On the non-linear elastic stresses in an adhesively bonded T-joint with double support

Structures consisting of single or more materials, such as adhesive joints, may undergo large displacements and rotations under reasonably high loads, although all materials are still elastic. The linear elasticity theory cannot predict correctly the deformation and stress states of these structures, since it ignores the squares and products of partial derivatives of the displacement components with respect to the material coordinates. When these derivatives are not small, these terms result in a non-linear effect called geometrical non-linearity. In this study, the geometrically non-linear stress analysis of an adhesively bonded T-joint with double support was carried out using the incremental finite element method. Different T-joint configurations bonded to a rigid base and to a flexible base were considered. For each configuration, linear and geometrically non-linear stress analyses of the T-joint were carried out and their results were compared for different horizontal and vertical plate end conditions. The geometrically non-linear analysis showed that the large displacements had a considerable effect on the deformation and stress states of both adherends and the adhesive layer. High stress concentrations were observed around the adhesive free ends and the peak adhesive stresses occurred inside the adhesive fillets. The adherend regions corresponding to the free ends of the adhesive–plate interfaces also experienced stress concentrations. In addition, the effects of the support length on the peak adhesive and adherend stresses were investigated; increasing the support length had a considerable effect in reducing the peak adhesive and adherend stresses.     

Geometrically Non-Linear Analysis of Adhesively Bonded Double Containment Corner Joints

In cases where adhesively bonded joints may experience large displacements and rotations whilst the strains remain small, although all joint members behave elastically the small strain-small displacement (SSSD) theory cannot correctly predict the stresses and deformations in the adhesive joint members. Previous studies have shown that the small strain-large displacement theory considering the non-linear effects of the large displacements in the stresses and deformations has to be used in the analysis of adhesively bonded joints. In this study, the geometrical non-linear analysis of an adhesively bonded double containment corner joint was carried out using the incremental finite element method based on the small strain-large displacement (SSLD) theory. The objective of the study was to determine the effects of the large displacements on the adhesive and adherend stresses of the corner joint. Therefore, the corner joint was analysed for two different loading conditions; a compressive applied load, P_x, at the free end of the horizontal plate and one normal to the plane of the horizontal plate, P_y. The plates, support and adhesive layer were assumed to have elastic properties. In practice, the adhesive accumulations, called spew fillets, arising around the adhesive free ends were taken into account in the analysis since their presence results in a considerable decrease in the peak stresses around the free ends of the adhesive. The SSLD and SSSD analyses showed that the stress concentrations occurred around the free end of the adhesive, thus at the adherend (slot) corners inside the right vertical and the lower horizontal adhesive fillets, and inside the left vertical and the upper horizontal adhesive fillets for the loading conditions P_x and P_y, respectively. In addition, the plate regions around the adherend (slot) free ends along the outer fibres of the vertical and horizontal plates undergo very high stress concentrations. The SSLD analysis predicted a non-linear effect in the displacement and stress variations at the critical adhesive and plate locations, whereas the SSSD analysis showed their variations were lower and proportional to the applied incremental load. This non-linear effect became more evident for the loading condition P_x, whereas both analyses predicted very close displacement and stress variations in the adhesive fillets and in the horizontal plate for the loading condition P_y. As a result, the geometrical non-linear behaviour of the corner joint is strictly dependent on the loading condition and the large displacements affect the stress and deformation states in the joint members, and result in higher stresses than those predicted by the SSSD theory.     

Geometrically non-linear analysis of adhesively bonded corner joints

When adhesively bonded joints are subjected to large displacements, the small strain-small displacement (linear elasticity) theory may not predict the adhesive or adherend stresses and deformations accurately. In this study, a geometricaly non-linear analysis of three adhesively bonded corner joints was carried out using the incremental finite element method based on the small strain-large displacement (SSLD) theory. The first one, a corner joint with a single support, consisted of a vertical plate and a horizontal plate whose left end was bent at right angles and bonded to the vertical plate. The second corner joint, with a double support, had two plates whose ends were bent at right angles and bonded to each other. The final corner joint, with a single support plus angled reinforcement, was a modification of the first corner joint. The analysis method assumes that the joint members, such as the support, plates, and adhesive layers, have linear elastic properties. Since the adhesive accumulations (spew fillets) around the adhesive free ends have a considerable effect on the peak adhesive stresses, they were taken into account. The joints were analyzed for two different loading conditions: one loading normal to the horizontal plate plane P_y and the other horizontal loading at the horizontal plate free edge P_x. In addition, three corner joints were analyzed using the finite clement method based on the small strain-small displacement (SSSD) theory. In predicting the effect of the large displacements on the stress and deformation states of the joint members, the capabilities of both analyses were compared. Both analyses showed that the adhesive free ends and the outer fibres of the horizontal and vertical plates were subjected to stress concentrations. The peak stresses appeared at the slot corners inside the adhesive fillets and at the horizontal and vertical plate outer fibres corresponding to the locations where the horizontal and vertical adhesive fillets finished. The SSLD analysis predicted that the displacement components and the peak adhesive and plate stress components would show a non-linear variation for the loading condition P_x, whereas the SSSD analysis showed smaller stress variations proportional to the applied load. However, both the SSLD and the SSSD analyses predicted similar displacement and stress variations for the loading condition P_y. Therefore, the stress and deformation states of the joint members are dependent on the loading conditions, and in the case of large displacements, the SSSD analysis can be misleading in predicting the stresses and deformations. The SSLD analysis also showed that the vertical and horizontal support lengths and the angled reinforcement length played an important role in reducing the peak adhesive and plate stresses.     

Geometrically non-linear analysis of adhesively bonded double containment cantilever j oints

Under an increasing load, the adhesively bonded joints may undergo large rotations and displacements while strains are still small and even all joint members are elastic. In this case, the linear elasticity theory cannot predict correctly the nature of stress and deformation in the adhesive joints. In this study, an attempt was made to develop an analysis method considering the large displacements and rotations in the adhesive joints, assuming all joint members to be still elastic. An incremental finite element method was used in the application of the small strain-large displacement theory to the adhesively bonded joints. An adhesively bonded double containment cantilever (DCC) joint was analysed using this incremental finite element method under two different loadings: a tensile loading at the horizontal plate free end, P_x. and one normal to the horizontal plate plane, P_y. The adhesive and plates were assumed to have elastic properties, and some amount of adhesive, called spew fillet, that accumulated at the adhesive free ends was also taken into account. The analysis showed that the geometrical non-linear behaviour of adhesively bonded joints was strictly dependent on the loading and boundary conditions. Thus, a DCC joint exhibits a high non-linearity in the displacements, stresses, and strains in the critical sections of the adhesive and horizontal plate under a tensile loading at the free end of the horizontal plate, P_x, while a similar behaviour in these regions was not observed for a loading normal to the horizontal plate plane, P_y. However, an increasing non-linear variation in the stresses and deformations of the horizontal plate appeared from the free ends of the adhesive-horizontal plate interfaces to the free end of the horizontal plate for both loading conditions. Consequently, joint regions with a low stiffness always undergo high rotations and displacements, and if these regions include any adhesive layer, the non-linear effects will play an important role in predicting correctly the stresses and deformations in the joint members, especially at the adhesive free ends at which high stress concentrations occurred. In addition, the DCC joint exhibited a higher stiffness and lower stress and strain levels in the joint region in which the support and horizontal plate are bonded than those in the horizontal plate.     

Photoelastic thermal stress measurements in scarf adhesive joints under uniform temperature changes

This study deals with the investigation of thermal stresses and delamination growth in scarf joints under a uniform temperature change by photoelastic measurements and a two-dimensional finite element analysis. The adherends were fabricated from aluminum plates, and an adhesive layer was modeled and fabricated from an epoxide resin plate. The adherends and the epoxide resin plate were bonded using a heat-setting and one-component-type adhesive. The adhesive was cured at 85 °C and cooled down to room temperature. The thermal stress was then generated in the scarf joint under a temperature change and measured by photoelasticity. After the scarf joints were cooled in a stepwise manner, the delamination growth, which initiates from the edge of the interface, was measured. It was found that the delamination initiates from the edge of the interface with the acute angle side and it never initiates from the edge with the obtuse angle side. When the scarf angle is 90°, i.e. in adhesive butt joints, the resistance against the delamination is minimal. The thermal stresses in the scarf joints with a thin adhesive layer were also analyzed. It was found that the thermal strength increases as the adhesive thickness decreases. The stress singularity near the edge of the interface was calculated from the stress distributions in the joints with different scarf angles. As a result, it was found that the stress singularity in the scarf joints under thermal loads is quite different from that under static tensile loads.     

Analysis of tubular adhesive joints with a functionally modulus graded bondline subjected to axial loads

The strength and lifetime of adhesively bonded joints can be significantly improved by reducing the stress concentration at the ends of overlap and distributing the stresses uniformly over the entire bondline. The ideal way of achieving this is by employing a modulus graded bondline adhesive. This study presents a theoretical framework for the stress analysis of adhesively bonded tubular lap joint based on a variational principle which minimizes the complementary energy of the bonded system. The joint consists of similar or dissimilar adherends and a functionally modulus graded bondline (FMGB) adhesive. The varying modulus of the adhesive along the bondlength is expressed by suitable functions which are smooth and continuous. The axisymmetric elastic analysis reveals that the peel and shear stress peaks in the FMGB are much smaller and the stress distribution is more uniform along its length than those of mono-modulus bondline (MMB) adhesive joints under the same axial tensile load. A parametric evaluation has been conducted by varying the material and geometric properties of the joint in order to study their effect on stress distribution in the bondline. Furthermore, the results suggest that the peel and shear strengths can be optimized by spatially controlling the modulus of the adhesive.     

Geometrically non-linear analysis of an adhesively bonded modified double containment corner joint — I

In this study, the geometrically non-linear analysis of an adhesively modified double containment corner joint was carried out using the incremental finite element method based on the small strain-large displacement (SSLD) theory. The plates, support, and adhesive layers were assumed to have linear elastic properties. The joint was analysed for two different loading conditions: one normal loading to the horizontal plate plane P _y and one horizontal loading at the horizontal plate free edge P _x . In addition, the small strain-small displacement (SSSD) analysis of this adhesive joint was also carried out in order to compare the capability of the two theories in predicting the effect of large displacements on the stress and deformation states of the joint members. Both analyses showed that stress and strain concentrations occurred around the adhesive free ends, corresponding to the vertical and horizontal slot free ends, and along the outer fibres of the horizontal and vertical plates. The peak stresses appeared at the slot corners inside the adhesive fillets and at the horizontal and vertical plate outer fibres corresponding to the two slot free ends. The variations of the Von Mises stresses at these critical adhesive and plate locations were evaluated versus increasing loads. The SSLD theory predicted an evident non-linear effect, as a result of the large displacements, on the stress variations for the loading P _x , whereas this non-linear effect disappeared on the stresses for the loading P _y ; thus, the stresses presented very close variations to those obtained by the SSSD theory. However, the SSSD theory predicted a lower stress variation proportional to the increasing load for both loading conditions. In the case of the loading P _y , the right vertical adhesive fillet and both plates appeared as the most critical joint regions, whereas the lower horizontal fillet and both plates were determined as the most critical regions for the loading P _x . The behaviour of all joint members towards the applied load is strictly dependent on the boundary and loading conditions. Finally, the SSSD theory may be misleading in the prediction of the stress and deformations, but the SSLD theory includes the non-linear effect of the large displacements and rotations and gives more realistic results, although it requires more computational effort. In addition, it was observed that the geometrical parameters, such as the support length, vertical support length, and vertical slot depth, had a considerable effect on the peak adhesive and plate stresses, depending on the loading condition.     

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.     

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.     

Thermal Residual Stresses in Adhesively Bonded In-plane Functionally Graded Clamped Plates Subjected to an Edge Heat Flux

In this study we have carried out the thermal residual stress analyses of adhesively bonded functionally graded clamped plates for different edge heat fluxes. The material properties of the functionally graded plates were assumed to vary with a power law along an in-plane direction not through the plate thickness direction. The transient heat conduction and Navier equations describing the two-dimensional thermo-elastic problem were discretized using the finite-difference method, and the set of linear equations was solved using the pseudo singular value method. The plate material properties near the interfaces played an important role in the interfacial adhesive stresses. The compositional gradient affected considerably both in-plane temperature distributions and heat transfer periods. The type of in-plane heat flux had only a minor effect on the temperature profiles but affected both the temperature levels and heat transfer period. Both plates undergo considerable compressive normal strains and stresses, but shear strains were more effective. Peak equivalent strains were observed for a constant heat flux and plates with a metal-rich composition. The compositional gradient and direction played important role in the profiles and levels of normal, shear and equivalent stresses as well as strains. The equivalent stress and strains concentrated along the free edges of the adhesive layer. The adhesive layer experienced a considerable distortional deformation rather than volumetric deformation. The equivalent stress exhibited small changes through the adhesive thickness and along the overlap length. The equivalent stress remained uniform in a large region of the overlap length and increased to a peak level around the free edges of the first plate–adhesive interface, whereas it increased to a peak level in a large region of the overlap length from a minimum level around the free edges of the second plate–adhesive interface. The strains and equivalent strains were higher for a metal-rich material composition. The direction of the material composition of the plates affected both stress and strain levels; thus, the CM–CM and CM–MC plates exhibited lower strain and stress levels than those in the MC–CM and MC–MC plates. However, only the adhesively bonded CM–MC plate configuration could achieve the lowest deformations and stresses in both plates and adhesive layer.     

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.     

Geometrically non-linear analysis of adhesively bonded modified double containment corner j oints - II

In this study, the geometrical non-linear analysis of an adhesively bonded modified double containment comer joint, which is presented as an alternative to previous comer joints, was carried out using the incremental finite element method based on the small strain-large displacement (SSLD) theory. The analysis method assumes the joint members such as the support, plates, and adhesive layers to have linear elastic properties. Since the adhesive accumulations (spew fillets) around the adhesive free ends have an important effect on the peak adhesive stresses, their presence was taken into account by idealizing them as triangular in shape. The joint was analysed for two different loading conditions: one load normal to the horizontal plate plane, P_y, and one load horizontal at the horizontal plate free edge, P_x. Finally, small strain-small displacement (SSSD) analysis of the joint was carried out and the results of both analyses were compared in order to determine the capability of the two theories in predicting the effects of large displacements on the stress and deformation states in the joint members. Both analyses showed that the peak stress values appeared at the slot comers inside the adhesive fillets and at the upper and lower longitudinal fibres (top and bottom longitudinal surfaces) of the horizontal and vertical plates corresponding to the horizontal and vertical slot free ends. In the case of the load P_y, the right vertical adhesive fillet and both plates were the most critical joint regions, whereas the lower horizontal fillet and both plates were determined to be the most critical regions for the load P_x. The SSLD theory predicted a non-linear effect on the variations of the displacement and stress components at these critical adhesive and plate locations for the load P_x, whereas the stress components at the critical adhesive locations presented variations very close to those determined by the SSSD theory for the load P_y, but this non-linear effect appeared on the displacement and stress variations at the critical locations of both plates. In addition, the SSSD theory predicted that the displacement and stress components would have lower variations proportional to the increasing load for both loading conditions. The stress and deformation states of all joint members are strictly dependent on the boundary and loading conditions. In addition, whereas the SSSD theory may be misleading for some loading conditions, the SSLD theory gives more realistic results, since it takes into account the non-linear effect of large displacements and rotations.     

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.     

Failure behavior of adhesively bonded joints with a rubber modified epoxy adhesive under tensile-shear combined cyclic loading

Rubber-modified epoxy adhesives are used widely as structural adhesive owing to their properties of high fracture toughness. In many cases, these adhesively bonded joints are exposed to cyclic loading. Generally, the rubber modification decreases the static and fatigue strength of bulk adhesive without flaw. Hence, it is necessary to investigate the effect of rubber-modification on the fatigue strength of adhesively bonded joints, where industrial adhesively bonded joints usually have combined stress condition of normal and shear stresses in the adhesive layer. Therefore, it is necessary to investigate the effect of rubber-modification on the fatigue strength under combined cyclic stress conditions. Adhesively bonded butt and scarf joints provide considerably uniform normal and shear stresses in the adhesive layer except in the vicinity of the free end, where normal to shear stress ratio of these joints can cover the stress combination ratio in the adhesive layers of most adhesively bonded joints in industrial applications.

In this study, to investigate the effect of rubber modification on fatigue strength with various combined stress conditions in the adhesive layers, fatigue tests were conducted for adhesively bonded butt and scarf joints bonded with rubber modified and unmodified epoxy adhesives, wherein damage evolution in the adhesive layer was evaluated by monitoring strain the adhesive layer and the stress triaxiality parameter was used for evaluating combined stress conditions in the adhesive layer. The main experimental results are as follows: S–N characteristics of these joints showed that the maximum principal stress at the endurance limit indicated nearly constant values independent of combined stress conditions, furthermore the maximum principal stress at the endurance limit for the unmodified adhesive were nearly equal to that for the rubber modified adhesive. From the damage evolution behavior, it was observed that the initiation of the damage evolution shifted to early stage of the fatigue life with decreasing stress triaxiality in the adhesive layer, and the rubber modification accelerated the damage evolution under low stress triaxiality conditions in the adhesive layer.     

Effect of adhesive free-end geometry on the initiation and propagation of damaged zones in adhesively bonded lap joints

In this study the effect of adhesive free-end geometry on the initiation and propagation of damaged zones in adhesively bonded single- and double-lap joints was investigated considering the material non-linear behaviour of both adhesive and adherends and the geometrical non-linearity. The damaged adhesive and adherend zones exceeding the specified ultimate strains were determined based on the modified von Mises criterion for adherends and the failure criterion, including the effects of the hydrostatic stress states for the epoxy adhesives proposed by Raghava and Cadell. The stiffness of each finite element in the damaged zones was reduced to a negligible value, thus not contributing to the overall stiffness of the adhesive joint. This simple method provides useful information on the initiation and propagation of damaged zones in both the adhesive layer and adherends. The damaged adhesive zones due to a tensile load were observed to initiate around the rounded adherend corners inside the adhesive fillets and to propagate first towards both the free surface of the adhesive fillet and across the adhesive layer, and later along the adherend–adhesive interface. The damaged adhesive zones initiate at the left free-end of the adhesive-upper adherend interface and at the right free-end of the adhesive-lower adherend interface and propagate along these interfaces in the large adhesive fillets. In the bending test, the damaged adhesive zones appeared only at the left free-end in tension of the adhesive-upper adherend interface for the large adhesive fillets, but around the lower adherend corner for the smaller adhesive fillets. Later, it propagated with a similar mechanism as in the tensile load. In a double-lap joint subjected to a tensile load, the damaged zone appeared around the upper adherend corner inside the right adhesive fillet in tension, and propagated first towards the free surface of the adhesive fillet and through the adhesive layer towards the adhesive-middle adherend interface, and later along this interface. For all loading conditions, increasing the adhesive fillet size caused the damaged zone initiation to occur at a larger load level. The SEM micrographs of fracture surfaces around the adhesive fillets showed that the damaged zones initiated around the adherend corner inside the adhesive fillet and propagated through the adhesive fillets.     

Modeling of single-lap composite adhesive joints under mechanical and thermal loads

Two-dimensional (plane-stress and plane-strain) theoretical models are presented for stress analysis of adhesively bonded single-lap composite joints subjected to either thermal or mechanical loading or a combination thereof. The joints consist of similar/dissimilar orthotropic or isotropic adherends and an isotropic adhesive interlayer. The governing differential equation of the problem is obtained using a variational method which minimizes the complementary strain energy in the bonded assembly. In this formulation, through-thickness variation of shear and peel stresses in the interlayer is considered. Both shear and normal traction-free boundary conditions are exactly satisfied. Peel and shear stresses obtained from plane-strain analytical models considering a homogeneous adhesive interlayer are in close agreement with those of the finite element predictions. A systematic parametric study is also conducted to identify an ideal set of geometric and material parameters for the optimal design of single-lap composite joints.     

Development of a Failure Model for the Adhesively Bonded Tubular Single Lap Joint

The accurate calculation of the stresses and torque capacities of adhesively bonded joints is not possible without understanding the failure phenomena of the adhesive joints and the nonlinear behavior of the adhesive.

In this paper, an adhesive failure model of the adhesively bonded tubular single lap joint with steel-steel adherends was proposed to predict the torque capacity accurately.

The model incorporated the nonlinear behavior of the adhesive and the different failure modes in which the adhesive failure mode changed from bulk shear failure, via transient failure, to interfacial failure between the adhesive and the adherend, according to the magnitudes of the residual thermally-induced stresses from fabrication.     

Stress Analysis of Adhesively Bonded Electroprimed Steel Lap Shear Joints

Structural applications for adhesive bonding have been increasing in recent years due to improvements in the types of adhesives available and in improved knowledge of bonding procedures. Consequently, there exists a demand for precise numerical modeling of adhesive joint behavior, particularly along bondline interfaces where low surface energy adhesives contact high surface energy metallic oxides. The purpose of the present study is to determine the effect of electrodeposited organic paint primer (ELPO) on the stress and strain distributions within an adhesively bonded single-lap-shear joint. Initial experimental studies have shown that bonding to ELPO-primed steel adherends has enhanced strength and durability characteristics compared to conventional bonds to unprimed steel surfaces. Recent studies based on finite element analysis of varied single-lap-shear joint moduli and thicknesses, and subsequent testing of joints with two different adhesive moduli, have indicated the mechanisms involved in this phenomenon. The presence of the ELPO-primer reduced peak peel and shear stresses and allowed for more uniform stress distribution throughout the joint.     

Stress Analysis of Generally Asymmetric Single Lap Adhesively Bonded Joints

An analysis is presented that predicts shear and peel stresses in an adhesively bonded single lap joint having general asymmetric configuration. The single lap joint is under tension loading together with moments induced by geometric eccentricity. Because these eccentricity moments are the key elements of this analysis, a general relationship between the eccentricity moments and simple geometric moments has been determined with the aid of finite element analysis (FEA). Example calculations show that the shear- and peel-stress profiles from the closed-form model are well matched to FEA results except in the small regions near the free ends of the joints, because of the shear lag basis of the model. For asymmetric joints, the model predictions are more accurate for the case of modulus eccentricity than thickness eccentricity. Elastic-limit load predictions accounting for both shear and peel stress in the adhesive have been used to find optimal joint configurations between asymmetric adherends.     

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.