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.     

Behaviour of Bi-adhesive Joints

The use of relatively low modulus adhesive at the ends of overlap in a bi-adhesive bondline of a bonded joint can reduce the stress concentration significantly and, therefore, potentially lead to higher strength of the joint. This study presents the two-dimensional and three-dimensional nonlinear (geometric and material) finite element analyses of adhesively bonded single lap joints having modulus-graded bondline under monotonic loading conditions. The adhesives were modelled as an elasto-plastic multi-linear material, while the substrates were regarded as both linear elastic and bi-linear elasto-plastic material. The computational simulations have been performed to investigate the bondline behaviour by studying the stress and strain distributions both at the mid-plane as well as at the interface of the bondline. It has been observed that the static strength is higher for joints with bi-adhesive bondlines compared to those with single adhesives in bondline. Higher joint strength has also been observed for optimum bi-adhesive bondline ratio through parametric studies. Effects of load level, and bondline thickness on stress distribution in the bi-adhesive bondline have also been studied. 3D analysis results reveal the existence of complex multi-axial stress/strain state at the ends of the overlap in the bondline which cannot be observed in 2D plane strain analysis. About 1/3rd of the width of the joint from the free edge in the width direction has 3D stress state, especially in the compliant adhesive of the bondline. Magnitudes of longitudinal and lateral stress/strain components are comparable to peel stress/strain components. It has also been analytically shown that the in-plane global stiffness of the joint remains unaffected by modulus gradation of the bondline adhesive.     

Stress Analysis of Adhesively Bonded Electroprimed Steel Lap Shear Joints

Structural applications for adhesive bonding have been increasing in recent years due to improvements in the types of adhesives available and in improved knowledge of bonding procedures. Consequently, there exists a demand for precise numerical modeling of adhesive joint behavior, particularly along bondline interfaces where low surface energy adhesives contact high surface energy metallic oxides. The purpose of the present study is to determine the effect of electrodeposited organic paint primer (ELPO) on the stress and strain distributions within an adhesively bonded single-lap-shear joint. Initial experimental studies have shown that bonding to ELPO-primed steel adherends has enhanced strength and durability characteristics compared to conventional bonds to unprimed steel surfaces. Recent studies based on finite element analysis of varied single-lap-shear joint moduli and thicknesses, and subsequent testing of joints with two different adhesive moduli, have indicated the mechanisms involved in this phenomenon. The presence of the ELPO-primer reduced peak peel and shear stresses and allowed for more uniform stress distribution throughout the joint.     

Stress Analysis of Adhesively Bonded Electroprimed Steel Lap Shear Joints

Structural applications for adhesive bonding have been increasing in recent years due to improvements in the types of adhesives available and in improved knowledge of bonding procedures. Consequently, there exists a demand for precise numerical modeling of adhesive joint behavior, particularly along bondline interfaces where low surface energy adhesives contact high surface energy metallic oxides. The purpose of the present study is to determine the effect of electrodeposited organic paint primer (ELPO) on the stress and strain distributions within an adhesively bonded single-lap-shear joint. Initial experimental studies have shown that bonding to ELPO-primed steel adherends has enhanced strength and durability characteristics compared to conventional bonds to unprimed steel surfaces. Recent studies based on finite element analysis of varied single-lap-shear joint moduli and thicknesses, and subsequent testing of joints with two different adhesive moduli, have indicated the mechanisms involved in this phenomenon. The presence of the ELPO-primer reduced peak peel and shear stresses and allowed for more uniform stress distribution throughout the joint.     

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

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

Analysis of the Effect of Piezoelectric Patches on the Behavior of Adhesively Bonded Scarf Joints — An Analytical Study

In order to reduce the maximum peel and shear stress concentrations in the adhesive layer, a smart adhesively bonded scarf joint system was developed by surface bonding of piezoelectric patches onto a typical scarf joint. The forces and bending moments at the edges of the developed smart joint system can be adaptively controlled by adjusting the applied electric field on the piezoelectric patches, thus reducing the peel and shear stresses concentration in the adhesive layer. In order to verify the effect of surface bonding of piezoelectric patches in smart scarf adhesive joints, an analytical model was developed to evaluate the shear stress distribution and to predict the peel stress. It was established that the piezoelectric patched joint could reduce the stress concentrations at the scarf joint edges. The influence of the electric field and the effects of the scarf angle and the adherend Young's modulus on the peel and shear stresses were investigated. It was found that the effect of scarf angle is more significant at higher angles to raise the stresses. The effect of the electric field on the shear stress is more significant than on the peel stress.     

Numerical analysis of the stress distribution in single-lap shear tests under elastic assumption—Application to the optimisation of the mechanical behaviour

The single lap joint is the most used test in order to analyse the behaviour of an adhesive in an assembly as on one hand, the manufacturing of such specimens is quite easy, and on the other hand they require only a classic tensile testing machine. However, such specimens are associated with complex loading of the adhesive, i.e. non-uniform shear stress along the overlap length, quite large peel stress at the two ends of the overlap and significant edge effects associated with geometrical and material parameters. In addition, the stress concentrations can contribute to fracture initiation in the adhesive joints and thus can lead to an incorrect analysis of the adhesive behaviour. Therefore, understanding the stress distribution in an adhesive joint can lead to improvements in adhesively bonded assemblies. The first part of this paper presents the influence of edge effects on the stress concentrations in single lap joints under elastic assumption of the material and using a pressure-dependent elastic limit of the adhesive. In the second part, some usual geometries, proposed in the literature about stress limitation, are compared with respect to the maximum load transmitted by single lap joint. The last part presents some geometries, which significantly limit the influence of edge effects and are more appropriate for analysing the behaviour of the adhesive.     

Experimental and Numerical Study of Adhesively Bonded CFRP Scarf-Lap Joints Subjected to Tensile Loads

The tensile performance of adhesively bonded CFRP scarf-lap joints was investigated experimentally and numerically. In this study, scarf angle and adherend thickness were chosen as design parameters. The lap shear strength is not directly proportional to scarf angle and adherend thickness for the brittle adhesive studied in the paper. The major failure mode includes cohesive shear failure and adherend delamination failure. The results present a stepped failure morphology along the bondline in the adhesive layer. A finite element model based on cohesive zone model was established to further investigate the stress distribution of scarf-lap joints with different lap parameters. The numerical results were compared with the experiment results, showing a good agreement, thus verifying the validity of the established numerical model.     

Design of adhesive joints based on peak elastic stresses

The paper is focused on the static strength of adhesively bonded structural joints and seeks a simple calculation rule that can assist the designer in everyday engineering practice. The work encompasses three steps. In the first step, an experimental campaign is carried out on an assortment of customized bonded joints (single lap and T-peel) made of steel strips bonded by an acrylic structural adhesive. The dimensions of the joints are chosen so as to produce a wide range of combinations of shear and peel stresses in the adhesive layer. In the second step, the stress analysis of the joints is performed by means of a sandwich model that describes the variability of shear and peel stresses over the overlap length but disregards the stress singularities at the corners. In the third step, a design rule is inferred by noting that, in a chart having as axes the peak values of the peel and shear components in the adhesive at failure, the points—calculated for each joint at the 2% (deviation from linearity) proof load—define a limit zone. The inferred design rule is that the adhesive withstands the load if the representative point of the stress state lies inside this zone. For the tested case, the envelope of the limit zone has an approximately rectangular shape. This criterion predicts the failure load of the joints far better than the simplistic approach based on the nominal stress calculated as the ratio of the load to the bonded area.The paper also discusses the response which is obtained by applying, to the same experimental data, the traditional calculation based on the mean stress (force to area ratio), and the more sophisticated approach based on the stress intensity factor, which accounts for the singularity of the stress field. Applied to our experimental data, the performance of both has been unsatisfactory.     

Stress Analysis of Generally Asymmetric Single Lap Adhesively Bonded Joints

An analysis is presented that predicts shear and peel stresses in an adhesively bonded single lap joint having general asymmetric configuration. The single lap joint is under tension loading together with moments induced by geometric eccentricity. Because these eccentricity moments are the key elements of this analysis, a general relationship between the eccentricity moments and simple geometric moments has been determined with the aid of finite element analysis (FEA). Example calculations show that the shear- and peel-stress profiles from the closed-form model are well matched to FEA results except in the small regions near the free ends of the joints, because of the shear lag basis of the model. For asymmetric joints, the model predictions are more accurate for the case of modulus eccentricity than thickness eccentricity. Elastic-limit load predictions accounting for both shear and peel stress in the adhesive have been used to find optimal joint configurations between asymmetric adherends.     

An analytical model for interfacial stresses in double-lap bonded joints

Due to their many advantages, adhesively bonded joints are widely used to join components in composite structures. However, premature failure due to debonding and peeling of the joint is the major concern for this technique. Existing analytical models suffer from two major drawbacks: 1) not satisfying zero-shear stress boundary conditions at the adhesive layer’s free edges^[1] and 2) failure to distinguish the peel stress along two adherend/adhesive interfaces^[2]. In this study, we develop a novel three parameter elastic foundation (3PEF) model to analyze a representative adhesively bonded joint, the symmetric double-lap joint, which is believed to have relatively low peel stresses. Explicit closed-form expressions of shear and peel stresses along two adhesive/adherend interfaces are yielded. This new model overcomes the existing model’s major drawbacks by satisfying all boundary conditions and predicting various peeling stresses along two adherend/adhesive interfaces. It not only reaches excellent agreement with existing solutions and numerical results based on finite element analysis but also correctly predicts the failure mode of an experimentally tested double-lap joint. This new model therefore reveals the peel stresses’ significant role in the failure of the double-lap joint, but the classical 2PEF model cannot create it.     

Design of functionally graded joints using a polyurethane-based adhesive with varying amounts of acrylate

Adhesives with graded properties along the bondline are being developed to increase the strength of adhesively bonded joints. Efforts to do this in the past have resulted in mixed results. Two adhesive parameters need to be considered: the geometry of the gradation and the material properties of the adhesive at different gradation levels. In order to consider both of these aspects, a computational model was created to aid in not only the design of adhesive gradations but also judge whether a specific adhesive gradation method will be able to result in strength increases. In this study, the model was introduced and compared with published results. A new adhesive gradation system was created by using a polyurethane-based adhesive with varying amounts of acrylate, and a numerical analysis was performed to determine the potential advantages of the adhesive gradation.     

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.     

Experimental and numerical investigations of adhesively bonded CFRP single-lap joints subjected to tensile loads

In this study, both experimental tests and numerical simulation are implemented to investigate the tensile performance of adhesively bonded CFRP single-lap joints (SLJs). The study considers 7 different overlap lengths, 5 adherend widths and 3 stacking sequences of the joints. Three-dimensional (3D) finite element (FE) models are established to simulate the tensile behavior of SLJs. The failure loads and failure modes of SLJs are investigated systematically by means of FE models and they are in good agreement with those of experiments, proving the accuracy of finite element method (FEM). It is found that increasing the adherend width can improve the load-carrying capacity of the joint better than increasing the overlap length does. Moreover, choosing 0° ply as the first ply is also beneficial for upgrading joint's strength. With respect to failure modes, cohesive failure in adhesive and delamination in adherend take dominant, while matrix cracking and fiber fracture only play a small part. With overlap length increasing or adherend width decreasing, cohesive failure takes up a smaller and smaller proportion of whole failure area, but the opposite is true for delamination. SLJs bonded with [0/45/-45/90]_3S adherends are prone to cohesive failure, and [90/-45/45/0]_3S adherends are easy to appear delamination. Both shear and peel stress along the bondline indicate symmetrical and non-uniform distributions with great stress gradient near the overlap ends. As the load increases, the high stress zone shifts from the end to the middle of the bondline, corresponding to the damage initiation and propagation in the adhesive layer.     

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 Preliminary Study of the Use of Kynar® Piezoelectric Film to Measure Peel Stresses in Adhesive Joints

A variety of test techniques have been developed to test the performance of adhesives bonded in situ within joints. Most of these techniques measure strength, fracture toughness, or adhesive modulus of the bonded joint. Techniques to measure actual stress or strain values within a bonded joint are quite few in number. The Krieger gage¹ is able to measure the average shear displacement along a 12.5 mm. gage length of a thick adherend joint. It has been used primarily to measure in situ shear moduli of adhesives. Brinson and his colleagues² proposed bonding strain gages within adhesive joints to measure strains within the adhesive. Unfortunately, these gages are only sensitive to the lateral strains and not shear or peel strains. Because the lateral strains are dominated by the behavior of the adherends rather than the adhesive, the information which can be gained is incomplete.     

Functionally graded adhesives for composite joints

Adhesives with functionally graded material properties are being considered for use in adhesively bonded joints to reduce the peel stress concentrations located near adherend discontinuities. Several practical concerns impede the actual use of such adhesives. These include increased manufacturing complications, alterations to the grading due to adhesive flow during manufacturing, and whether changing the loading conditions significantly impact the effectiveness of the grading. An analytical study is conducted to address these three concerns. An enhanced joint finite element, which uses an analytical formulation to obtain exact shape functions, is used to model the joint. Furthermore, proof-of-concept testing is conducted to show the potential advantages of functionally graded adhesives. In this study, grading is achieved by strategically placing glass beads within the adhesive layer at different densities along the joint.     

Photoelastic Determination of Flaw Size and Distribution Effects on Adhesively Bonded Lap Joints

It is well known that the load carrying capacity of adhesively bonded lap joints can be influenced by the presence of flaw-like defects which are often created during its bonding process. To design an effective adhesive joint containing possible bonding defects, adequate knowledge and understanding of the shear stress distribution along the entire lap joint are necessary.

This paper describes an investigation into the effects of internal adhesive flaw size and distribution on the fracture behaviour of adhesively bonded lap joints. Photoelasticity is used to gain a quantitative understanding of the localized shear stress concentrations due to the presence of the internal flaws along the bonding layer. It is observed that a 20% increase in the maximum shear stress may be induced when an isolated central flaw of S. O mm was extended to 37.5 mm representing a flaw size of 75% of the lap length. For the presence of multiple flaws along the bonding line, there is no significant effect of the flaw separation distance on the maximum shear stresses. There is, however, a marked increase in the maximum shear stress up to about 45% when a flaw size is increased from 2.5 mm to 7.5 mm.     

The mechanics of bondline thickness in balanced sandwich structures

Assuming negligible in-plane stress, non-varying shear stress, and linearly varying transverse stress along the thickness of the adhesive, the closed-form solutions for the interfacial shear and the interfacial peeling stresses in balanced bonded sandwich structures was derived. The nil-shear-stress condition at the free edge of the adhesive was enforced through the use of a decay function. The solutions for the shear and the peel stresses along the interfaces right up to the free edge were validated with the finite element analysis. The solutions were used to investigate (i) the observed increase susceptibility of single lap joints with increase bondline thickness and (ii) the nil report of such susceptibility for electronic assemblies experiencing differential thermal strain. The first investigation was compromised by the inability of the solutions to model the singular stress/strain field at the free-edge of the interfaces. The second investigation revealed a far higher rate of reduction in the magnitudes of the interfacial shear and peeling stresses in structures (electronic assemblies) that experience differential thermal strain than in structures (single lap joints) that experience bending strain.     

A Preliminary Study of the Use of Kynar® Piezoelectric Film to Measure Peel Stresses in Adhesive Joints

A variety of test techniques have been developed to test the performance of adhesives bonded in situ within joints. Most of these techniques measure strength, fracture toughness, or adhesive modulus of the bonded joint. Techniques to measure actual stress or strain values within a bonded joint are quite few in number. The Krieger gage¹ is able to measure the average shear displacement along a 12.5 mm. gage length of a thick adherend joint. It has been used primarily to measure in situ shear moduli of adhesives. Brinson and his colleagues² proposed bonding strain gages within adhesive joints to measure strains within the adhesive. Unfortunately, these gages are only sensitive to the lateral strains and not shear or peel strains. Because the lateral strains are dominated by the behavior of the adherends rather than the adhesive, the information which can be gained is incomplete.