Prediction of the tensile load-bearing capacity of a co-cured single lap joint considering residual thermal stresses

In this paper, stress distributions in a co-cured single lap joint subjected to a tensile load were investigated using the finite element analysis. Residual thermal stresses, which resulted from the curing process of the co-cured single lap joint, were also considered. Since the adhesive layer in the co-cured single lap joint was about 10 μm thick, very thin compared with the thickness of both adherends, the interface between the steel and composite adherends was assumed to be perfectly bonded. The co-cured single lap joint was analyzed with respect to several bond parameters such as the bond length and stacking sequence of the composite adherend. The failure mechanism of the co-cured single lap joint was partial cohesive failure in the composite material, which was significantly affected by the interfacial tensile stress at the free edge of the co-cured single lap joint. Interfacial tensile stress was a primary factor that caused interfacial delamination between the steel and composite adherends in the co-cured single lap joint. Finally, tensile load-bearing capacities calculated from the Ye-delamination failure criterion were compared with the experimental results, and relatively good agreement was found.     

Optimal Design of the Adhesively-Bonded Tubular Single Lap Joint

In this paper, a method for the optimal design of the adhesively-bonded tubular single lap joint was proposed based on the failure model of the adhesively-bonded tubular single lap joint. The failure model incorporated the nonlinear mechanical behavior of the adhesive as well as the different failure modes in which the adhesive failure mode changed from bulk shear failure, via transient failure, to interfacial failure between the adhesive and the adherend, according to the magnitudes of the residual thermal stresses induced by fabrication.

The effects of the design parameters for the adhesively-bonded tubular single lap joint, such as the thicknesses of adhesive layer and adherends, the bonding length, and the scarfs of adherends, on the torque transmission capability and the efficiency of the adhesive joint were investigated.     

Optimal Design of the Adhesively-Bonded Tubular Single Lap Joint

In this paper, a method for the optimal design of the adhesively-bonded tubular single lap joint was proposed based on the failure model of the adhesively-bonded tubular single lap joint. The failure model incorporated the nonlinear mechanical behavior of the adhesive as well as the different failure modes in which the adhesive failure mode changed from bulk shear failure, via transient failure, to interfacial failure between the adhesive and the adherend, according to the magnitudes of the residual thermal stresses induced by fabrication.

The effects of the design parameters for the adhesively-bonded tubular single lap joint, such as the thicknesses of adhesive layer and adherends, the bonding length, and the scarfs of adherends, on the torque transmission capability and the efficiency of the adhesive joint were investigated.     

Geometric Factors Impacting Adhesive Lap Joint Strength and Design

Too often adhesive thickness, adherend thickness and other geometric factors are not explicitly considered in adhesive joint design. This study includes experimental and computational research exploring the means of enhancing the engineering design process for adhesive lap joints to include such effects. It clearly demon-strated that both the cleavage stresses and the shear stresses, near the bond termini, play important roles in lap 'shear' joint failure. Finite Element and Fracture Mechanics analyses were used to examine the energy release rate applied to growth of cracks in adhesive lap joints. Lap joints with similar geometries to those analyzed were designed, fabricated and tested. In a separate set of experiments the bond termini were constrained in the direction normal to the uniaxial loading. If the strength of lap shear joints is dominated by the adhesive shear strength, then constraining the lateral motion of the bond termini should have little or no effect on the overall shear strength of the adhesive joint. This work clearly demonstrates that this is not the case. If cleavage stresses are important in lap joints then constraining the bond termini, in a direction normal to the bond area, should have a commensurate effect on the overall strength of the lap joint. None of the ASTM standardized 'lap shear tests' provide any insight into this premise. This paper also presents analyses and experimental results for lap joints to which several methods of lateral constraint were applied near the bond termini. The analytical and numerical methods described and used for explaining and predicting such effects might be a useful adhesive joint design tool.     

A Method of Predicting the Stresses in Adhesive Joints after Cyclic Moisture Conditioning

The durability of adhesive joints is of special concern in structural applications and moisture has been identified as one of the major factors affecting joint durability. This is especially important in applications where joints are exposed to varying environmental conditions throughout their life. This paper presents a methodology to predict the stresses in adhesive joints under cyclic moisture conditioning. The single lap joints were manufactured from aluminium alloy 2024 T3 and the FM73®-BR127® adhesive-primer system. Experimental determination of the mechanical properties of the adhesive was carried out to measure the effect of moisture uptake on the strength of the adhesive. The experimental results revealed that the tensile strength of the adhesive decreased with increasing moisture content. The failure strength of the single lap joints also progressively degraded with time when conditioned at 50°C, immersed in water; however, most of the joint strength recovered after drying the joints. A novel finite element based methodology, which incorporated moisture history effects, was adopted to determine the stresses in the single lap joints after curing, conditioning, and tensile testing. A significant amount of thermal residual stress was present in the adhesive layer after curing the joints; however, hygroscopic expansion after the absorption of moisture provided some relief from the curing stresses. The finite element model used moisture history dependent mechanical properties to predict the stresses after application of tensile load on the joints. The maximum stresses were observed in the fillet areas in both the conditioned and the dried joints. Study of the stresses revealed that degradation in the strength of the adhesive was the major contributor in the strength loss of the adhesive joints and adhesive strength recovery also resulted in recovered joint strength. The presented methodology is generic in nature and may be used for various joint configurations as well as for other polymers and polymer matrix composites.     

Comparison of cohesive zone elements and smoothed particle hydrodynamics for failure prediction of single lap adhesive joints

This research investigates the use of a meshless smoothed particle hydrodynamics (SPH) method for the prediction of failure in an adhesively bonded single lap joint. A number of issues concerning the SPH based finite element modelling of single lap joints are discussed. The predicted stresses of the SPH finite element model are compared with the results of a cohesive zone based finite element model. Crack initiation and crack propagation in the adhesive layer are also studied. The results show that the peel stresses predicted by the SPH finite element model are higher and the shear stresses are lower than those predicted by the cohesive zone finite element model. The crack initiation and propagation response of the two models is similar, however, the SPH finite element model predicted a lower failure load than the cohesive zone finite element model. It is concluded that the current implementation of SPH method is a promising method for modelling cohesive failure in bonded joins but requires further development to allow for interfacial crack growth and better stress prediction under tensile loading to compete with existing methods.     

A numerical and experimental study of preformed angle in the lap zone on adhesively bonded steel single lap joint

The effect of a preformed angle in the lap zone of steel adherends on the stress distribution in adhesively bonded single lap joints was investigated using an elasto-plastic finite element analysis (FEA). The ultimate loads of the joints were determined by shear tests and the failure surfaces of the lap zone were analyzed using scanning electron microscopy (SEM). The results from the numerical simulation showed that all the peak stresses in the mid-bondline of the adhesively bonded single lap joint were reduced as the preformed deflection angle was increased from 0° to 15°. The highest value of the average ultimate load of the experimental joints occurred when the preformed angle was equal to 7° (about 64% higher than the standard one). The SEM images also indicated that the failure mode in the overlap zone of the joint changed from that of a mainly adhesion one to a mixed one as the preformed angle increased.     

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.     

A study on the lap shear strength of a co-cured single lap joint

In this paper, the lap shear strength of a co-cured single lap joint subjected to a tensile load was investigated by experimental analysis. Co-cured joint specimens with several different bonding parameters such as bond length, surface roughness, and stacking sequence of the composite laminate were fabricated and tested. The dependence of the lap shear strength of the co-cured joint on the bonding parameters was investigated from the experimental results. The failure mechanism of the co-cured single lap joint was partially cohesive failure. The lap shear strength of the co-cured single lap joint was significantly affected by the bond length and the stacking sequence of the composite laminate. However, the effect of surface roughness on the lap shear strength of the co-cured single lap joint was not so significant.     

An improved four-parameter model on stress analysis of adhesive layer in plated beam

The prediction of stresses in an adhesive layer is helpful in revealing the mechanism of debonding failure in plated beams. This study proposes an improved analytical model for the stress analysis of an adhesive layer in a plated beam. The beam and the soffit plate are individually modelled as a single Timoshenko sub-beam with separate rotations, while the adhesive layer is modelled as a two-dimensional elastic continuum in plane stress, which considers different adherend-adhesive interface stresses. The internal forces of the adhesive layer are assumed to satisfy the Timoshenko beam theory, and the shear deformation and bending moment of the adhesive layer can be considered. The internal forces and displacements of the adhesive layer are fully considered in the displacement compatibility equations, and deformable interfaces are assembled so that the effect of interface stresses on local deformation is captured. Based on equilibrium equations and displacement continuity, the governing differential equations of beam forces are derived, and then the analytical solutions of interface stresses and stresses along the thickness of the adhesive layer are obtained. Comparisons of the results of the finite-element analysis and the existing four-parameter model solutions show that the present model is reasonable. The influence of adhesive thickness on stress distributions in adhesive layers is also investigated.     

Elasto-Plastic Analysis of Adhesively Bonded Symmetric Single Lap Joints Under In-Plane Tension and Edge Moments

An analysis is presented that predicts adhesive shear and peel stresses and strains in an adhesively bonded single lap joint having symmetric configuration with adhesive behavior. The single lap joint is under tension loading together with moments induced by the interactions of the geometric eccentricity and the boundary conditions of the joint. The von Mises yielding criterion is used to relate the adhesive stress components within the yielded region. The adhesive strains are computed from the relative displacements of the adherends and can be considered as an average of the strain variation through the adhesive thickness direction. Example calculations show that the predicted adhesive shear and peel stress and strain profiles are well matched to detailed finite element analysis results. Generally, the analytical model predictions are found to be more accurate when the adhesive thickness is small.     

Strength Analysis of Adhesively-Bonded Tubular Single Lap Steel-Steel Joints Under Axial Loads Considering Residual Thermal Stresses

The static tensile load bearing capability of adhesively-bonded tubular single lap joints calculated using linear mechanical adhesive properties is usually far less than the experimentally-determined one because the majority of the load transfer of adhesively-bonded joints is accomplished by the nonlinear behavior of the rubber-toughened epoxy adhesive

In this paper, both the nonlinear mechanical properties and the residual thermal stresses in the adhesive resulting from joint fabrication were included in the stress calculation of adhesively-bonded joints. The nonlinear tensile properties of the adhesive were approximated by an exponential equation which was represented by the initial tensile modulus and ultimate tensile strength of the adhesive.

From the tensile tests and the stress analyses of adhesively-bonded joints, a failure model for adhesively-bonded tubular single lap joints under axial loads was proposed.     

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.     

Elasto-Plastic Analysis of Adhesively Bonded Symmetric Single Lap Joints Under In-Plane Tension and Edge Moments

An analysis is presented that predicts adhesive shear and peel stresses and strains in an adhesively bonded single lap joint having symmetric configuration with adhesive behavior. The single lap joint is under tension loading together with moments induced by the interactions of the geometric eccentricity and the boundary conditions of the joint. The von Mises yielding criterion is used to relate the adhesive stress components within the yielded region. The adhesive strains are computed from the relative displacements of the adherends and can be considered as an average of the strain variation through the adhesive thickness direction. Example calculations show that the predicted adhesive shear and peel stress and strain profiles are well matched to detailed finite element analysis results. Generally, the analytical model predictions are found to be more accurate when the adhesive thickness is small.     

Development of a Failure Model for the Adhesively Bonded Tubular Single Lap Joint

The accurate calculation of the stresses and torque capacities of adhesively bonded joints is not possible without understanding the failure phenomena of the adhesive joints and the nonlinear behavior of the adhesive.

In this paper, an adhesive failure model of the adhesively bonded tubular single lap joint with steel-steel adherends was proposed to predict the torque capacity accurately.

The model incorporated the nonlinear behavior of the adhesive and the different failure modes in which the adhesive failure mode changed from bulk shear failure, via transient failure, to interfacial failure between the adhesive and the adherend, according to the magnitudes of the residual thermally-induced stresses from fabrication.     

Experimental Analysis of the Bondline Stress Concentrations to Characterize the Influence of Adhesive Ductility on the Composite Single Lap Joint Strength

Adhesively bonded composite single lap joints were experimentally investigated to analyze the bondline stress concentrations and characterize the influence of adhesive ductility on the joint strength. Two epoxy paste adhesives—one with high tensile strength and low ductility, and the other with relatively low tensile strength and high ductility—were used to manufacture composite single lap joints. Quasi-static tensile tests were conducted on the single lap joints to failure at room temperature. High magnification two-dimensional digital image correlation was used to analyze strain distributions near the adhesive fillet regions. The failure mechanisms were examined using scanning electron microscopy to understand the effect of adhesive ductility on the joint strength. For a given surface treatment and laminate type, the results show that adhesive ductility significantly increases the joint strength by positively influencing stress distribution and failure mechanism near the overlap edges. Moreover, it is shown that high magnification two-dimensional digital image correlation can successfully be used to study the damage initiation phase in composite bonded joints.     

Stress analysis in a classical double lap,adhesively bonded joint with a layerwise model

This paper focuses on stress analysis in classical double lap, adhesively bonded joints having constant layer thicknesses. Several analytical methods found in the literature do not provide adequate information on stresses at the adherend/adhesive interfaces. In these methods, the adhesive thickness is assumed to be small compared to that of the adherends and the stresses to be uniform through the adhesive thickness. Herein, the model proposed by the authors can be considered as a stacking of Reissner–Mindlin plates (six plates for a double lap joint). The equations based on stacked plates were applied to the geometry of a symmetrical, double-lap, adhesively bonded joint. Finally, the model has been validated by comparing the model results with those of a finite element calculation.     

Tensile load-bearing capacity of co-cured double lap joints

The co-cured joining method has several advantages over the adhesively bonded joining method because both the curing and the joining processes for the composite structures are achieved simultaneously. In this study, the tensile load-bearing capacities of co-cured double lap joints were investigated experimentally and compared with the analytical results calculated by finite element analysis. Co-cured double lap joint specimens with several bond parameters such as bond length, surface roughness, and stacking sequence of the composite laminate were fabricated and tested. From the experimental results, it was found that the failure mechanism of the co-cured double lap joint was cohesive failure by delamination at the first ply of the composite laminate in the co-cured double lap joint. Finally, optimum values of several bond parameters were determined. Analytical tensile load-bearing capacities of the co-cured double lap joints were calculated by the three-dimensional Tsai-Wu failure criterion using stress distributions obtained from finite element analysis.     

Development of a Computer Program for the Design of Adhesive Joints

Adhesive joints are increasingly being used due to their improved mechanical performance and a better understanding of the mechanics of failure. To predict the joint strength, one must have the stress distribution and a suitable failure criterion. The literature contains many closed-form solutions for the stress distribution. However, the models are sometimes difficult to implement and use. The objective of the present work was to compile existing models of increasing complexity into user friendly software. Three main situations were considered: elastic adherends and adhesive, elastic adherends with nonlinear adhesive and nonlinear analyses for both adherends and adhesive. The adherends were both isotropic (metals) and anisotropic (composites). The joints considered are the single and double lap joints for most of the models. However, a sandwich model initially proposed by Crocombe can be used for any type of joint provided the boundary conditions are known. For each model proposed the compatible failure criteria are included to enable the user not only to have the stress distribution but also the failure load for a given joint/load scenario. Experimental tests corresponding to the three cases described above were carried out to validate the models implemented.     

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.