Finite element analysis of torsional free vibration of adhesively bonded single-lap joints

Adhesively bonding is a high-speed fastening technique which is suitable for joining advanced lightweight sheet materials that are dissimilar, coated and hard to weld. In this paper, the free torsional vibration characteristics of adhesively bonded single-lap joints are investigated in detail using finite element method. The effectiveness of finite element analysis technique used in the study is validated by experimental tests. The focus of the analysis is to reveal the influence on the torsional natural frequencies and mode shapes of these joints caused by variations in the material properties of adhesives. It is shown that the torsional natural frequencies and the torsional natural frequency ratios of the adhesively bonded single-lap joints increases significantly as the Young′s modulus of the adhesives increase, but only slight changes are encountered for variations of Poisson's ratio. The mode shapes analysis show that the adhesive stiffness has a significant effect on the torsional mode shapes. When the adhesive is relatively soft, the torsional mode shapes at the lap joint are slightly distorted. But when the adhesive is relatively very stiff, the torsional mode shapes at the lap joint are fairly smooth and there is a relatively higher local stiffening effect. The consequence of this is that higher stresses will be developed in the stiffer adhesive than in the softer adhesive.     

Characterization of fracture in adhesively bonded double-lap joints

A broad finite element study was carried out to understand the stress fields and stress intensity factors behavior of cracks in adhesively bonded double-lap joints, which are representative of loading in real aerospace structures. The interaction integral method and fundamental relationships in fracture mechanics were used to determine the mixed-mode stress intensity factors and associated strain energy release rates for various cases of interest. The numerical analyses of bonded joints were also studied for various kinds of adhesives and adherends materials, joint configurations, and thickness of adhesive and different crack lengths. The finite element results obtained show that the patch materials of low stiffness, low adhesive moduli and low tapering angles are desirable for a strong double-lap joint. In the double-lap joint, the shearing-mode stress intensity factor is always larger than that of the opening-mode and both shearing and opening mode stress intensity factors increase as the crack length increases, but their amplitudes are not sensitive to adhesive thickness. Results are discussed in terms of their relationship to adhesively bonded joints design and can be used in the development of approaches aimed at using adhesive bonding and extending the lives of adhesively bonded repairs for aerospace structures.     

Numerical and experimental investigations of the dynamic response of bonded beams with a single-lap joint

The need to design lightweight structures and the increased use of lightweight materials in industrial fields, have led to wide use of adhesively bonding in recent years. In the design of mechanical systems, which consist of adhesively bonded joints, for minimum vibration response, a specific knowledge of the damping capacity of the component materials and joints is important. It is believed that adhesively bonded joints act to augment the system damping capacity in view of the increasing use of viscoelastic materials in their design. The aim of this paper is to provide an efficient numerical technique for the prediction of the dynamic response of bonded beams with a single-lap joint and to validate the predictions via experimental tests. The finite element method was used to predict the natural frequencies, mode shapes and frequency response functions of the beams. The dynamic test software and the data acquisition hardware were used in the experimental measurement of the dynamic response of the joints. The frequency response functions of the joints of different adherend widths and of different adhesive layer thickness were measured. The frequency response functions and mode shapes predicted using the finite element method were compared with those measured experimentally. The coordination of the numerical and experimental techniques makes it possible to find an efficient tool for studying the dynamic response of bonded beams with a single-lap joint.     

Fatigue Analysis of Adhesive Joints Under Vibration Loading

Adhesively bonded joints have been used extensively for many structural applications. However, one disadvantage usually limiting the service life of adhesive joints is the relatively low strength for peel loading, especially under dynamic cyclic loading such as impulsive or vibrational forces. Moreover, accurately predicting the fatigue life of bonded joints is still quite challenging. In this study, a combined experimental–numerical approach was developed to characterize the effect of the cyclic-vibration-peel (CVP) loading on adhesively bonded joints. A damage factor is introduced into the traction-separation response of the cohesive zone model (CZM) and a finite element damage model is developed to evaluate the degradation process in the adhesive layer. With this model, the adhesive layer stress states before and after being exposed to various CVP loading cycles are investigated, which reveals that the fatigue effect of the CVP loading starts first in the regions close to the edges of the adhesive layer. A good correlation is achieved when comparing the simulation results to the experimental data, which verifies the feasibility of using the proposed model to predict the fatigue life of adhesively bonded joints under the CVP type of loading.     

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.     

Numerical study of the local behaviour of adhesive bonds under dynamic loading

Nowadays, adhesively bonded structures are widely used in the transport sector for the development of lightweight vehicles. In order to guarantee passenger safety, it is thus necessary to understand the behaviour of such assemblies under dynamic and combined loadings. This paper presents a numerical study of the local behaviour of adhesively bonded assemblies under dynamic loading. In the first part, the ASTM D950-03 block impact test is studied. This device does not enable a homogeneous loading of the adhesive and causes stress concentrations. On the basis of existing quasi-static works, strategies are then implemented at a local scale. By combining a specific substrate geometry and by limiting the stiffness gradient between the substrates and the adhesive, results show that it is possible to obtain a qualitatively acceptable stress fields in the adhesive for mechanical characterization under dynamic loadings. The Arcan TCS device mentioned below uses such solutions to characterize the mechanical behaviour of bonded joints subjected to combined quasi-static loadings. In this study, the question of its extensibility to dynamic loadings by the use of an impactor guided into a drop tower is investigated. A dedicated finite element model is built under the plane stress assumption. The stress distributions in the adhesive are analysed through time and space for several loading conditions. The stress versus time signals are then compared with the results coming from modal analysis in order to highlight the vibration behaviour of the device, directly linked to the 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.     

Flexural behavior of metallic fiber-reinforced adhesively bonded single lap joints

Incorporation of additives into the adhesive layer in adhesively bonded joints can improve the stress distriution in the adhesive layer and increase adhesive toughness. In this paper, the geometric and material parameters of metal fibers utilized for strengthening adhesively bonded single lap joints under flexural loading were investigated by using experimental investigations and finite element modeling. According to the experimental results, incorporating metal fibers in the adhesive layer of a bonded joint can have a significant impact on the flexural load bearing of the joint. This was in relationship with the numerical results foreseeing enhanced stress distributions of the adhesive layer, when the metal fibers were added to the adhesive layer. Some important parameters in the design of metal fiber-reinforced adhesive joints include the volume fraction (the distance between the fibers and the fiber diameter), orientation, and mechanical properties of the fibers. It was concluded that the peak normal stresses in the adhesive layer can be reduced, and consequently the load bearing of the joint can be improved by reducing the distance between the fibers, increasing the fiber diameter and choosing a stiffer material for the fibers in the longitudinal direction.     

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.     

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.     

Stress Analysis of Tubular Adhesive Joints with Delaminated Adherend

The use of adhesive joints is becoming increasingly important in aerospace, automotive and other industries where the use of traditional fasteners is discouraged. When using composite adherends, the use of adhesively bonded joints is preferable rather than the traditional bolts and other types of fasteners, because they do not require holes, thereby removing the problems of stress concentrations around the holes. However, when using an adhesively bonded joint, there will be concentrations of the distributions of shear and peel stresses within the adhesive layer which should be controlled effectively. Therefore, the investigation of such stress variation has attracted many researchers. The aforementioned stress distributions become more complicated if the composite adherend contains a pre-existing delamination. Delamination is one of the most common failure modes in laminated composite materials; it can occur due to sudden impact by an external object, during the manufacturing process (e.g., during the filament winding process), or as a result of excessive stresses due to an applied load. It is clear that the existence of a delamination in any composite structure causes a reduction in its stiffness and in some critical situations, it may cause complete failure. This paper investigates the effect of delamination on the structural response of an adhesively bonded tubular joint with composite and aluminum adherends. The finite element method, using the commercial package ABAQUS, is used to conduct a parametric investigation. The effects of the delamination's spatial location, length, width, and the applied loading are studied. Results provide interesting insight (not necessarily intuitive) into the effect of an interlayer delamination on the stress distribution within the adhesive.     

Analysis of the adhesively bonded three-point bending specimen for evaluation of adhesive shear behaviour

The adhesive shear stress-strain behaviour is an essential input for the design of structural adhesive joints. Relative to current standard tests, the main advantage of bonded beams is reducing spurious adhesive joint end effects on strength measurements. A beam model was developed in this work for the three-point bending test considering metal adherends, support effects and adhesive elastic-perfectly plastic stress-strain behaviour. Model predictions were in good agreement with finite element analyses for specimens with the thin bondlines typical of structural joints. The present results show that the adhesively bonded three-point bending test can be an interesting approach for the thin bondlines used in structural joints. Nevertheless, there are limitations on the range of measurable properties and data analysis requires models such as the one developed herein.     

Cohesive/adhesive failure interaction in ductile adhesive joints Part I: A smeared-crack model for cohesive failure

This paper proposes a new methodology for the finite element (FE) modelling of failure in adhesively bonded joint. Unlike current methods, cohesive and adhesive failures are treated separately. Initial results show the method׳s ability to give accurate prediction of failure of adhesive joints subjected to thickness-induced constraint and complex multi-axial loading using a single set of material parameters. The present paper (part I), focuses on the development of a smeared-crack model for cohesive failure. Model verification and validation are performed comparing the model predictions with experimental data from 3 point bending End Notched Flexure (3ENF) and Double Cantilever Beam (DCB) fracture tests conducted on adhesively bonded composite panels of different adhesive thicknesses.     

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

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

Numerical Study of Adhesive Single-Lap Joints with Composite Adherends Subjected to Combined Tension–Torsion Loads

The present investigation focuses on modifying the strength of single-lap adhesively bonded joints under tension–torsion loading with the use of three-dimensional finite element (FE) modeling. A single-lap adhesively bonded joint is reinforced by fibers and analyzed by means of ABAQUS-6.9.1 FE code. The adherends are considered to be made of orthotropic materials, while the adhesive is neat resin or reinforced by various types of fibers. The carbon and glass unidirectional fibers are used for adhesive reinforcement. In the FE modeling, the behavior of all the members is assumed to be linear elastic. The ultimate bond strength is increased as the fiber volume fraction in the adhesive is increased. By changing the properties and the behavior of the adhesive from neat resin (isotropic) to fiber composite adhesive (orthotropic) and with various fiber volume fractions and by changing the orientation of the fibers in the adhesive region with respect to the global axes, the bond strength in tension–torsion loadings are changed. Also, the excessive adhesive layer is modeled and its effect on the joint strength is investigated.     

Fatigue strength estimation of adhesively bonded tongue and groove joint of thick woven composite sandwich structures using genetic algorithm approach

In the present work, the fatigue behavior of tongue and groove joints bonded by a toughened epoxy adhesive was investigated. Axial cyclic tests were performed by different design configuration conditions and the effects of design parameters were evaluated. The bonding strength of adhesives under fatigue loading is influenced by many factors such as, the length of bondline, adhesive thickness, traverse pre-stress on near the free edges of bond line and material of the joining parts. Since all these factors affect the fatigue strength of the adhesively joined parts, the effects of these parameters need to be investigated. The present paper describes the use of the stochastic search process that is the basis of a Genetic Algorithm, in developing fatigue strength estimation of adhesively bonded thick woven E-glass/vinyl ester laminates. Non-linear estimation models were developed using genetic algorithm. Developed models are validated with experimental data. Genetic Algorithm Fatigue Strength Estimation Model for Tongue and Groove Joints was developed to estimate the fatigue strength of the adhesively bonded joint. The strongest adhesively bonded joints can be achieved by selecting optimum design parameters obtained from the models. The logarithmic number of cycles was increased 2.46 times by selecting aluminum EN AW 5083 insert instead of composite insert materials. The joint fatigue strength was significantly improved by selecting appropriate design parameter values.     

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.     

Three dimensional finite element analysis of bi-adhesively bonded double lap joint

Hybrid-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 flexible adhesive at the ends. In this study, the effect of the hybrid-adhesive bondline on the shear and peeling stresses of a double lap joint were investigated using a three-dimensional finite element model. We developed a three dimensional model of the double lap joint based on solid and contact elements. Contact problem is considered to model the interface as two surfaces belonging to adherend and adhesive. Finite element analyses were performed for four different bond-length ratios (0.2,0.4,0.7 and 1.3). The results show that the stress components can be optimized using appropriate bond-length ratios. To validate the finite element analysis results, comparisons were made with available closed-form solutions. The numerical results were found in good agreement with the analytical solutions.     

Review on adhesive joints and their application in hybrid composite structures

Composites have been used extensively in various engineering applications including automotive, aerospace, and building industries. Hybrid composites made from two or more different reinforcements show enhanced mechanical properties required for advanced engineering applications. Several issues in composites were resolved during the last few years through the development of new materials, new methods and models for hybrid joints. Many components in automobile are joined together either by permanent or temporary fastener such as rivets, welding joint and adhesively bonded joints. Increasing use of bonded structures is envisaged for reducing fastener count and riveted joints and there by drastically reducing assembly cost. Adhesive bonding has been applied successfully in many technologies. In this paper, scientific work on adhesively bonded composites and hybrid composites are reviewed and discussed. Several parameters such as surface treatment, joint configuration, material properties, geometric parameters, failure modes, etc. that affect the performance of adhesive bonded joints are discussed. Environmental factors like pre-bond moisture and temperature, method of adhesive application are also cited in detail. A specific case of adhesive joints in hybrid bonded-bolted joints is elaborated. As new applications are expanding in the field of composites joining and adhesive joints, it is imperative to use information on multiple adhesives and their behaviour in different environmental conditions to develop improved adhesive joint structure in mechanical applications.     

Determination of traction-separation laws on an acrylic adhesive under shear and tensile loading

Structural acrylic adhesives are of special interest because those adhesives are cured at room temperature and can be bonded to oily substrates. To use those adhesives widely for structural bonding, it is necessary to clarify the methodology for predicting strengths of bonding structures with those adhesives. Recently, cohesive zone models (CZMs) have been receiving intensive attentions for simulation of fracture strengths of adhesive joints, especially when bonded with ductile adhesives. The traction-separation laws under mode I and mode II loadings require to estimate fracture toughness of adhesively bonded joints. In this paper, the traction-separation laws of an acrylic adhesive in mode I and mode II were directly obtained from experiments using Arcan type adhesively bonded specimens. The traction-separation laws were determined by simultaneously recording the J-integral and the opening displacements in the directions normal and tangential to the adhesive layer, respectively.