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 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 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.     

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 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.     

Three-Dimensional Finite Element Analysis of the Stress Distribution in Bi-Adhesive Bonded Joints

A 3-D elastic finite element model was developed to investigate the stresses distribution of bi-adhesive bonded joints (i.e., the bond line of joints filled with two adhesives of dissimilar toughness). The effects of the loading mode on the stress distribution of joints, including the single-lap joints under tensile loading (i.e., single-lap joints) and the butt joints under cleavage loading (i.e., cleavage joints), were also studied in detail. Results showed that higher stress, distributed at the contact position of the dissimilar adhesives placed along the bond line of bi-adhesive bonded joints. Also, the maximum stress of the adhesive layer decreased when the length ratios and bonding sequence along the bond line, filled with two dissimilar adhesives, was appropriately designed. At the same time, stress convergence in the adhesive layer of bi-adhesive joints was also obviously reduced in contrast to the mono-adhesive joints. The numerical investigation shows that it is necessary to take into account the change of loading modes when optimizing the bi-adhesive joint design, because of the uneven and complex loading modes of the adhesive bonding structure in the engineering applications.     

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.     

An efficient analysis model for functionally graded adhesive single lap joints

Employing a functionally graded adhesive the efficiency of adhesively bonded lap joints can be improved significantly. However, up to now, analysis approaches for planar functionally graded adhesive joints are still not addressed well. With this work, an efficient model for the stress analysis of functionally graded adhesive single lap joints which considers peel as well as shear stresses in the adhesive is proposed. Two differential equations of the displacements are derived for the case of an axially loaded adhesive single lap joint. The differential equations are solved using a power series approach. The model incorporates the nonlinear geometric characteristics of a single lap joint under tensile loading and allows for the analysis of various adhesive Young׳s modulus variations. The obtained stress distributions are compared to results of detailed Finite Element analyses and show a good agreement for several single lap joint configurations. In addition, different adhesive Young׳s modulus distributions and their impact on the peel and shear stresses as well as the influence of the adhesive thickness are studied and discussed in detail.     

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.     

Stress analyses of composite tee joints at elevated temperature

Thermal–structural coupling nonlinear finite element analyses are conducted in this paper to determine three-dimensional stresses of a composite tee joint, which is formed when a right angled plate is adhesively bonded to a base plate at elevated temperature. The von-Mises stresses of the adhesive layer of the tee joint with three different laminate stacking sequences viz. unidirectional [0]₈, cross-ply [(0/90)_s]₂, and angle-ply [(+45/?45)_s]₂ laminates have been evaluated when the tee joint is subjected to an out-of-plane loading through the right angled plate in addition to an elevated temperature applied at the undersurface of the base plate. The effects of laminate stacking sequence and temperature on von-Mises stresses have been investigated in this paper. The effects of the coefficient of thermal expansion and thermal conduction of the adhesive layer on von-Mises stresses have also been studied. Conclusions about the stresses of the composite tee joint with different stacking sequence, different coefficient of thermal expansion, and different thermal conduction of the adhesive layer are drawn.     

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

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

Design and analysis of functionally graded adhesively bonded double supported tee joint of laminated FRP composite plates under varied loading

The present research deals with three-dimensional nonlinear finite element analyses for a functionally graded adhesively bonded tee joint made of laminated fiber reinforced polymeric composites when the tee joint is subjected to different types of loadings. The out-of-plane stress components have been evaluated along the interfacial surfaces of bond line of the tee joint. Using the stress values, the failure indices are computed by using Tsai–Wu coupled stress failure criterion in order to predict the location of onset of failures within the interfacial surfaces. Accordingly, critical location is identified based on the magnitude of failure indices for varied load conditions. It has been observed that tee joint under bending load is vulnerable for early failure compared with that when the joint is subjected to tensile and compressive loading. The location of failure is found to be different in tee joint under bending load compared with tensile and compressive loadings. Further, efforts have been made to reduce out-of-plane stress concentration by implementing functionally graded adhesive (FGA) with appropriate smooth and continuous gradation function profile. Further, effects of material gradation function profile with varied modulus ratios on out-of-plane stresses and failure indices are observed along the different interfacial surfaces. Series of numerical simulation result significant reduction in peak values failure index. Based on the present research findings, the FGA is recommended for higher and efficient joint strength. Results also exhibit delayed failure onset and improved structural integrity in the tee joint structure with the use of FGA material.     

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.     

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.     

A two-dimensional stress analysis and strength evaluation of band adhesive butt joints subjected to tensile loads

The stresses in band adhesive butt joints, in which two adherends are bonded partially at the interfaces, are analyzed, using a two-dimensional theory of elasticity, in order to demonstrate the usefulness of the joints. In the analysis, similar adherends and adhesive bonds, which are bonded at two or three regions, are, respectively, replaced by finite strips. In the numerical calculations, the effects of the ratio of Young's moduli for adherends to that for adhesives, the adhesive thickness, the bonding area and position, and the load distribution are shown on the stress distributions at interfaces. It is seen that band adhesive joints are useful when the bonding area and positions are changed with external load distributions. Photoelastic experiments and the measurement of the adherend strains were carried out. The analytical results are in a fairly good agreement with the experimental results. In addition, a method for estimating the joint strength is proposed by using the interface stress distribution obtained by the analysis. Experiments concerning joint strength were performed and fairly good agreement is found between the estimated values and the experimental results.     

Analytical solutions for adhesively bonded composite single-lap joints under mechanical loadings using full layerwise theory

In this paper, analytical solutions for adhesively bonded composite single-lap joints (SLJs) are presented within the framework of the full layerwise theory (FLWT). The adhesively bonded composite SLJ is divided into a large number of mathematical plies through the thickness and three regions along its length. The equilibrium equations of each region are obtained using the principle of minimum total potential energy. The three sets of fully-coupled governing equations then are simultaneously solved by introducing the state space variables. The effects of adhesive thickness and loading conditions including uniaxial tension and bending moment on the interfacial peel and shear stress as well as the von Mises stress distributions along the length and through the thickness of the adhesive layer are studied. The present results, which are verified via analytical, experimental, and numerical investigations available in the literature, can be introduced as scaling solutions to verify the authenticity of other methods.     

An In-Situ Failure Model for Adhesive Joints

In this paper, a theoretical model based on the fracture mechanics principle is built to describe the in-situ failure process of adhesive joints. The central concept of the model is that the adhesive fracture is controlled by the plastic zone developed at the crack tip. On the basis of an approximate crack tip stress distribution, a quantitative representation is found to relate the adhesive fracture energy G_1c(joint) to certain bulk resin properties: fracture toughness G_1c(bulk), yield stress σ_y, and Young's modulus E. It is found that the factor σ_y ²/E is sometimes more important than G_1c(bulk) in controlling G_1c(joint). The in-situ failure model interprets well the temperature and loading rate dependent phenomena of adhesive joint fracture reported in the literature. A correlation between the resin material variables and the adhesive fracture is thus established.     

Fatigue Failure Criterion of Adhesively-Bonded Joints Under Combined Stress Conditions

A study was conducted to investigate fatigue failure criteria for adhesively-bonded joints under combined stress conditions. Two types of adhesively-bonded joint specimens were used: the scarf joint and the butterfly-type butt joint. Both types of joints have considerably uniform combined stress distributions in the adhesive layer. Furthermore, the stress distributions of these joints were analyzed by a finite element method. The results showed that the maximum principal, the von Mises equivalent and the maximum shear stresses in the uniform stress region of the adhesive layer at the endurance limit are correlated with the principal stress ratio.     

Load transfer in adhesive double-sided patch joints

In this work, the application of adhesively bonded joints to connect two structural elements with a double-sided patch is studied. On the basis of the shear lag model, a simple closed-form solution was obtained. The analytical solutions can be used to predict the shear stress in the adhesive and the load transfer between the structural elements and the external patches. The load and shear stress distributions in the adhesively bonded region are presented. For verification of the analytical model, finite element analyses were employed to calculate the load transfer and shear stress for the double-sided patch joint under static tensile loadings. Good agreement was found between the theoretical predictions and numerical results. To obtain a better understanding of the joints, the effects of adhesive thickness, adhesive shear modulus and patch Young's modulus on the load transfer and shear stress distributions were investigated. The results show that the maximum shear stress occurs at the edge of the adhesive. The maximum value of the shear stress increases as the adhesive shear modulus and patch Young's modulus increase and as the adhesive thickness decreases. A more gradual load transfer can be achieved by increasing the adhesive thickness and decreasing the adhesive shear modulus. The simple analytical solution presented in this paper has the advantages of avoiding the numerical difficulties and giving explicit relationship between the stress state and joint parameters. Moreover, from the designer's point of view a closed-form and easy-to-use solution is preferred.     

FEM stress analysis and strength prediction of scarf adhesive joints under static bending moments

The stress distributions at the interfaces in the scarf adhesive joints under static bending moments were analyzed using two-dimensional and three-dimensional finite element (FEM) calculations. The effects of the scarf angle, adhesive Young's modulus and the adhesive thickness on the interface stress distribution were examined. It was found that the singular stress at the edges of the interfaces decreased as the adhesive Young's modulus increased and the adhesive thickness decreased. The singular stress at the edges of the interfaces obtained from the 3-D was larger than that from the 2-D FEM. The joint strength was also predicted using the elasto-plastic 3-D FEM calculations. For verification of the FEM calculation results, the strains in the adherends and the joint strengths were measured. The measured results of the strains and the joint strengths were fairly consistent with the results obtained from the 3-D FEM calculations and indicated that the rupture bending moment (joint strength) was the maximum when the scarf angle was around 60°.