Single Lap Joints with Rounded Adherend Corners: Experimental Results and Strength Prediction

The objective of the present study was to better understand the effect of the change in the geometry of the adherend corners on the stress distribution in single lap joints and, therefore, on the joint strength. Various degrees of rounding were studied and two different types of adhesives were used: one very brittle and another which had a large plastic deformation. Experimental results on the strength of joints with different degrees of rounding are presented. For joints bonded with brittle adhesives, the effect of the rounded adherend corners is larger than that with ductile adhesives. The strength of joints with brittle adhesives with a large radius adherend corner increases by about 40% compared to that with a sharp adherend corner. It is shown that for joints bonded with brittle adhesives, crack propagation occurs for a short period before it grows into catastrophic failure. However, for ductile adhesives, there is large adhesive yielding and small crack propagation before final failure. Another important feature of joints bonded with ductile adhesives is that there may be more than one crack in the adhesive layer before failure. This makes strength predictions more difficult. The second part of the paper presents an approximate method for predicting the strength of joints bonded with brittle and ductile adhesives, with and without adherend corner rounding. The predictions, based on an average value around the singularity, compare well with the experimental results, especially for joints bonded with ductile adhesives.     

The influence of local geometry on the strength of adhesive joints

This paper describes a two-part investigation into the effect of local geometry changes at the edges of the overlap in single lap joints. In the first part, finite element analysis has been used to model the effects on the stress distribution of geometry changes which are small in relation to the dimensions of the local geometry, in order to provide an improved model for failure prediction. The model used is that of an adhesive around a rigid corner, and the effect of rounding the corner has been considered.The second part deals with local geometry changes of the same order of magnitude as the dimensions of the geometry and their effect on joint strength. Three types of joint — one with a square-edged adhesive layer, one with a fillet of adhesive and one with an adhesive fillet plus a radiused adherend — were manufactured, tested and analysed. Improvements to the finite element models were also made following the results of part 1.It is found that finite element analysis is capable of predicting the significant strength increases that may be achieved in single lap joints by filleting the adhesive at the edges of the overlap and rounding the ends of the adherends.     

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 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 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.     

Effect of adhesive free-end geometry on the initiation and propagation of damaged zones in adhesively bonded lap joints

In this study the effect of adhesive free-end geometry on the initiation and propagation of damaged zones in adhesively bonded single- and double-lap joints was investigated considering the material non-linear behaviour of both adhesive and adherends and the geometrical non-linearity. The damaged adhesive and adherend zones exceeding the specified ultimate strains were determined based on the modified von Mises criterion for adherends and the failure criterion, including the effects of the hydrostatic stress states for the epoxy adhesives proposed by Raghava and Cadell. The stiffness of each finite element in the damaged zones was reduced to a negligible value, thus not contributing to the overall stiffness of the adhesive joint. This simple method provides useful information on the initiation and propagation of damaged zones in both the adhesive layer and adherends. The damaged adhesive zones due to a tensile load were observed to initiate around the rounded adherend corners inside the adhesive fillets and to propagate first towards both the free surface of the adhesive fillet and across the adhesive layer, and later along the adherend–adhesive interface. The damaged adhesive zones initiate at the left free-end of the adhesive-upper adherend interface and at the right free-end of the adhesive-lower adherend interface and propagate along these interfaces in the large adhesive fillets. In the bending test, the damaged adhesive zones appeared only at the left free-end in tension of the adhesive-upper adherend interface for the large adhesive fillets, but around the lower adherend corner for the smaller adhesive fillets. Later, it propagated with a similar mechanism as in the tensile load. In a double-lap joint subjected to a tensile load, the damaged zone appeared around the upper adherend corner inside the right adhesive fillet in tension, and propagated first towards the free surface of the adhesive fillet and through the adhesive layer towards the adhesive-middle adherend interface, and later along this interface. For all loading conditions, increasing the adhesive fillet size caused the damaged zone initiation to occur at a larger load level. The SEM micrographs of fracture surfaces around the adhesive fillets showed that the damaged zones initiated around the adherend corner inside the adhesive fillet and propagated through the adhesive fillets.     

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.     

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 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 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.     

The Effect of Moment and Flexural Rigidity of Adherend on the Strength of Adhesively Bonded Single Lap Joints

In the present study, mechanical properties of different single lap joint configurations derived from adherends with different thicknesses subjected to tensile loading were investigated experimentally and numerically. For this purpose, experimental studies were conducted on two different types of SLJ samples, the first type with identical upper and lower adherend thicknesses and the second with different upper and lower adherend thicknesses. For the first type, five different thickness values were tested. For the second type, the lower adherend thickness was constant while five different upper adherend thickness values were tested. The adhesive was prepared from a two-part paste. After the experimental studies, stress analyses on the SLJs were performed with three-dimensional finite element analysis by considering the geometrical non-linearity and the material non-linearities of the adhesive (DP460) and adherend (AA2024-T3). It was observed that, in single lap joint geometry, variation in the thickness of the adherend and the use of lower and upper adherends with different thickness values changed the stress concentrations at the edges of the overlap regions, affecting the experimental failure load of the joints.     

Dynamic strength of single lap joints with similar and dissimilar adherends

The increased use of adhesives for joining structural parts demands a thorough understanding of their load carrying capacity. The strength of the adhesive joints depends on several factors such as the joint geometry, adhesive type, adherend properties and also on the loading conditions. Particularly polymer based adhesives exhibit sensitivity to loading rate and therefore it is important to understand their behavior under impact like situations. The effect of similar versus dissimilar adherends on the dynamic strength of adhesive lap joints is addressed in this study. The dynamic strength is evaluated using the split-cylinder lap joint geometry in a split Hopkinson pressure bar setup. The commercial adhesive Araldite 2014 is used for preparing the joints. The adherend materials considered included steel and aluminum. The results of the study indicated that the dynamic strength of the lap joint is influenced by the adherend material and also by the adherent combination. Even in the case of joints with similar adherends, the strength was affected by the adherend type. The strength of steel–steel joints was higher than that for aluminum–aluminum joints. In the case of dissimilar adherends, the strength was lower than that of the case of similar adherends. The results of this study indicate that the combination of adherend material should also be accounted for while designing lap joints.     

Effect of protrusion at the ends of bondline in single lap joints under tension and bending

In this work, elasto-plastic stress analysis of single lap joints with and without protrusion in adhesive bondline subjected to tension and bending was carried out using 2D non-linear finite element analysis and confirmed experimentally. AA 2024-T3 aluminum adherends were bonded with SBT 9244 film adhesive. The protrusion was obtained by extending the adhesive film by 2?mm from the overlap length at both overlap ends. Three different adherend thicknesses and overlap lengths for each loading and bondline type were used. The joints with and without protrusion, for comparison, were loaded with the same load for each adherend thickness and overlap length. Finally, it was observed that the protrusion reduces the strength in the joint under tension, while the protrusion increases the strength in the joint under bending.     

Modeling of cohesive failure processes in structural adhesive bonded joints

This paper presents an approach to predicting the strength of joints bonded by structural adhesives using a finite element method. The material properties of a commercial structural adhesive and the strength of single-lap joints and scarf joints of aluminum bonded by this adhesive were experimentally measured to provide input for and comparison with the finite element model. Criteria based on maximum strain and stress were used to characterize the cohesive failure within the adhesive and adherend failure observed in this study. In addition to its simplicity, the approach described in this paper is capable of analyzing the entire deformation and failure process of adhesive joints in which different fracture modes may dominate and both adhesive and adherends may undergo inelastic deformation. It was shown that the finite element predictions of the joint strength generally agreed well with the experimental measurements.     

The behaviour of single lap joints under bending loading

Four-point bend tests were performed on single lap joints with hard steel adherends and a structural epoxy adhesive. The effect of the overlap, the adherend thickness and the adhesive thickness was studied. It was found that the length of the overlap has no significant effect on the strength of the joints. This is because the load transfer is occurring in a very localised area around the edges of the overlap, being the failure governed by peel mechanisms. The thickness of the adherends strongly affects the strength of the joints. The thicker the adherend, the stronger is the joint. The experimental results are compared with a finite element model and reinforce the fact that the failure takes place due to local strains at the ends of the overlap in tension. An analytical model is also given to predict in a simple but effective way the joint strength and its dependence on the adherend thickness.     

Single lap joints loaded in tension with high strength steel adherends

Single lap joints in many different geometric and material configurations were analysed using finite element analysis and tested in tension. Geometric parameters, such as the overlap length and adherend thickness, together with material parameters such as the adherend and adhesive stress–strain behaviour, were all tested. The mechanisms and modes of failure were observed for different cases, and positions of damage initiation were identified. Failure patterns were related to failure mechanisms. A failure prediction methodology has been proposed and a good correlation was obtained between the experimental and finite element predictions of strength for a variety of joint configurations. The study is presented in two parts. In the first (present paper), high strength steel adherends are considered and in the second paper ductile steel adherends are studied. For high strength steel adherends and a relatively short overlap, failure is dominated by adhesive global yielding. As the overlap gets longer, however, failure is no longer due to global yielding, but due to high local shear strains.     

The effect of adhesive thickness on tensile and shear strength of polyimide adhesive

The effect of adhesive thickness on tensile and shear strength of a polyimide adhesive has been investigated. Tensile and shear tests were carried out using butt and single lap joints. Commercially available polyimide (Skybond 703) was used as adhesive and aluminum alloy (5052-H34) was used as adherends. The tensile strength of the butt joints decreased with increasing adhesive thickness. In contrast, adhesive thickness did not seem to affect the shear strength of single lap joints. The fabricated joints using the polyimide adhesive failed in an interfacial manner regardless of adhesive thickness. The linear elastic stress analysis using a finite element method (FEM) indicates that the normal stress concentrated at the interface between the adherend and the adhesive. The FEM analysis considering the interfacial stress well explains the effect of adhesive thickness on the joint strength.     

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.     

Stress Distribution in Single Lap Joints with a Cracked Composite Adherend—Part II: Laminated Adherends

The effect of a crack in the overlap region of an adhesive single lap joint is studied on the shear stress distribution in adhesive layer. Each adherend is considered to be a laminated composite material with unidirectional fibers aligned in the direction of the applied load. Crack location is selected to be in the top adherend laminate, in the form of cut fibers and matrix bays. The crack can occur in any layer. The shear-lag model is used to derive the equilibrium equations which are then solved by means of eigenvector expansion. The effects of adhesive thickness, crack size, and location in the adherend, total number of layers in each adherends, volume fraction of fibers, and type of fibers are investigated on the shear distribution in the adhesive as well as load distribution in the intact fiber at the crack tip located in the top adherend. The effect of dissimilar laminated adherends is also investigated on the adhesive shear stress distribution. According to the results, in the presence of a crack, the peak shear stress in the adhesive layer and load concentration in the fibers are very susceptible to the adhesive thickness and number of layers in laminated adherends.     

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.