Theoretical and experimental studies for the failure criterion of adhesively bonded joints

The objective of this work was to develop a criterion for predicting the failure strength of joints bonded by ductile adhesives. To obtain the criterion, first, fracture tests were carried out on T-peel joints and single-lap joints with various joint geometries, adhesives, and adherend materials. Then using the fracture loads obtained in the tests, a finite element analysis was performed by which the stresses in the adhesive joints were calculated. It is concluded that the failure of an adhesively bonded joint occurs when the maximum of the ratio of the mean to effective stresses exceeds a certain value, which can be considered a new material constant of a ductile adhesive.     

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

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

Progressive failure and experimental study of adhesively bonded composite single-lap joints subjected to axial tensile loads

Experimental tests and finite element method (FEM) simulation were implemented to investigate T700/TDE86 composite laminate single-lap joints with different adhesive overlap areas and adherend laminate thickness. Three-dimensional finite element models of the joints having various overlap experimental parameters have been established. The damage initiation and progressive evolution of the laminates were predicted based on Hashin criterion and continuum damage mechanics. The delamination of the laminates and the failure of the adhesive were simulated by cohesive zone model. The simulation results agree well with the experimental results, proving the applicability of FEM. Damage contours and stress distribution analysis of the joints show that the failure modes of single-lap joints are related to various adhesive areas and adherend thickness. The minimum strength of the lap with defective adhesive layer was obtained, but the influence of the adhesive with defect zone on lap strength was not decisive. Moreover, the adhesive with spew-fillets can enhance the lap strength of joint. The shear and normal stress concentrations are severe at the ends of single-lap joints, and are the initiation of the failure. Analysis of the stress distribution of SL-2-0.2-P/D/S joints indicates that the maximum normal and shear stresses of the adhesive layer emerge on the overlap ends along the adhesive length. However, for the SL-2-0.2-D joint, the maximum normal stress emerges at the adjacent middle position of the defect zone along the adhesive width; for the SL-2-0.2-S joint, the maximum normal stress and shear stress emerge on both edges along the adhesive width.     

Analytical solutions for nonlinear analysis of composite single-lap adhesive joints

This paper presents analytical nonlinear solutions for composite single-lap adhesive joints. The ply layups of each composite adherend can be arbitrary, but in the overlap region the ply layups of the upper and lower adherends are assumed to be symmetrical about the adhesive layer. In the present formulation, equilibrium equations of the overlap are derived on the basis of geometrical nonlinear analysis. The governing equations are presented in terms of adherend displacements by taking into account large deflections of the overlap adherends and adhesive shear and peel stresses simultaneously. Closed-form nonlinear solutions for adherend displacements, an edge moment factor and adhesive stresses are formulated and then simplified for practical applications. To verify the present analytical solutions for nonlinear analysis of composite single-lap joints, the geometrically nonlinear 2D finite element analysis is conducted using commercial package MSC/NASTRAN. The numerical results of the edge moment factor, deflections and adhesive stresses predicted by the present solutions correlate well with those of the geometrically nonlinear finite element analysis. This indicates that the present analytical solutions capture key features of geometrical nonlinearity of composite single-lap adhesive joints.     

Stress analysis and strength evaluation of single-lap band adhesive joints of dissimilar adherends subjected to external bending moments

Single-lap band adhesive joints of dissimilar adherends subjected to external bending moments are analyzed as a four-body contact problem using a two-dimensional theory of elasticity (plane strain state). In the analysis, the upper and lower adherends and the adhesive which are bonded in two regions are replaced by finite strips. In the numerical calculations, the effects of the ratio of Young's moduli of the adherends, the ratio of the adherend thicknesses, and the ratio of the band length to the half lap length on the stress distributions at the interfaces are examined. A method for estimating the joint strength is proposed using the interface stress and strain obtained by the analysis. An elasto-plastic finite element analysis (EP-FEA) was conducted for predicting the joint strength more exactly. Experiments to measure strains and the joint strength were also carried out. The results show that the strength of a single-lap band adhesive joint is almost the same as that of a single-lap adhesive joint in which the two adherends are completely bonded at the interfaces. Thus, the single-lap band adhesive joints are useful in the design of single-lap 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.     

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.     

Shear and peel stress analysis of an adhesively bonded scarf joint

The shear and peel stress distributions in a scarf joint made of two isotropic adherends with blunt adherend tips are analysed using a linear elastic analysis. The limits of the analysis with respect to adherend tip thickness have been investigated. A finite difference method is used to solve the differential equations for the shear and peel stress distributions over the joint. The boundary conditions used limit the analysis to the two adherends having the same thicknesses, lengths, and material properties. The adherends are modelled as plates with extensional and bending stiffnesses bonded together with an elastic interlayer. The stresses across the adhesive layer are assumed to be constant. The current analysis applied to cases known from the literature shows good agreement with the shear stresses but the peel stresses are overestimated.     

Strength Improvement of Adhesively-Bonded Joints Using a Reverse-Bent Geometry

Adhesive bonding of components has become more efficient in recent years due to the developments in adhesive technology, which has resulted in higher peel and shear strengths, and also in allowable ductility up to failure. As a result, fastening and riveting methods are being progressively replaced by adhesive bonding, allowing a big step towards stronger and lighter unions. However, single-lap bonded joints still generate substantial peel and shear stress concentrations at the overlap edges that can be harmful to the structure, especially when using brittle adhesives that do not allow plasticization in these regions. In this work, a numerical and experimental study is performed to evaluate the feasibility of bending the adherends at the ends of the overlap for the strength improvement of single-lap aluminium joints bonded with a brittle and a ductile adhesive. Different combinations of joint eccentricity were tested, including absence of eccentricity, allowing the optimization of the joint. A Finite Element stress and failure analysis in ABAQUS^® was also carried out to provide a better understanding of the bent configuration. Results showed a major advantage of using the proposed modification for the brittle adhesive, but the joints with the ductile adhesive were not much affected by the bending technique.     

Effect of hole drilling at the overlap on the strength of single-lap joints

Bonded unions are gaining importance in many fields of manufacturing owing to a significant number of advantages to the traditional fastening, riveting, bolting and welding techniques. Between the available bonding configurations, the single-lap joint is the most commonly used and studied by the scientific community due to its simplicity, although it endures significant bending due to the non-collinear load path, which negatively affects its load bearing capabilities. The use of material or geometric changes in single-lap joints is widely documented in the literature to reduce this handicap, acting by reduction of peel and shear peak stresses at the damage initiation sites in structures or alterations of the failure mechanism emerging from local modifications. In this work, the effect of hole drilling at the overlap on the strength of single-lap joints was analyzed experimentally with two main purposes: (1) to check whether or not the anchorage effect of the adhesive within the holes is more preponderant than the stress concentrations near the holes, arising from the sharp edges, and modification of the joints straining behaviour (strength improvement or reduction, respectively) and (2) picturing a real scenario on which the components to be bonded are modified by some external factor (e.g. retrofitting of decaying/old-fashioned fastened unions). Tests were made with two adhesives (a brittle and a ductile one) varying the adherend thickness and the number, layout and diameter of the holes. Experimental testing showed that the joints strength never increases from the un-modified condition, showing a varying degree of weakening, depending on the selected adhesive and hole drilling configuration.     

Closed-form solutions for elastic stress-strain analysis in unbalanced adhesive single-lap joints considering adherend deformations and bond thickness

A theoretical model is developed for the stress analysis in adhesive-bonded single-lap joints under tension, for which the two adherends could have different thicknesses and consist of different materials. A two-dimensional (2D) elasticity theory is adopted in the analysis, which simultaneously incorporates the complete strain-displacement and the complete stress-strain relationships for the adherends and adhesive. The approach provides a unified treatment for any possible adhesive layer flexibility and capable of satisfying the stress-free condition at the ends of the bondline. An explicit closed-form analytical solution is formulated for upper and lower adherends/adhesive stresses (strains) and tensile, shear and bending loads acting on the adherends along the overlap and then simplified for practical applications, and simple design formulae for adhesive stresses are produced. The results predicted by the present full and simplified solutions were compared with the previously theoretical solution by Bigwood and Crocombe (1989) [35], and the 2D geometrically nonlinear finite element model using MSC/NASTRAN. The agreement validates the present formulation and solutions for unbalanced bonded joints. The effects of the stiffness unbalanced parameters on the adhesive stress distributions were also discussed.     

Three-parameter,elastic foundation model for analysis of adhesively bonded joints

A novel three-parameter, elastic foundation model is proposed in this study to analyze interface stresses of adhesively bonded joints. The classical two-parameter, elastic foundation model of adhesive joints models the adhesive layer as a layer of normal and a layer of shear springs. This model does not satisfy the zero-shear-stress boundary conditions at the free edges of the adhesive layer due to the inherent flaw of the two-parameter, elastic foundation model, which violates the equilibrium condition of the adhesive layer. To eliminate this flaw, this study models the adhesive layer as two normal spring layers interconnected by a shear layer. This new three-parameter, elastic foundation model allows the peel stresses along the two adherend/adhesive interfaces of the joint to be different, and therefore, satisfies the equilibrium condition of the adhesive layer. This model regains the missing “degree of freedom” in the two-parameter, elastic foundation model of the adhesive layer by introducing the transverse displacement of the adhesive layer as a new independent parameter. Explicit closed-form expressions of interface stresses and beam forces are obtained. The new model not only satisfies all boundary conditions, but also predicts correctly which interface has the strongest stress concentration. The new model is verified by continuum models existing in the literature and finite element analysis. The new three-parameter, elastic foundation model provides an effective and efficient tool for analysis and design of general adhesive joints.     

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.     

An efficient analysis model for functionally graded adhesive single lap joints

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

Shear properties of isotropic conductive adhesive joints under different loading rates

Epoxy-based conductive adhesives have been widely used in the electronic field given the lead-free development of electronic packaging. The conductive adhesive joints must be subjected to shear loads during the service of electronic products considering the mismatch in mechanical properties between packaged chip and substrate. In this study, INSTRON 5544 universal material testing machine was used for tensile–shear tests of isotropic conductive adhesive joint specimens, which were prepared using pure copper plate adherend in the form of single-lap joints. Four loading rates, that is, 0.05, 0.5, 5, and 10 mm/min, were adopted. The relationship between shear load and displacement of two overlapping copper plates is deduced from a mechanical perspective. A mechanical model of the conductive adhesive shear specimen was developed by introducing dimensionless parameters, which are obtained from interfacial fracture energy and shear strength, to interpret the effect of loading rate on the shear properties of the conductive adhesive specimen considering the loading rate. Results show that this model can effectively reflect the relationship between shear load and displacement in the range of 0.05–10 mm/min.     

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

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

Strength of epoxy adhesive-bonded stainless-steel joints

The strength of stainless-steel joints bonded with two epoxy adhesives was investigated. The experimental programme included tests on single-lap and butt joints, as well as thick-adherend and napkin ring shear tests. Results suggested that the tensile and shear strengths of the epoxy adhesives were quite similar. However, finite element (FE) analyses raised doubts on the true adhesive strengths, due to the complex stress state in joint tests and pressure-dependent adhesive behaviour. In spite of some uncertainties, FE analyses showed that failure could be fairly well predicted by a maximum shear strain criterion.     

Failure behavior of adhesively bonded joints with a rubber modified epoxy adhesive under tensile-shear combined cyclic loading

Rubber-modified epoxy adhesives are used widely as structural adhesive owing to their properties of high fracture toughness. In many cases, these adhesively bonded joints are exposed to cyclic loading. Generally, the rubber modification decreases the static and fatigue strength of bulk adhesive without flaw. Hence, it is necessary to investigate the effect of rubber-modification on the fatigue strength of adhesively bonded joints, where industrial adhesively bonded joints usually have combined stress condition of normal and shear stresses in the adhesive layer. Therefore, it is necessary to investigate the effect of rubber-modification on the fatigue strength under combined cyclic stress conditions. Adhesively bonded butt and scarf joints provide considerably uniform normal and shear stresses in the adhesive layer except in the vicinity of the free end, where normal to shear stress ratio of these joints can cover the stress combination ratio in the adhesive layers of most adhesively bonded joints in industrial applications.

In this study, to investigate the effect of rubber modification on fatigue strength with various combined stress conditions in the adhesive layers, fatigue tests were conducted for adhesively bonded butt and scarf joints bonded with rubber modified and unmodified epoxy adhesives, wherein damage evolution in the adhesive layer was evaluated by monitoring strain the adhesive layer and the stress triaxiality parameter was used for evaluating combined stress conditions in the adhesive layer. The main experimental results are as follows: S–N characteristics of these joints showed that the maximum principal stress at the endurance limit indicated nearly constant values independent of combined stress conditions, furthermore the maximum principal stress at the endurance limit for the unmodified adhesive were nearly equal to that for the rubber modified adhesive. From the damage evolution behavior, it was observed that the initiation of the damage evolution shifted to early stage of the fatigue life with decreasing stress triaxiality in the adhesive layer, and the rubber modification accelerated the damage evolution under low stress triaxiality conditions in the adhesive layer.     

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

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

An investigation of fatigue failure prediction of adhesively bonded metal/metal joints

A fracture mechanics-based model for fatigue failure prediction of adhesive joints has been applied in this work. The model is based on the integration of the kinetic law of evolution of defects originated at stress concentrations within the joint. Final failure can be either brittle (fracture toughness-driven) or ductile (tensile/shear strength-driven) depending on the adhesive. The model has been validated against experiments conducted on single-lap shear joints bonded with a structural adhesive. Three different kinds of adhesives, namely a modified methacrylate, a one-part epoxy and a two-part epoxy supplied by Henkel, have been considered and three different overlap lengths have been tested. Fracture toughness and fatigue crack growth properties of the adhesives have been determined with mode I tests. The number of cycles to failure has been successfully predicted in several cases. It is interesting to notice that in the case of joints loaded at the same average shear stress, the shorter the joint, the longer the duration. This fact is also captured by the model.