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.     

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%.     

A three-dimensional finite-element stress analysis and strength evaluation of stepped-lap adhesive joints subjected to static tensile loadings

Stress distributions in stepped-lap adhesive joints subjected to static tensile loadings are analyzed using three-dimensional finite-element calculations. For establishing an optimum design method of the joints, the effects of the adhesive Young's modulus, adhesive thickness and number of steps on the interface stress distributions are examined. The results show that the maximum value of the maximum principal stress σ₁ occurs at the edge of the adhesive interfaces. The maximum value of the stress σ₁ decreases as the adhesive Young's modulus and number of steps increase and as the adhesive thickness decreases under static loadings. A method for estimating the joint strength under static loadings is proposed using interface stress distributions. For verification of the finite-element method calculations, experiments were carried out to measure the strains and the joint strengths under static loadings. Fairly good agreements were found between the numerical and the experimental results.     

Strength prediction of epoxy adhesively bonded scarf joints of dissimilar adherends

In this study, strength of epoxy adhesively bonded scarf joints of dissimilar adherends, namely SUS304 stainless steel and YH75 aluminum alloy is examined on several scarf angles and various bond thicknesses under uniaxial tensile loading. Scarf angle, θ=45°, 60° and 75° are employed. The bond thickness, t between the dissimilar adherends is controlled to be ranged between 0.1 and 1.2 mm. Finite element (FE) analysis is also executed to investigate the stress distributions in the adhesive layer of scarf joints by ANSYS 11 code. As a result, the apparent Young's modulus of adhesive layer in scarf joints is found to be 1.5-5 times higher than those of bulk epoxy adhesive, which has been obtained from tensile tests. For scarf joint strength prediction, the existing failure criteria (i.e. maximum principal stress and Mises equivalent stress) cannot satisfactorily estimate the present experimental results. Though the measured stress multiaxiality of scarf joints proportionally increases as the scarf angle increases, the experimental results do not agree with the theoretical values. From analytical solutions, stress singularity exists most pronouncedly at the steel/adhesive interface corner of joint having 45-75° scarf angle. The failure surface observations confirm that the failure has always initiated at this apex. This is also in agreement with stress-y distribution obtained within FE analysis. Finally, the strength of scarf joints bonded with brittle adhesive can be best predicted by interface corner toughness, Hc parameter.     

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 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 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.     

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.     

Failure analysis of AA8011-pultruded GFRP adhesively bonded similar and dissimilar joints

In this work, a comparative failure analysis of aluminum (AA8011/AA8011) and glass fiber reinforced polyester (GFRP/GFRP) based similar and dissimilar joints is presented. The GFRP is prepared using pultrusion technique. Single lap joints are prepared by using Araldite R2011 epoxy as an adhesive. The lap joints are then tested under tension to estimate the average shear strength of the assembly. It is observed that the average bond strength of AA8011/AA8011 is lesser than that of the GFRP/GFRP joint. The failure of similar joints occurred by fracture within the adhesive. The dissimilar joint is failed predominantly by interface debonding. Further, a detailed three dimensional stress analysis of the joints is carried out using finite element method (FEM). The damage analysis of adhesive layer is carried out by coupling FEM with cohesive zone model (CZM). The stress, damage distributions and failure mechanisms are compared for similar joints in detail. A failure mechanism is proposed for AA8011/AA8011 type joint that favours a rapid crack growth in the adhesive after crack initiation, which is responsible for lesser bond strength. The increase in overlap length has positive effect that the peak load increases proportionally with overlap length.     

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 Stress Analysis of Butt Adhesive Joints Under Torsional Loads

The stress distribution and the displacement are examined when a butt adhesive joint, in which two dissimilar tubular shafts are joined, is subjected to a torsional load. In the analyses, general representations of the stresses and the displacements are given as a torsion problem when two dissimilar tubular shafts are band-adhesively bonded. Next, in the case of shafts with the same material, effects of the ratio of the shear modulus of an adhesive to that of shafts, the thickness of the adhesive and the bonded position of band-adhesive on the stress distribution are made clear by numerical computations. Moreover, when solid shafts are joined, these effects are made clear by the similar analyses and numerical computations.     

A Stress Analysis of Butt Adhesive Joints Under Torsional Loads

The stress distribution and the displacement are examined when a butt adhesive joint, in which two dissimilar tubular shafts are joined, is subjected to a torsional load. In the analyses, general representations of the stresses and the displacements are given as a torsion problem when two dissimilar tubular shafts are band-adhesively bonded. Next, in the case of shafts with the same material, effects of the ratio of the shear modulus of an adhesive to that of shafts, the thickness of the adhesive and the bonded position of band-adhesive on the stress distribution are made clear by numerical computations. Moreover, when solid shafts are joined, these effects are made clear by the similar analyses and numerical computations.     

3-D FEM stress analysis and strength evaluation of single-lap adhesive joints subjected to impact tensile loads

The stress wave propagations and interface stress distributions in the single-lap adhesive joint under impact tensile loads are analyzed using the three-dimensional finite element method (3D-FEM) taking into account the strain rate sensitive of the adhesive using Cowper–Symonds constitutive model. It is found that the rupture of the joint initiates near the middle area of the edges of the interfaces along the width direction. In addition, the effects of Young's modulus of the adherend, the overlap length and the thickness of the adhesive layer, and the initial impact velocity of the impacted mass on the stress wave propagations and the interface stress distributions are examined. The characteristics are compared with those of the joint under static loads, which show the different properties. Furthermore, experiments are also carried out for measuring the strain responses and the joint strength. A fairly good agreement is observed between the numerical and the measured results. The strength of the single-lap adhesive joint, which is described using impact energy, is obtained between 5.439 and 5.620 J for the present joint.     

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.     

A Stress Analysis of Adhesive Butt Joints of Dissimilar Materials Subjected to Cleavage Loads

Stress distributions are examined when an adhesive butt joint, in which two thin plates made of dissimilar materials are joined, is subjected to cleavage loads. General representations of the stress and displacement fields are given using the two-dimensional theory of elasticity. The effects of the ratios of young's modulus among two adherends and an adhesive and the thickness of the adhesive on the stress distributions of the joints are clarified by numerical calculations. In addition, the stress singularity near the edge of the interface in the load application side is evaluated. For verification, the strain distributions near the interface of each adherend were measured. The analytical results are closely consistent with the experimental ones.     

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.     

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.     

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.     

Stress Analysis of T-type Butt Adhesive Joint Subjected to External Bending Moments

Stress distributions and displacements at the interface between an adhesive and an adherend are examined when a T-type butt adhesive joint, in which two thin plates are joined, is subjected to an external bending moment. In the analyses, general representations of the stresses and the displacements are given using a two-dimensional theory of elasticity in the case where two dissimilar plates are joined. Next, in the case of plates with the same material, effects of Young's modulus of plates to that of an adhesive and the thickness of the adhesive on the stress distribution are made clear by numerical computations. For verification, experiments are performed and an analytical result is in a fairly good agreement with an experimental one.     

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°.