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 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.     

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.     

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.     

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.     

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.     

Thermal non-linear elastic stress analysis of an adhesively bonded T-joint

Adhesive joints consist of adherends and an adhesive layer having different thermal and mechanical properties. When they are exposed to uniform thermal loads the mechanical-thermal mismatches of the adherends and adhesive layer result in uniform but different thermal strain distributions in the adhesive and adherends. The thermal stresses arise near and along the adherend-adhesive interfaces. The present thermal stress analyses of adhesively bonded joints assume a uniform temperature distribution or a constant temperature imposed along the outer boundaries of adhesive lap joints. This paper outlines the thermal analysis and geometrically non-linear stress analysis of adhesive joints subjected to different plate edge conditions and varying thermal boundary conditions causing large displacements and rotations. In addition, the geometrically non-linear thermal stress analysis of an adhesively bonded T-joint with single support plus angled reinforcement was carried out using the incremental finite element method, which was subjected to variable thermal boundary conditions, i.e. air streams with different temperatures and velocities parallel and perpendicular to its outer surfaces. The steady state heat transfer analysis showed that the temperature distribution through the joint members was non-uniform and high heat fluxes occurred inside the adhesive fillets at the adhesive free ends. Based on the geometrically non-linear stress analysis of the T-joint bonded to both rigid and flexible bases for different plate edge conditions, stress concentrations were observed at the free ends of adhesive-adherend interfaces and inside the adhesive fillets around the adhesive free ends, and the horizontal and vertical plates also experienced considerable stress distributions along outer surfaces. In addition, the effect of support length on the peak thermal adhesive stresses was found to be dependent on the plate edge conditions, when a support length allowing moderate adhesive stresses was present.     

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.     

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.     

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.     

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.     

The effect of cyclic loading on residual stresses and strains in a bonded joint

The mechanical performance of a structural bonded joint is mainly dependent on the interlaminar stresses and strains, the high concentration of which is close to the free edges of the adhesive. Under cyclic loading these stresses and strains are expected to be intensified and to accumulate. The present study deals with the distribution of the residual stresses and strains along the interlaminar adhesive layer under cyclic loading and how it is affected by geometrical edge conditions. A numerical non-linear finite element method was applied, the adhesive layer being regarded as an elasto-plastic bi-linear material with kinematic hardening (Bauschinger effect) which accounts for cyclic plasticity. Findings indicate that lateral normal residual strains in the edge of the adhesive layer are the major component which increases significantly with cycling and are probably responsible for failure initiation and propagation. It was also found that a significant reduction of stress concentration at the adhesive edge may be achieved by a modification of the free-edge geometry of both the adhesive and the adherend phases.     

Free Vibration Analysis and Design of an Adhesively Bonded Corner Joint with Double Support

This study carries out the three dimensional free vibration analysis of an adhesively bonded corner joint and investigates the effect of an additional horizontal support to the adhesive corner joint with single support on the first ten natural frequencies and mode shapes. In the presence of a horizontal support the effects of the vertical support length, the adhesive thickness, the plate thickness, and the joint length on the natural frequencies and modal strain energies of the adhesive joint were also investigated using the back-propagation Artificial Neural Network (ANN) method and the finite element method. The natural frequencies and modal strain energies increased with increasing plate thickness, whereas an adverse effect was observed for increasing joint length. Both horizontal and vertical support lengths exhibited similar effects but the adhesive thickness had a negligible effect. The plate thickness and the joint length are dominant geometrical parameters in comparison with both horizontal and vertical support lengths. The proposed ANN models were combined with the Genetic Algorithm in order to determine the optimal corner joint in which the maximum natural frequency and minimum elastic modal strain energy are achieved for each natural frequency and mode shape of the adhesive corner joint and the optimal dimensions were given versus one geometrical parameter.     

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.     

Free Vibration Analysis and Design of an Adhesively Bonded Corner Joint with Double Support

This study carries out the three dimensional free vibration analysis of an adhesively bonded corner joint and investigates the effect of an additional horizontal support to the adhesive corner joint with single support on the first ten natural frequencies and mode shapes. In the presence of a horizontal support the effects of the vertical support length, the adhesive thickness, the plate thickness, and the joint length on the natural frequencies and modal strain energies of the adhesive joint were also investigated using the back-propagation Artificial Neural Network (ANN) method and the finite element method. The natural frequencies and modal strain energies increased with increasing plate thickness, whereas an adverse effect was observed for increasing joint length. Both horizontal and vertical support lengths exhibited similar effects but the adhesive thickness had a negligible effect. The plate thickness and the joint length are dominant geometrical parameters in comparison with both horizontal and vertical support lengths. The proposed ANN models were combined with the Genetic Algorithm in order to determine the optimal corner joint in which the maximum natural frequency and minimum elastic modal strain energy are achieved for each natural frequency and mode shape of the adhesive corner joint and the optimal dimensions were given versus one geometrical parameter.     

An analytical model for interfacial stresses in double-lap bonded joints

Due to their many advantages, adhesively bonded joints are widely used to join components in composite structures. However, premature failure due to debonding and peeling of the joint is the major concern for this technique. Existing analytical models suffer from two major drawbacks: 1) not satisfying zero-shear stress boundary conditions at the adhesive layer’s free edges^[1] and 2) failure to distinguish the peel stress along two adherend/adhesive interfaces^[2]. In this study, we develop a novel three parameter elastic foundation (3PEF) model to analyze a representative adhesively bonded joint, the symmetric double-lap joint, which is believed to have relatively low peel stresses. Explicit closed-form expressions of shear and peel stresses along two adhesive/adherend interfaces are yielded. This new model overcomes the existing model’s major drawbacks by satisfying all boundary conditions and predicting various peeling stresses along two adherend/adhesive interfaces. It not only reaches excellent agreement with existing solutions and numerical results based on finite element analysis but also correctly predicts the failure mode of an experimentally tested double-lap joint. This new model therefore reveals the peel stresses’ significant role in the failure of the double-lap joint, but the classical 2PEF model cannot create it.     

A Method for the Stress Analysis of Lap Joints

A theory is presented for the adhesive stresses in single and double lap joints under tensile loading, while subjected to thermal stress. The formulation includes the effects of bending, shearing, stretching and hygrothermal deformation in both the adherend and adhesive. All boundary conditions, including shear stress free surfaces, are satisfied. The method is general and therefore applicable to a range of material properties and joint configurations including metal-to-metal, metal-to-CFRP or CFRP-to-CFRP. The solution is numerical and is based on an equilibrium finite element approach. Through the use of an iterative procedure, the solution has been extended to cater for non-linear adhesive materials.     

A Method for the Stress Analysis of Lap Joints

A theory is presented for the adhesive stresses in single and double lap joints under tensile loading, while subjected to thermal stress. The formulation includes the effects of bending, shearing, stretching and hygrothermal deformation in both the adherend and adhesive. All boundary conditions, including shear stress free surfaces, are satisfied. The method is general and therefore applicable to a range of material properties and joint configurations including metal-to-metal, metal-to-CFRP or CFRP-to-CFRP. The solution is numerical and is based on an equilibrium finite element approach. Through the use of an iterative procedure, the solution has been extended to cater for non-linear adhesive materials.     

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.     

Metallic multi-material adhesive joint testing and modeling for vehicle lightweighting

While adhesive bonding has been shown to be a beneficial technique to join multi-material automotive bodies-in-white, quantitatively assessing the effect of adherend response on the ultimate strength of adhesively bonded joints is necessary for accurate joint design.In the current study, thin adherend single lap shear testing was carried out using three sheet metals used to replace mild steel when lightweighting automotive structures: hot stamped Usibor® 1500 AS ultra-high strength steel (UHSS), aluminum (AA5182), and magnesium (ZEK 100). Six combinations of single and multi-material samples were bonded with a one-part toughed structural epoxy adhesive and experimentally tested to measure the force, displacement across the bond line, and joint rotation during loading. Finite element models of each test were analyzed using LS-DYNA to quantitatively assess the effects of the mode mixity on ultimate joint failure. The adherends were modeled with shell elements and a cohesive zone model was implemented using bulk material properties for the adhesive to allow full three-dimensional analysis of the test, while still being computationally efficient.The UHSS-UHSS joint strength (27.2 MPa; SD 0.6 MPa) was significantly higher than all other material combinations, with joint strengths between 17.9 MPa (SD 0.9 MPa) and 23.9 MPa (SD 1.4 MPa). The models predicted the test response (average R2 of 0.86) including the bending deformation of the adherends, which led to mixed mode loading of the adhesive. The critical cohesive element in the UHSS-UHSS simulation predicted 85% Mode II loading at failure while the other material combinations predicted between 41% and 53% Mode II loading at failure, explaining the higher failure strength in the UHSS-UHSS joint.This study presents a computational method to predict adhesive joint response and failure in multi-material structures, and highlights the importance of the adherend bending stiffness and on joint rotation and ultimate joint strength.