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.     

Effect of Bondline Thickness on Mixed-Mode Fracture of Adhesively Bonded Joints

The effect of bondline thickness on the critical strain energy release rate (CSERR) was investigated using aluminum adherends and an epoxy adhesive. Complete mixed Mode I/II fracture envelopes for adhesive thicknesses ranging from 0.203 to 1.52 mm were developed using double cantilever beam (DCB), mixed-mode bending (MMB), and end notch flexure (ENF) tests methods. Bondline thickness strongly affects the CSERR for different amounts of Mode II component. Pure Mode II had the largest CSERR and showed monotonic increase with bondline thickness, whereas pure Mode I had the lowest CSERR and exhibited non monotonic relationship with bondline thickness. The shape and size of the plastic zone that develops prior to crack propagation was predicted by finite element analysis. Variation of CSERR as a function of adhesive layer thickness was shown to be related to the size of the plastic zone for Mode I and MMB 50% fracture. No correlation was observed for the MMB 75% and Mode II, however.     

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.     

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.     

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.     

Stress Analysis of Adhesively Bonded Electroprimed Steel Lap Shear Joints

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

Stress Analysis of Adhesively Bonded Electroprimed Steel Lap Shear Joints

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

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 Comparison of Numerous Lap Joint Theories for Adhesively Bonded Joints

Numerous authors have investigated the state of stress in the adhesive of adhesively bonded joints. They have made various assumptions concerning the behavior of the adhesive and adherends to yield tractable differential equations which remove the stress singularities which occur at the edges of the bi-material interfaces. By examining several test problems, this paper investigates the effect of these assumptions on predicted adhesive stress. It was found that predicted maximum adhesive shear stress is insensitive to underlying assumptions and that maximum adhesive peel stress is relatively unaffected by most assumptions except that neglecting shear deformation of the adherends can affect results by as much as 30%. Peel stresses from the well known theory of Goland and Reissner which neglects shear deformation of the adherends and makes several inconsistent assumptions vary as much as 30% from stresses from a consistent lap joint theory which considers shear deformation of the adherends. However, in most cases the effects of the inconsistencies cancel the effects of neglecting the shear deformation of the adherends and the variation is less than 15%. This paper points out that finite element analyses of bonded joints where one layer of 4 node isoparametric elements are used to model the adhesive give results very close to those from consistent lap joint theories.     

Similarity Concepts in the Fatigue Fracture of Adhesively Bonded Joints

Cyclic debond data obtained from fatigue testing of four different specimen geometries having the same adhesive is considered. Fatigue properties of the adhesive are characterized in terms of linear elastic fracture mechanics concepts whereby debond growth rates are correlated to appropriate mixed mode fracture parameters. Stress analyses of the four specimens under maximum load indicate that in most cases inclusion of geometric nonlinearities is required for the determination of the fracture parameters. For three of the specimens considered, the debond growth laws based on total energy release rate as correlating mixed-mode fracture parameter were found to be similar. A number of potential reasons for the lack of similarity in debond growth laws in all four specimens are explored.     

Experimental and Numerical Study of Adhesively Bonded CFRP Scarf-Lap Joints Subjected to Tensile Loads

The tensile performance of adhesively bonded CFRP scarf-lap joints was investigated experimentally and numerically. In this study, scarf angle and adherend thickness were chosen as design parameters. The lap shear strength is not directly proportional to scarf angle and adherend thickness for the brittle adhesive studied in the paper. The major failure mode includes cohesive shear failure and adherend delamination failure. The results present a stepped failure morphology along the bondline in the adhesive layer. A finite element model based on cohesive zone model was established to further investigate the stress distribution of scarf-lap joints with different lap parameters. The numerical results were compared with the experiment results, showing a good agreement, thus verifying the validity of the established numerical model.     

Joint Strength Optimization of Adhesively Bonded Patches

Aircraft face damage from impact with objects or birds or due to ageing that leads to fatigue cracks. The conventional methods of repairing aircraft metallic structures generally include the use of a plate joined by screws or rivets. Although these methods are efficient in the short term, they introduce stress concentrations leading to the initiation of new cracks that are difficult or impossible to detect by non-destructive methods. For these reasons, it is necessary to develop new methods to improve the behaviour of the structure (especially for long term) and its manufacture cost. One of the solutions that have been studied by the aeronautical industry is the use of patches bonded with structural adhesives. However, adhesively bonded patches have problems of stress concentration at the edges where crack initiation is prone to occur. This problem can be reduced by the use of a taper and a spew fillet at the end of the patch and by the use of a mixed adhesive technique where a ductile adhesive is placed at the edges of the patch. Double strap specimens from 3 mm thick 6063-T6 aluminium alloy sheet were analysed. Aluminium and straps (or patches) with an internal taper, an adhesive spew fillet, and dual adhesives were experimentally tested. The results obtained were explained by a finite element analysis. A taper angle is beneficial only for the brittle adhesive. The use of two adhesives is advantageous for the taperless configuration.     

Improvement in Strength of Adhesively Bonded Single-Lap Joints Using Reinforcements

In order to enhance the strength of adhesively bonded single-lap joints (SLJs), the adhesively bonded SLJs with reinforcements were proposed. Adhesively bonded SLJs of different substrates and with different reinforcements were investigated experimentally and numerically. Scanning electron microscopy was performed on the fracture surfaces of the joints to analyze the failure mechanism. Shear stresses and peeling stresses of the adhesive layer were calculated with finite element analyses (FEA). Results showed that the deformation of the joints decreased with an increase in stiffness at the end of the overlap region. The strength increase in adhesively bonded SLJs with reinforcements was validated by the results from experimental tests and FEA.     

A Method of Estimating the Strength of Adhesive Bonded Joints of Metals

The strength of adhesive bonded joints is investigated both analytically and experimentally. The deformed states of lap joints under tensile shear loading are analysed by the finite element method on the assumption of elastic deformation. A method of using the adhesive strength law is proposed to estimate the joint strength. The adhesive strength law is experimentally determined by subjecting butt joints of two thin-walled tubes to combined axial load and torsion. The strength of lap joints is determined by adopting the adhesive strength law to the adhering interface as well as the strength law of adherend and adhesive resin. The calculated strain distribution and strength of the joints are compared with the experimental results. The effects of the joint configurations on the deformation and strength are discussed. It is shown that the proposed method is useful to predict the joint strength.     

A Method of Estimating the Strength of Adhesive Bonded Joints of Metals

The strength of adhesive bonded joints is investigated both analytically and experimentally. The deformed states of lap joints under tensile shear loading are analysed by the finite element method on the assumption of elastic deformation. A method of using the adhesive strength law is proposed to estimate the joint strength. The adhesive strength law is experimentally determined by subjecting butt joints of two thin-walled tubes to combined axial load and torsion. The strength of lap joints is determined by adopting the adhesive strength law to the adhering interface as well as the strength law of adherend and adhesive resin. The calculated strain distribution and strength of the joints are compared with the experimental results. The effects of the joint configurations on the deformation and strength are discussed. It is shown that the proposed method is useful to predict the joint strength.     

Effect of Curing Pressure on the Strength of Adhesively Bonded Joints

It is important to be able to predict the mechanical response of adhesively bonded joints. To succeed in this, the accurate simulation of the behavior of adhesively bonded joints is an essential requirement because of the strain rate, temperature, and hydrostatic sensitivity of adhesive properties, which should be taken into consideration when developing a material model [1-111, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]. On the other hand, the load capabilities of adhesively bonded joints are affected by both applied pressure and temperature during cure. For this reason, in this study, the tensile load capabilities of single lap joints (SLJs) bonded with a flexible adhesive that possesses pressure-sensitive properties were experimentally investigated with respect to the applied pressure during the curing operation, and the experimental results were compared with finite element analysis (FEA) results. Finally, in addition to other parameters, such as the dependence on strain rate and the lack of yield criteria of adhesives, it was seen that the residual thermal stresses that occurred as a result of the applied pressure during the curing process at elevated temperature need to be taken into consideration to accurately simulate the mechanical behavior of adhesively bonded joints.     

Effect of Curing Pressure on the Strength of Adhesively Bonded Joints

It is important to be able to predict the mechanical response of adhesively bonded joints. To succeed in this, the accurate simulation of the behavior of adhesively bonded joints is an essential requirement because of the strain rate, temperature, and hydrostatic sensitivity of adhesive properties, which should be taken into consideration when developing a material model [1-11 Dean , G. D. and Crocker , L. E. , Comparison of the Measured and Predicted Deformation of an Adhesively Bonded Lap-Joint Specimen, NPL CMMT(A) 293 ( National Physical Laboratory , Teddington , UK , 2000 ). Read , B. E. , Dean , G. D. , and Ferriss , D. H. , An Elastic–Plastic Model for the Non-linear Mechanical Behaviour of Rubber-Toughened Adhesives, NPL CMMT(A) 289 ( National Physical Laboratory , Teddington , UK , 2000 ). Broughton , W. R. , Crocker , L. E. , and Urquhart , J. M. , Strength of Adhesive Joints: A Parametric Study , NPL MATC(A) 27 ( National Physical Laboratory , Teddington , UK , 2000 ). Dean , G. D. , Crocker , L. E. , Read , B. , and Wright , L. , Int. J. Adhes. Adhes. 24 , 295 – 306 ( 2004 ). Adams , R. D. , Coppendale , J. , Mallick , V. , and Al-Hamdan , H. , Int. J. Adhes. Adhes. 12 ( 3 ), 185 – 190 ( 1992 ). Wang , C. H. and Chalkley , P. , Int. J. Adhes. Adhes. 20 ( 2 ), 155 – 164 ( 2000 ). Adams , R. D. , The Mechanics of Bonded Joints Structural Adhesives in Engineering ( ImechE Conference Publications , Suffolk , UK 1986 ). Harris , J. A. and Adams , R. D. , Int. J. Adhes. Adhes. 4 ( 2 ), 65 – 78 ( 1984 ). Crocombe , A. D. , Int. J. Adhes. Adhes. 15 ( 1 ), 21 – 27 ( 1995 ). Zgoul , M. and Crocombe , A. D. , Int. J. Adhes. Adhes. 24 ( 4 ), 355 – 366 ( 2004 ). Adams , R. D. and Harris , J. A. , Int. J. Adhes. Adhes. 7 ( 2 ), 69 – 80 ( 1987 ). ]. On the other hand, the load capabilities of adhesively bonded joints are affected by both applied pressure and temperature during cure. For this reason, in this study, the tensile load capabilities of single lap joints (SLJs) bonded with a flexible adhesive that possesses pressure-sensitive properties were experimentally investigated with respect to the applied pressure during the curing operation, and the experimental results were compared with finite element analysis (FEA) results. Finally, in addition to other parameters, such as the dependence on strain rate and the lack of yield criteria of adhesives, it was seen that the residual thermal stresses that occurred as a result of the applied pressure during the curing process at elevated temperature need to be taken into consideration to accurately simulate the mechanical behavior of adhesively bonded joints.