part of the overlap length. However, near the overlap end, the stress variation across the thickness can be high, resulting in higher stresses and so lower strengths than would be expected considering average stress levels in the joint, but even after including the effect of this variation the maximum adhesive stresses have usually been found to be considerably lower than corresponding peak values predicted by closed form analysis of square ended joints.     

Analysis and design of adhesively bonded corner joints

In this study, the stress and stiffness analyses of corner joints with a single corner support, consisting of two plates, one of which plain and the other bent at right angles, have been carried out using the finite element method. It was assume that the plates and adhesive had linear elastic properties. Corner joints without a fillet at the free ends of the adhesive layer were considered. The joint support was analysed under three loading conditions, two linear and one bending moment. In the stress analysis, it was found that for loading in the y-direction and by bending moment, the maximum stresses occurred around the lower end of the vertical adhesive layer/ vertical plate interface; for loading in the x-direction, the maximum stresses occurred around the right free end of the horizontal adhesive layer/vertical plate interface. The effects of upper support length, support taper length and adhesive thickness on the maximum stresses have been investigated. Since the peel stresses are critical for this type of joint, a second corner joint with double corner support (i.e., one in which the horizontal plate is reinforced by a support that is an extension of the vertical plate) was investigated which showed considerable decreases in the stresses, particularly peel stresses. A third type of corner joint with single corner support plus an angled reinforcement member was investigated as an alternative to the previous two configurations. It was found that increasing the length and particularly the thickness of the angled reinforcement reduced the high peel stresses around the lower free end of the adhesive/vertical plate interface, but resulted in higher compressive stresses. In the stiffness analysis, the effects of the geometry of the joints, relative stiffness of adhesive/adherends and adhesive thickness were investigated under three loading conditions. For three types of corner joint, results were compared and recommended designs were determined based on the overall static stiffness of the joints and on the stress analysis.     

The Stresses in an Adhesive Layer

A simple method has been developed for calculating the stresses near the ends of a parallel-sided adhesive layer. The method can be applied to adhesive layers having aspect ratios of 10 or greater, and Poisson's ratios of 0.49 or less. For a layer subject to uniform boundary conditions of displacement at the adhering surfaces, the stress fields at distances greater than about five layer thicknesses from the free surfaces are uniform. The stress field throughout the layer is uniquely determined by the stresses in the uniform stress region. If the stress field is expressed by functions of reduced coordinates of position, obtained by dividing the cartesian coordinates by the layer thickness, these functions are for practical purposes independent of the aspect ratio or the thickness.

The method has been used to calculate shrinkage stresses, the stresses in a joint under tension perpendicular to the plane of the adhesive layer, and the stresses in a joint under shear. The features of the stress fields are described, and where necessary, shown in the form of graphs or contour plots.     

Elasto-Plastic Analysis of Adhesively Bonded Symmetric Single Lap Joints Under In-Plane Tension and Edge Moments

An analysis is presented that predicts adhesive shear and peel stresses and strains in an adhesively bonded single lap joint having symmetric configuration with adhesive behavior. The single lap joint is under tension loading together with moments induced by the interactions of the geometric eccentricity and the boundary conditions of the joint. The von Mises yielding criterion is used to relate the adhesive stress components within the yielded region. The adhesive strains are computed from the relative displacements of the adherends and can be considered as an average of the strain variation through the adhesive thickness direction. Example calculations show that the predicted adhesive shear and peel stress and strain profiles are well matched to detailed finite element analysis results. Generally, the analytical model predictions are found to be more accurate when the adhesive thickness is small.     

Elasto-Plastic Analysis of Adhesively Bonded Symmetric Single Lap Joints Under In-Plane Tension and Edge Moments

An analysis is presented that predicts adhesive shear and peel stresses and strains in an adhesively bonded single lap joint having symmetric configuration with adhesive behavior. The single lap joint is under tension loading together with moments induced by the interactions of the geometric eccentricity and the boundary conditions of the joint. The von Mises yielding criterion is used to relate the adhesive stress components within the yielded region. The adhesive strains are computed from the relative displacements of the adherends and can be considered as an average of the strain variation through the adhesive thickness direction. Example calculations show that the predicted adhesive shear and peel stress and strain profiles are well matched to detailed finite element analysis results. Generally, the analytical model predictions are found to be more accurate when the adhesive thickness is small.     

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.     

Analysis and evaluation of bondline thickness effects on failure load in adhesively bonded structures

It is well known that adhesive joints have their optimum strength for thin bondline thicknesses (0.1-0.5 mm). The most common analytical methods used for adhesive joint analysis show an improved strength with increasing bondline thickness. This erroneous trend in prediction is investigated in this article. It is found that the through-the-thickness stress distribution in the adhesive is the main cause for the errors. The stresses, both peel and shear, at the interface between the adhesive and the adherend are found to increase, after an initial decrease in the low bondline thickness range, with increasing bondline thickness while the average stresses decrease. This trend explains the trends found in experiments. Further, as experimental results have shown, a theoretical optimum bondline thickness is found.     

An improved four-parameter model on stress analysis of adhesive layer in plated beam

The prediction of stresses in an adhesive layer is helpful in revealing the mechanism of debonding failure in plated beams. This study proposes an improved analytical model for the stress analysis of an adhesive layer in a plated beam. The beam and the soffit plate are individually modelled as a single Timoshenko sub-beam with separate rotations, while the adhesive layer is modelled as a two-dimensional elastic continuum in plane stress, which considers different adherend-adhesive interface stresses. The internal forces of the adhesive layer are assumed to satisfy the Timoshenko beam theory, and the shear deformation and bending moment of the adhesive layer can be considered. The internal forces and displacements of the adhesive layer are fully considered in the displacement compatibility equations, and deformable interfaces are assembled so that the effect of interface stresses on local deformation is captured. Based on equilibrium equations and displacement continuity, the governing differential equations of beam forces are derived, and then the analytical solutions of interface stresses and stresses along the thickness of the adhesive layer are obtained. Comparisons of the results of the finite-element analysis and the existing four-parameter model solutions show that the present model is reasonable. The influence of adhesive thickness on stress distributions in adhesive layers is also investigated.     

Effect of Adhesive Stiffness and Thickness on Stress Distributions in Structural Finger Joints

Environmental, political, and socioeconomic actions over the past several years have resulted in a decreased wood supply at a time when there is an increased demand for forest products. This combination of increased demand and decreased supply has forced more emphasis on engineered wood products, a varied category usually connected with adhesively-bonded end joints, of which the most common type is the finger joint. This paper presents the results of a finite-element analysis of structural finger joints, and focuses primarily on the effect of adhesive stiffness and thickness on stress distribution patterns in finger joints. Results indicate that a flexible adhesive layer concentrates adherend longitudinal and radial stresses at the finger base, whereas a stiff adhesive layer minimizes adherend stresses but increases adhesive stress levels. Results also show that a thin adhesive layer concentrates longitudinal adherend stresses at the juncture of the finger tip and flexible finger base and concentrates radial stresses at all finger bases. However, these increased longitudinal and radial stresses are balanced by reduced adhesive shear stresses.     

An Experimental Study of the Static Torque Capacity of the Adhesively-Bonded Tubular Single Lap Joint

With the wide application of fiber-reinforced composite materials in aircraft, space structures and robot arms, the design and manufacture of composite joints have become a very important research area because they are often the weakest areas in composite structures. In this study, the effects of the adhesive thickness and tensile thermal residual stress on the torque capacity of tubular single lap joints were studied. The torque capacities of the adhesive joints were experimentally determined and found to be inversely proportional to the adhesive thickness. In order to match the experimental results to the theoretical analyses, the elastic-perfectly plastic material properties of the adhesive were used in the closed form solution. Also, the tensile thermal residual stresses of the joints were calculated by the finite element method and it was found that the thermal residual stresses could play an important role in the torque capacity when the adhesive thickness was large.     

Experimental Studies of the Strength of an Adhesive Joint in a State of Combined Stress

The adhesive strength of a butt-type specimen of two cylinders is experimentally studied. Combined stresses are applied on the adhesive layer by subjecting the specimen to combined axial load, torsion and internal pressure. The effects of the surface roughness, the thickness of adhesive layers and the combined stresses on the adhesive strength are examined for the specimens of various metals bonded with epoxy resin. The adhesive failure locus under the combined stress state are represented by a polynominal equation of stress tensors.     

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.     

3D models of specimens with a scarf joint to test the adhesive and cohesive multi-axial behavior of adhesives

In this paper, accurate numerical analyses of the stress distributions within the adhesive in scarf joints under elastic assumption using 3D models are developed. An elastic limit model that takes into account the hydrostatic stress and von Mises equivalent stress, permit to define the more stressed parts of the adhesive with respect to the scarf angle. It is shown that high stress concentrations are generated near the edges and the corners of the specimen at the interface between the substrate and the adhesive. The use of ronded substrates does not lead to decrease significantly these stress concentrations. It is shown that cleaning the free edge of the adhesive changes the location of edge effects without completely erasing them. A modification of the geometry, has been proposed. This modification leads to a quasi-homogeneous distribution of the stresses in the thickness of the adhesive with stresses that tend to 0 near the edges.     

Stresses in the Joints of Bonded Prism Assemblies

The distribution of thermally induced shear and normal stresses at the interface between a prism and an adhesive in bonded assemblies has been obtained using the finite element method. The loading was due to a nominal uniform temperature drop of 50°C. The effects of thickness of adhesive layer, profile form at the end of the adhesive layer, angle of edge chamfer on glass and elastic moduli of glass and adhesive on these stresses have been established. The general results are also applicable to other assemblies and for stresses induced by adhesive shrinkage.     

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.     

Spatially-degraded adhesive anchors under material uncertainty

The classic problem of stress transfer in a cylinder through shear to a surrounding medium, is analyzed here in the context of pullout of an anchor under material uncertainty. Assuming a log-normal distribution for the random shear stiffness field of the adhesive, the stochastic differential equation (SDE) is formulated for spatially-tailored/degraded adhesive anchors. The stochastic shear stress distribution in the adhesive is presented for various embedment lengths and adhesive thicknesses clearly demarcating the regime over which failure would initiate. The stochastic variation of maximum shear stress of the adhesive as a function of embedment length and adhesive thickness is also presented. It is observed that the mean maximum shear stresses in the degraded adhesive for both fixed and free embedded-end cases converge and the influence of boundary condition at the embedded-end on shear stress field disappears as the embedment length is increased. For the parameters considered here, about 45% longer embedment length is required compared to an intact bondline for shear-dominated load transfer, suggesting that the design of adhesive anchors should adequately account for likely in-service damage that causes material uncertainty to avoid premature failure.     

Stress analysis in a classical double lap,adhesively bonded joint with a layerwise model

This paper focuses on stress analysis in classical double lap, adhesively bonded joints having constant layer thicknesses. Several analytical methods found in the literature do not provide adequate information on stresses at the adherend/adhesive interfaces. In these methods, the adhesive thickness is assumed to be small compared to that of the adherends and the stresses to be uniform through the adhesive thickness. Herein, the model proposed by the authors can be considered as a stacking of Reissner–Mindlin plates (six plates for a double lap joint). The equations based on stacked plates were applied to the geometry of a symmetrical, double-lap, adhesively bonded joint. Finally, the model has been validated by comparing the model results with those of a finite element calculation.     

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.     

Analysis and design of adhesively bonded modified double containment corner joints -II

This study comprises the stress and stiffness analyses of a second type of modified double containment corner joint which is presented as an alternative to two previous designs in order to reduce the effect of bending moment on the adhesive stresses. Plates are bonded at a right angle into slots of a corner support and the vertical slot depth is kept as large as possible in order to produce a joint which is stiffer and sustainable to high loads, provided that high stress concentration regions are under compression, and to obtain savings of the corner joint volume. The analyses were carried out using the finite element method and assuming that the adhesive, plates, and corner support had linear-elastic properties. Since the geometry of the adhesive free end has an important effect on the high adhesive stresses, the adhesive spew fillet arising from the applied pressure to provide the physical contact between the adhesive and plates was taken into account. In order to show the effect of boundary and loading conditions on the stresses and the overall joint stiffness, the joint was analysed for three loading conditions: two linear and a bending moment. It was found that the loading in the normal direction to the horizontal plate plane at its free end was the most critical and that maximum stress concentrations occurred around the adhesive free ends. A detailed study of adhesive stresses showed that the peak adhesive stresses occurred at the lower free end of the left vertical adhesive layer-slot interface for this loading condition and bending moment, respectively, and at the lower free end of the right vertical adhesive layer-slot interface for the loading condition in another direction. In addition, the effects of geometrical dimensions of the corner support, such as the horizontal and vertical support lengths, slot depth, and support thickness, on the peak adhesive stresses and on the overall joint stiffness were investigated and it was found that whereas the support lengths had a considerable effect, the effect of the slot depth and support thickness was negligible. The dimensions of the corner support were determined relative to the plate thickness based on the results.     

Progressive failure and experimental study of adhesively bonded composite single-lap joints subjected to axial tensile loads

Experimental tests and finite element method (FEM) simulation were implemented to investigate T700/TDE86 composite laminate single-lap joints with different adhesive overlap areas and adherend laminate thickness. Three-dimensional finite element models of the joints having various overlap experimental parameters have been established. The damage initiation and progressive evolution of the laminates were predicted based on Hashin criterion and continuum damage mechanics. The delamination of the laminates and the failure of the adhesive were simulated by cohesive zone model. The simulation results agree well with the experimental results, proving the applicability of FEM. Damage contours and stress distribution analysis of the joints show that the failure modes of single-lap joints are related to various adhesive areas and adherend thickness. The minimum strength of the lap with defective adhesive layer was obtained, but the influence of the adhesive with defect zone on lap strength was not decisive. Moreover, the adhesive with spew-fillets can enhance the lap strength of joint. The shear and normal stress concentrations are severe at the ends of single-lap joints, and are the initiation of the failure. Analysis of the stress distribution of SL-2-0.2-P/D/S joints indicates that the maximum normal and shear stresses of the adhesive layer emerge on the overlap ends along the adhesive length. However, for the SL-2-0.2-D joint, the maximum normal stress emerges at the adjacent middle position of the defect zone along the adhesive width; for the SL-2-0.2-S joint, the maximum normal stress and shear stress emerge on both edges along the adhesive width.