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 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.     

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.     

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 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.     

Analysis of bonded double containment cantilever joints

An important part of adhesive development is the formulation of analyses for predicting the stresses and strains of bonded joints. An analysis of a double containment cantilever joint was made using the finite element method. A double containment joint comprising steel adherends bonded by a two-part epoxy resin adhesive was constructed and the strains in the adhesive layer were measured by a two axes co-ordinate table. The experimental results were found to be in good agreement with those of the theoretical analysis.     

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.     

胶层中间隙长度及位置对接头剪切强度的影响

研究了在单搭接接头上、胶缝中预留的不同长度间隙对接头剪切强度和剪切应力分布的影响。结果表明，随着间隙长度的增加，接头的承栽能力趋于减小，但接头的实际剪切强度却持续上升．当间隙长度再继续增加时，接头的实际强度趋于下降。研究中还发现间隙所处的位置对接头的剪切强度有较大的影响，胶层端部预留间隙使接头的承载能力和实际强度均显著下降。有限元数值分析的结果表明，间隙长度超过某特定值后，胶层中的应力集中系数会急剧上升，间隙位于端部时胶层中的应力集中程度明显高于位于中部处。     

Extension of a one-dimensional finite element model program for analysing elastic-plastic stresses and progressive failure of adhesive bonded joints

A program for stress analysis of adhesive bonded joints within an elastic range was extended to consider the elastic-plastic stress state in an adhesive layer and its progressive failure. The program is based on the one dimensional finite element method. The von Mises yield criterion and the Mohr-Coulomb failure criterion are used in the program. Numerical analysis of a single lap joint subjected to four-point bending load was conducted and its result was compared with the experimental result. Good agreements were obtained between both results except for the final failure load. The present extension has some advantages. The stress singularity in the adhesive layer at the lap end or crack tip can be avoided due to the simple assumption for adhesive strains. Shorter computing time by the present method than by other general two- or three-dimensional finite element model programs should be much emphasized as one of the advantages.     

Elastic analysis and engineering design formulae for bonded joints

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

基于有限元方法的单搭接接头可靠性设计

将概率统计的设计观念引入单搭接粘接接头,通过有限元分析方法分析了对粘接接头力学性能影响较大的因素,并在抽样100次的情况下,分析了单搭接粘接接头失效的概率。结果表明,该模型可以有效地反映接头的实际情况,为粘接结构的可靠度设计提供了依据。     

胶粘剂特性和厚度对劈裂载荷作用下胶接接头应力分布的影响

运用三维弹塑性有限元法对劈裂栽荷作用下的胶接接头(即劈裂接头)承载后的应力分布特征进行了分析，重点研究了胶粘剂层厚度对劈裂接头应力分布的影响。结果表明，胶粘剂的性能对应力分布有较大影响，提高胶粘剂强度和减小胶层厚度，均导致胶层应力集中加剧，各向正应力峰值呈上升趋势，各向剪切应力则正好相反；并且劈裂接头中应力分布以三向主应力为主，剪切应力的存在亦不可忽略。故在不引起过大应力集中和较大胶层缺陷条件下采用高强度的胶粘荆和较厚胶层对提高劈裂接头强度有利，实验结果与有限元分析相吻合。     

Experimental investigation on transverse low-speed impact behavior of adhesively bonded similar and dissimilar clamped plates

This experimental study investigates the low-speed impact behavior of adhesively bonded similar (Al–Al, St–St) and dissimilar (Al–St, St–Al) plates. The after-impact geometries of the front and back faces of the bonded plates, which were visualized by measuring the displacements, were in good agreement with the simulated surface geometries obtained by using explicit finite element method. The plate stiffness was affective on the deflections of the bonded plates; thus, the bonded Al–Al plates exhibited maximum deflections, contact durations, and minimal contact force levels, whereas the bonded St–St plates had minimum deflections, contact durations, and maximum contact force levels. As the impact energy is increased, the impact forces, durations, and deflections increased naturally; however, the impact force-time histories were not affected evidently. The bonded Al–Al plates can dissipate the impact energy more effectively than the bonded St–St plates. The experimental and simulated contact force-time histories were generally in good agreement. Based on the cross-section photographs of the damaged impact regions the bonded Al–Al plates with low stiffness can deform plastically and dissipate most of the impact energy, and the adhesive layer remains compatible with the deformation of the plates. The interfacial fractures appear along the back plate–adhesive interface for the low impact energy but along both front and back plate–adhesive interfaces and cracks propagated to the back interface to lower interface through the adhesive thickness near the boundaries of the impactor trace. The bonded St–St plates behave more rigid, transmit the impact energy directly to the adhesive layer and the high impact force distributions result severe fractures not only interfacially but also through the adhesive thickness. The color transformations, which are indications of fracture formation and propagation speed in some way, were observed around the adhesive fractures. Although the bonded St–Al and Al–St plates had a fracture mechanism similar to those of the bonded Al–Al plates but the color transformation near the fractures and the crack opening displacement levels were more evident. The existence of a stiffer plate affects considerably the damage formation in the adhesive layer and in the plates, whereas the less stiff plates can dissipate the impact energy by deforming plastically and the adhesive layer experiences less local damages.     

台阶搭接铝合金接头应力分布的数值分析

用弹塑性有限元法研究了被粘物上台阶高度和长度对铝合金单搭接接头胶层中应力分布的影响。结果表明,被粘物自由端内侧的台阶使搭接区接头端部处的应力峰值显著下降,应力向搭接区中部转移;胶层中应力峰值大体上随着台阶高度的增大而降低,随台阶长度的增大而向中部转移;当台阶高度为0．5mm而台阶长度为4．5mm时,接头上胶层中应力分布较好。     

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.     

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.     

Failure analysis of adhesively bonded tubular joints of laminated FRP composites subjected to combined internal pressure and torsional loading

Abstract

Finite element analysis has been carried in the present research to study individual and combined effect of internal pressure and torsional loading on stress and failure characteristics in case of an adhesively bonded Tubular Single Lap Joints (TSLJ) made of laminated Fiber reinforced polymer (FRP) composite materials. Effect of changing torsional load magnitude on an internally pressurised adhesively bonded TSLJ on interlaminar stresses and onset of different joint fracture modes (adhesion and cohesion failures) has also been studied in the present analysis. Three dimensional stress analysis of the adhesively bonded TSLJ has been carried out through suitable ANSYS Parametric Design Language (APDL) of ANSYS 14.0. Tsai-Wu coupled stress criterion has been used for predicting the onset of joint failures in the TSLJ. It has been observed that stresses (σ_r, σ_θ, σ_z, τ_rz) induced within the joint region under pure internal pressure loading are least affected through introduction of a torsional loading in the TSLJ. However, the stresses (τ_rθ and τ_θz) which are considered to be significant under pure torsional loading get tremendously enhanced due to the varying torsional loading. The interface between the outer tube and adhesive of the TSLJ has been observed to be the most critical bondline interface which is prone to undergo adhesion failure towards the free edges under pure internal loading conditions. However, under pure torsional loading conditions it tends to fracture through adhesion failure towards the clamped edge of the TSLJ. Under combined torsional and internal pressure loading the joint fails towards the clamped edge of the along the critical path which happens to be within the bondline interface, indicating predominance of torsional loading over the pure internal pressure loading. A comparative study based on the magnitude of failure index revealed that torsional loading marginally affects the joint failure as the internal pressure loading improves the compactness of the bonded joint hence improving the resistance of the TSLJ against initiation of joint fractures.     

Numerical analysis of adhesively bonded T-joints with structural sandwiches and study of design parameters

Adhesively bonded T-joints are extensively used in assembling sandwich structures. The advantage of adhesive bonded joints over bolted or riveted joints is that the use of fastener holes in mechanical joints inherently results in micro and local damages to the composite laminate during their fabrication. One type of adhesive joint in such structures is the T-joint between sandwich panels. The aim of this research paper is to study, by numerical analysis, the effect of fillet geometry and core material of sandwich panels on the performance of T-joints. The base angle of the core triangle (fillet) is the most important geometry parameter of the triangular T-joint. Nine geometrical models with different base angles of the core triangle are made to investigate the effect of the base angle on the performance of the T-joints. It should be mentioned that the base angle in the triangular foam is changed, so that the final volume of the filler is kept constant in all the cases. Different foams with different stiffness are used to model the core of the panels to study the effect of the core material of sandwich panels. To model the adhesive between joint components, contact elements and cohesive zone material models are used. Therefore, failure of adhesive and separation of joint elements can be modeled. Damage and core shear failure of the base panel are modeled by using a written macro-code in the ANSYS finite element method (FEM) program. The ultimate strength of the joint in each case is calculated by modeling adhesive failure and core shear failure of the sandwich panels. Finally, the results of FEM are validated by experimental results available in the literature. In general, the failure load predicted by the FEM is within 5% of the experimental results. The best angle of the core triangle was found to be 45°. Also, the results showed that by changing the core material of the sandwich panel, the joint failure load is also changed.