FEM stress analysis and strength prediction of scarf adhesive joints under static bending moments

The stress distributions at the interfaces in the scarf adhesive joints under static bending moments were analyzed using two-dimensional and three-dimensional finite element (FEM) calculations. The effects of the scarf angle, adhesive Young's modulus and the adhesive thickness on the interface stress distribution were examined. It was found that the singular stress at the edges of the interfaces decreased as the adhesive Young's modulus increased and the adhesive thickness decreased. The singular stress at the edges of the interfaces obtained from the 3-D was larger than that from the 2-D FEM. The joint strength was also predicted using the elasto-plastic 3-D FEM calculations. For verification of the FEM calculation results, the strains in the adherends and the joint strengths were measured. The measured results of the strains and the joint strengths were fairly consistent with the results obtained from the 3-D FEM calculations and indicated that the rupture bending moment (joint strength) was the maximum when the scarf angle was around 60°.     

A two-dimensional stress analysis of single-lap adhesive joints of dissimilar adherends subjected to tensile loads

Single-lap adhesive joints of dissimilar adherends subjected to tensile loads are analyzed as a three-body contact problem using the two-dimensional theory of elasticity. In the numerical calculations, the effects of Young's modulus ratio between different adherends, the ratio of the adherend thicknesses, the ratio of the adherend lengths, and the adhesive thickness on the contact stress distributions at the interfaces are examined. As a result, it is found that (1) the stress singularity occurs near the edges of the interfaces and it increases at the edge of the interface of an adherend with smaller Young's modulus; (2) the stress singularity increases at the edge of the interface of an adherend with thinner thickness; (3) the singular stresses increase at the edges of the two interfaces as the ratio of the upper adherend length to the lower one decreases; and (4) the singular stresses increase at the edges of the two interfaces as the adhesive thickness decreases when the adhesive is thin enough, and they also increase as the adhesive thickness increases when the adhesive is thick enough. In addition, the singular stresses obtained from the present analysis are compared with those obtained by Bogy. Fairly good agreement is seen between the present analysis and the results from Bogy. Strain measurement and finite element analysis (FEA) were carried out. The analytical results are in fairly good agreement with the measured and the FEA results.     

Three-dimensional finite element analysis of stress response in adhesive butt joints subjected to impact bending moments

The stress wave propagation and the stress distribution in adhesive butt joints of T-shaped similar adherends subjected to impact bending moments are calculated using a three-dimensional finite-element method (FEM). An impact bending moment is applied to a joint by dropping a weight. The FEM code employed is DYNA3D. The effects of the Young's modulus of adherends, the adhesive thickness, and the web length of T-shaped adherends on the stress wave propagation at the interfaces are examined. It is found that the highest stress occurs at the interfaces. In the case of T-shaped adherends, it is seen that the maximum principal stress at the interfaces increases as Young's modulus of the adherends increases. In the special case where the web length of T-shaped adherends equals the flange length, the maximum principal stress at the interfaces increases as Young's modulus of the adherends decreases. The maximum principal stress at the interfaces increases as the adherend thickness decreases. The characteristics of the T-shaped adhesive joints subjected to static bending moments are also examined by FEM and compared with those under impact bending moments. Furthermore, strain response of adhesive butt joints was measured using strain gauges. A fairly good agreement is observed between the numerical and the experimental results.     

Three-dimensional finite element stress analysis of single-lap adhesive joints of dissimilar adherends subjected to impact tensile loads

The stress-wave propagations and stress distributions in single-lap joints of dissimilar adherends were analyzed using an elastic three-dimensional finite-element method (DYNA3D). An impact tensile load was applied to the single-lap adhesive joint by dropping a weight. One end of the upper adherend in the single-lap adhesive joint was fixed and the other adherend (lower adherend) which was connected to a bar was impacted by the weight. The effects of Young's modulus and the thickness of each adherend on the stress wave propagations and stress distributions at the interfaces were examined. It was found that the maximum value of the maximum principal stress occurred near the edge of the interface of the fixed adherend. The maximum principal stress increased as Young's modulus of the fixed adherend increased. It was also observed that the maximum principal stress increased as the fixed adherend thickness decreased. In addition, strain responses in the single-lap adhesive joints of dissimilar adherends subjected to impact tensile loads were measured using strain gauges. Fairly good agreements were found between the FEM calculations and the experimental measurements.     

A two-dimensional stress analysis and strength evaluation of band adhesive butt joints subjected to tensile loads

The stresses in band adhesive butt joints, in which two adherends are bonded partially at the interfaces, are analyzed, using a two-dimensional theory of elasticity, in order to demonstrate the usefulness of the joints. In the analysis, similar adherends and adhesive bonds, which are bonded at two or three regions, are, respectively, replaced by finite strips. In the numerical calculations, the effects of the ratio of Young's moduli for adherends to that for adhesives, the adhesive thickness, the bonding area and position, and the load distribution are shown on the stress distributions at interfaces. It is seen that band adhesive joints are useful when the bonding area and positions are changed with external load distributions. Photoelastic experiments and the measurement of the adherend strains were carried out. The analytical results are in a fairly good agreement with the experimental results. In addition, a method for estimating the joint strength is proposed by using the interface stress distribution obtained by the analysis. Experiments concerning joint strength were performed and fairly good agreement is found between the estimated values and the experimental results.     

Three-dimensional finite element analysis of single-lap adhesive joints under impact loads

This paper deals with the stress wave propagation and stress distribution in single-lap adhesive joints subjected to impact tensile loads with small strain rate. The stress wave propagations and stress distributions in single-lap joints have been analyzed using an elastic three-dimensional finite-element method (DYNA3D). An impact load was applied to the single-lap adhesive joint by dropping a weight. One end of one of the adherends in the single-lap adhesive joint was fixed and the other adherend to which a bar was connected was impacted by the weight. The effects of Young's modulus of the adherends, the overlap length, the adhesive thickness and the adherend thickness on the stress wave propagations and stress distributions at the interfaces have been examined. It was found that the maximum stress occurred near the edge of the interface and that it increased with an increase of Young's modulus of the adherends. It was also seen that the maximum stress increased as the overlap length, the adhesive thickness and the adherend thickness decreased. In addition, strain response of single-lap adhesive joints subjected to impact tensile loads was measured using strain gauges. Fairly good agreements were observed between the numerical and experimental results.     

Three-dimensional finite element analysis of single-lap adhesive joints subjected to impact bending moments

This paper deals with the stress wave propagations and stress distributions in single-lap adhesive joints subjected to impact bending moments with small strain rate. The elastic stress wave propagation and the stress distribution in single-lap adhesive joints of similar adherends subjected to impact bending moments are analyzed using three-dimensional finite-element method (FEM). A three-point impact bending moment is applied to the joint by dropping a weight. FEM code employed is DYNA3D. The effects of Young's modulus of the adherends, the lap length, the adherend thickness and the adhesive thickness on the stress wave propagation at the interfaces are examined. It is found that the maximum value of the maximum principal stress, σ₁, appears at the interface between the adhesive and the upper surface of upper adherend which is impacted. The maximum stress, σ₁, increases as Young's modulus of adherends, the lap length and the adhered thickness increase. It is also found that the maximum stress, σ₁ increases with decreasing adhesive thickness. In addition, experiments were carried out to measure the strain response of single-lap joints subjected to impact bending moments using strain gauges. A fairy good agreement was observed between the numerical and experimental results.     

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.     

A Two-dimensional Stress Analysis and Strength of Single-lap Adhesive Joints of Dissimilar Adherends Subjected to External Bending Moments

The stress distributions of single-lap adhesive joints of dissimilar adherends subjected to external bending moments are analyzed as a three-body contact problem by using a two-dimensional theory of elasticity (plane strain). In the analysis, dissimilar adherends and an adhesive are replaced by finite strips. In the numerical calculations, the effects of the ratio of Young's moduli of adherends, the adherend thickness ratio and the adherend length ratio between dissimilar adherends on the stress distributions at the interfaces are examined. The results show that the stress singularity occurs at the ends of the interfaces, and its intensity is greater at the interface of the adherend with smaller Young's modulus. It is also noted that the singular stress is greater at the interface of the thinner adherend. It is found that the effect of the adherend length ratio on the stress singularity at the interfaces is very small. Joint strength is predicted by using the interface stress and it was measured by experiments. From the analysis and the experiments, it is found that the joint strength increases as Young's modulus of adherends and the adherend thickness increase while the effect of the adherend lengths on the joint strength is small. For verification of the analysis, a finite element analysis (FEA) is carried out. A fairly good agreement of the interface stress distribution is seen between the analytical and the FEA results.     

THREE-DIMENSIONAL FINITE ELEMENT ANALYSIS OF STRESS RESPONSE IN ADHESIVE BUTT JOINTS SUBJECTED TO IMPACT BENDING MOMENTS

The stress wave propagation and the stress distribution in adhesive butt joints of T-shaped similar adherends subjected to impact bending moments are calculated using a three-dimensional finite-element method (FEM). An impact bending moment is applied to a joint by dropping a weight. The FEM code employed is DYNA3D. The effects of the Young's modulus of adherends, the adhesive thickness, and the web length of T-shaped adherends on the stress wave propagation at the interfaces are examined. It is found that the highest stress occurs at the interfaces. In the case of T-shaped adherends, it is seen that the maximum principal stress at the interfaces increases as Young's modulus of the adherends increases. In the special case where the web length of T-shaped adherends equals the flange length, the maximum principal stress at the interfaces increases as Young's modulus of the adherends decreases. The maximum principal stress at the interfaces increases as the adherend thickness decreases. The characteristics of the T-shaped adhesive joints subjected to static bending moments are also examined by FEM and compared with those under impact bending moments. Furthermore, strain response of adhesive butt joints was measured using strain gauges. A fairly good agreement is observed between the numerical and the experimental results.     

Stress analysis and strength estimation of butt adhesive joints of dissimilar hollow cylinders under impact tensile loadings

The stress variations in butt adhesive joints of dissimilar hollow cylinders subjected to impact tensile loadings are analyzed in elastic and elasto-plastic deformation ranges using a finite element method (FEM). The FEM code name employed is DYNA3D. The effects of Young's modulus ratio between dissimilar adherends and the adhesive thickness on the stress variations at the interfaces are examined. In addition, the process of rupture at the interfaces of the joint is simulated. The stress distributions in the joints under static loadings are also analyzed by FEM. The characteristics of the stress variations in the joints under impact loadings are compared with those in the joints under static loadings. Also, the joint strengths under impact loadings are estimated by elasto-plastic FEM. It is found that the maximum value of the maximum principal stress σ ₁ occurs at the outside edge of the lower interface. It is also found that the maximum principal stress σ ₁ at the lower interface decreases as the adhesive thickness increases. The characteristics of the joints under impact loadings are found to be opposite to those under static loadings. Furthermore, differences in the characteristics of the stress variations are shown between the dissimilar joints and the similar joints. In addition, the experiments were carried out to measure the strain response and strains in the butt adhesive joints under both impact and static loadings using strain gauges. Furthermore, joint strengths under both impact and static loadings were measured. Fairly good agreements are observed between the numerical and the measured results.     

Three-dimensional Finite Element Analysis of Stress Response in Adhesive Butt Joints Subjected to Impact Tensile Loads

The stress wave propagation and the stress distribution in adhesive butt joints of similar adherends subjected to impact loads are analyzed using a three-dimensional finite-element method (FEM). The code employed is DYNA3D. An impact load is applied to a joint by dropping a weight. An adherend of a joint is fixed and the other adherend to which a bar is connected is impacted by the weight. The height of the weight is changed. The effect of Young's modulus ratio between the adherends and the adhesive, the adhesive thickness and the geometry of T-shaped adherends on the stress wave propagation at the interfaces are examined. It is found that the maximum stress is caused at the interfaces of the adherend subjected to an impact load. In the case of a T-shaped adherend, it is seen that the maximum stress is caused near the center of the interfaces and that it increases as Young's modulus of the adherends increases. In the special case where the web length of the T-shaped adherends equals the interface length, it is seen that the singular stress occurs at the edge of the interfaces and it increases as Young's modulus of the adherends decreases. The maximum principal stress increases as the adherend thickness increases. In addition, the strain response of adhesive butt joints subjected to impact loads was measured using strain gauges. A fairly good agreement is found between the numerical and the measured results.     

Experimental and FEM studies on mechanical properties of single-lap adhesive joint with dissimilar adherends subjected to impact tensile loadings

The rupture initiation position, the stress wave propagations and interface stress distributions of the single-lap adhesive joint with dissimilar adherends under impact tensile loadings are analyzed via experiments combined with FEM calculations taking account of the strain rate dependency property of the adhesive. It is obtained that rupture initiates at the interface of the adherend with higher Young's modulus (steel side in this study) in the joint under impact tensile loadings, which shows the opposite characteristic in the same type of joint under static loadings. A fairly good agreement is observed between the experimental measured and FEM calculated results. In addition, it is also found that the strength of the joint with dissimilar adherends is smaller than that of the joint with similar adherends when the joint is subjected to the impact tensile loadings owing to the different extent of the wave impedance mismatch which depends on the material properties. Finally, the design guideline for the single-lap adhesive joint is summarized and provided.     

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.     

Elastoplastic Finite Element Analysis and Strength Evaluation of Adhesive Butt Joints of Similar and Dissimilar Hollow Shafts Subjected to External Bending Moments

Stress distributions and deformation of adhesive butt joints are analyzed by an elastoplastic finite element method when the joints of similar and dissimilar shafts are subjected to external bending moments. The effects of the ratio of Young's modulus for the adherends to that for an adhesive and the effects of the adhesive thickness on the interface stress distribution are investigated. Joint strength is predicted by using the elastoplastic interface stress distributions. It is found that the singular stress at the edge of the interfaces increases with an increase of the ratio of Young's modulus. Measurement of strains in joints and experiments on joint strength were conducted. The numerical results are in fairly good agreement with the experimental results. It is observed that the joint strength for dissimilar shafts are smaller than those for similar shafts. A fracture of dissimilar adhesive up-bonded shafts occurred from the interface of the adherend with smaller Young's modulus. It is seen that joint strength increases as the adhesive thickness increases.     

An investigation on the initiation and propagation of damaged zones in adhesively bonded lap joints

In this study, the initiation and propagation of damaged zones in the adhesive layer and adherends of adhesively bonded single and double lap joints were investigated considering the geometrical non-linearity and the non-linear material behaviour of the adhesive and adherends. The modified von Mises criteria for adherends and Raghava and Cadell's failure criteria (J. Mater. Sci. 8, 225 (1973) [1]) including the effects of the hydrostatic stress states for the epoxy adhesive were used to determine the damaged adhesive and adherend zones which exceeded the specified ultimate strains. The stiffness of all finite elements corresponding to these zones was reduced so that they could not contribute to the overall stiffness of the adhesive joint. This approach simplifies to observe the initiation and propagation of the damaged zones in both the adhesive layer and adherends. A tensile load caused first the damaged adhesive zones to appear at the right free end of the adhesive-lower adherend interface and at the left free end of the adhesive-upper adherend interface, and then to propagate through the adhesive regions near the adhesive-adherend interfaces (interfacial failure). In the bending test, the damaged zone initiated at the left free end of the adhesive-upper adherend interface in tension, and similarly propagated through the adhesive regions close to the adhesive-adherend interface (interfacial failure). In the double-lap joint subjected to a tensile load, the damaged adhesive zones initiated first at the right free end of the adhesive-middle adherend interface and then propagated through the adhesive region near the adhesive-adherend interface. After the damaged zone reached a specific length it also grew through the adhesive thickness, and the adhesive joint failed. The SEM micrographs of fracture surfaces around the free edges of the overlap region indicated that the failure was interfacial. An additional damaged zone growth was observed in the side adhesive regions due to lateral straining, called the Poisson effect.     

Thermal residual stresses in an adhesively-bonded functionally graded single-lap joint

This study investigates three-dimensional thermal residual stresses occurring in an adhesively-bonded functionally graded single-lap joint subjected to a uniform cooling. The adherends are composed of a through-the-thickness functionally graded region between Al₂O₃ ceramic and Ni metal layers. Their mechanical properties were calculated using a power law for the volume fraction of the metal phase and a 3D layered finite element was implemented. In a free single-lap joint the normal stress σ_xx was dominant through the overlap region of the upper and lower adherends and along the adhesive free edges, whereas the transverse shear stress σ_xy concentrations appeared only along the free edges. The peel stress σ_yy and the transverse shear stress σ_xy became dominant along the free edges of the adhesive layer. In addition, the von Mises stress decreased uniformly through the adherend thickness from compressive in the top ceramic-rich layer to tensile in the bottom metal-rich layer. In addition, the layer number had only a minor effect on the through-the-thickness stress profiles after a layer number of 50, except for the peak stress values in the ceramic layer. In a single-lap joint fixed at two edges both adherends underwent considerable normal stress σ_xx concentrations varying from compressive in the top ceramic-rich layer to tensile in the bottom metal-rich layer along the free edges of both adherend–adhesive interfaces, whereas the peel stress σ_yy and transverse shear stress σ_xy reached peak levels along the left and right free edges of the adhesive layer. The layer number and the compositional gradient exponent had only minor effects on the through-the-thickness von Mises stress profiles but considerably affected the peak stress levels. The free edges of adhesive–adherend interfaces and the corresponding adherend regions are the most critical regions, and the adherend edge conditions play more important role in the critical adherend and adhesive stresses. Therefore, the first initiation of the joint failure can be expected along the left and right free edges of the upper and lower adherend–adhesive interfaces.     

Load transfer in adhesive double-sided patch joints

In this work, the application of adhesively bonded joints to connect two structural elements with a double-sided patch is studied. On the basis of the shear lag model, a simple closed-form solution was obtained. The analytical solutions can be used to predict the shear stress in the adhesive and the load transfer between the structural elements and the external patches. The load and shear stress distributions in the adhesively bonded region are presented. For verification of the analytical model, finite element analyses were employed to calculate the load transfer and shear stress for the double-sided patch joint under static tensile loadings. Good agreement was found between the theoretical predictions and numerical results. To obtain a better understanding of the joints, the effects of adhesive thickness, adhesive shear modulus and patch Young's modulus on the load transfer and shear stress distributions were investigated. The results show that the maximum shear stress occurs at the edge of the adhesive. The maximum value of the shear stress increases as the adhesive shear modulus and patch Young's modulus increase and as the adhesive thickness decreases. A more gradual load transfer can be achieved by increasing the adhesive thickness and decreasing the adhesive shear modulus. The simple analytical solution presented in this paper has the advantages of avoiding the numerical difficulties and giving explicit relationship between the stress state and joint parameters. Moreover, from the designer's point of view a closed-form and easy-to-use solution is preferred.     

FEM stress analysis and strength of adhesive butt joints of similar hollow cylinders under static and impact tensile loadings

The stress wave propagations in butt adhesive joints of similar hollow cylinders subjected to static and impact tensile loadings are analyzed in elastic and elasto-plastic deformation ranges using the finite-element method (FEM). The impact loading is applied to the joint by dropping a weight. The upper end of the upper adherend is fixed and the lower adherend of which the lower end is connected to a guide bar is subjected to the impact loading. The FEM code employed is DYNA3D. The effects of the adhesive thickness and Young's modulus of the adhesive on the stress wave propagation at the interfaces are examined. In addition, the characteristics of the joints subjected to impact loadings are compared with those of the joints under static loadings and the joint strengths are estimated by using the interface stress distributions. It is found that the maximum value of the maximum principal stress, σ₁ occurs at the outside edge of the interface of the lower adherend to which the impact loading is applied. The maximum value of the maximum principal stress, σ₁ increases as Young's modulus of the adhesive increases when the joints are subjected to impact loadings. It is found that the characteristics of the joints subjected to impact loadings are opposite to those subjected to static loadings. In addition, experiments were carried out to measure the strain response of the butt adhesive joints subjected to impact and static tensile loadings using strain gauges and the joint strengths were also measured. Fairy good agreements are observed between the numerical and the measured results.     

Elastoplastic finite element stress analysis and strength evaluation of adhesive lap joints of hollow shafts subjected to tensile loads

The stress distributions in adhesive lap joints of dissimilar hollow shafts subjected to tensile loads have been analyzed by the elastoplastic finite element method, taking the nonlinear behaviors of the adhesive and the hollow shafts into consideration. A prediction method for the joint strength has been proposed based on the Mises equivalent stress distribution in the adhesive and the frictional resistance between the adhesive and the shaft after rupture of the adhesive. In the experiments, three different kinds of adhesive lap joints were made, i.e. the inner and outer hollow shafts were aluminum alloy/aluminum alloy, steel/steel, and steel/aluminum alloy combinations, and the tensile strength of each joint was measured. From the numerical calculations, in the case of the two hollow shafts made of the same material, the tensile strength increases with an increase of Young's modulus of the shaft and in the case of the two hollow shafts made of different materials, the tensile strength increases when the inner hollow shaft of larger Young's modulus is bonded to the outer one of smaller Young's modulus. Also, the effects of the overlap length and the inner diameter of the inner shaft on the tensile strength of the joint are discussed. By comparing the predicted values of the tensile strength with the experimental results, it was shown that the proposed prediction method could estimate the tensile strength of the adhesive lap joints of hollow shafts within an error of about 15%.