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.     

Reliability Study of Ink on Stress in Single Lap Adhesive Joints

This paper investigates the experimental reliability of SN9000 ink on the chip on film and the axial and shear stress distributions across the squared and spew end of ink in single-lap joints. The glass transition temperature of SN9000 was analyzed by a regression analysis method. The results demonstrated that for the continuous heating of a single ink drop, the confidence level is more than 96.7%. The stress field in single-lap joints with square and spew geometries was simulated by the finite element method. The stress distribution across the lap length at the interface for joints with spew ends was compared to that of square ended single lap joints. The maximum magnitude of the von Mises stress was less than the yield strength of the substrate material. These results helped us to understand that the relationship between the glass transition temperature and von Mises stress is less than the yield strength of SN9000.     

Characterization of adhesive yield criteria usingmixed-mode loading

While structural adhesives are used widely, relatively little is known regarding their plastic behavior. Few studies exist, for instance, to experimentally validate yield criteria for adhesives. The following considered adhesive joints under biaxial stress using an Arcan fixture. Adhesive strain was measured from the relative displacement of the adherends using digital image correlation. Two adhesive systems showed better correlation with a von Mises yield criterion in comparison to the commonly used Drucker-Prager criterion. The results were applied to a single lap shear joint, with mixed mode stress in the gauge section, which again showed better agreement with von Mises. The Drucker-Prager criterion, for instance, overestimated the yield stress by up to 11% while von Mises was within 2%.     

Fatigue Failure Criterion of Adhesively-Bonded Joints Under Combined Stress Conditions

A study was conducted to investigate fatigue failure criteria for adhesively-bonded joints under combined stress conditions. Two types of adhesively-bonded joint specimens were used: the scarf joint and the butterfly-type butt joint. Both types of joints have considerably uniform combined stress distributions in the adhesive layer. Furthermore, the stress distributions of these joints were analyzed by a finite element method. The results showed that the maximum principal, the von Mises equivalent and the maximum shear stresses in the uniform stress region of the adhesive layer at the endurance limit are correlated with the principal stress ratio.     

Extension of a one-dimensional finite element model program for analysing elastic-plastic stresses and progressive failure of adhesive bonded joints

A program for stress analysis of adhesive bonded joints within an elastic range was extended to consider the elastic-plastic stress state in an adhesive layer and its progressive failure. The program is based on the one dimensional finite element method. The von Mises yield criterion and the Mohr-Coulomb failure criterion are used in the program. Numerical analysis of a single lap joint subjected to four-point bending load was conducted and its result was compared with the experimental result. Good agreements were obtained between both results except for the final failure load. The present extension has some advantages. The stress singularity in the adhesive layer at the lap end or crack tip can be avoided due to the simple assumption for adhesive strains. Shorter computing time by the present method than by other general two- or three-dimensional finite element model programs should be much emphasized as one of the advantages.     

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

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

Use of artificial neural networks for modelling rate dependent behaviour of adhesive materials

This research work highlights the use of artificial neural networks (ANN) for modelling the rate-dependent response of adhesive materials with the purpose of expanding the established method for modelling the response of adhesively bonded structures, and in particular single lap joints. The motivation for this work comes after a viscoplastic model developed in a previous research work failed to predict the response of single lap joints bonded with a rate dependent adhesive material. The viscoplastic model, however, was successful in replicating both bulk and shear properties of the used adhesive system. Predictions made using the rate-dependent von Mises material model proved to be successful in predicting the behaviour of single lap joints, but it could not model the shear data using the tensile data due to hydrostatic stress sensitivity in the adhesive itself. Accurate predictions of the rate-dependent behaviour using artificial neural networks are possible with the availability of stress and strain data sets from experiments. This is where the neural network constitutive model directly acquires the information on the material behaviour from experimental data sets. Material data defining both the tensile and shear response of the adhesive system was extracted from previous research work. An artificial neural network constitutive model was developed and then used to replicate experimental data and also to generate further data at other strain rates. The available model could be slightly modified and then used to investigate various geometrical parameters, such as overlap length, plate thickness and adhesive thickness on joint strength.     

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

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

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

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

Elastic stresses in an adhesively-bonded functionally-graded tubular single-lap joint in tension

In this study, the elastic stress analysis of an adhesively-bonded tubular lap joint with functionally-graded Ni-Al₂O₃ adherends in tension was carried out using a 3D 8-node isoparametric multilayered finite element with 3 degrees-of-freedom at each node. Stress concentrations were observed along the edges of both outer and inner tubes in the overlap region. Thus, the outer tube region near the free edge of the inner tube and the inner tube region near the free edge of the outer tube experienced considerable stress concentrations. Normal σ_zz and shear σ_rz stresses were dominant among the stress components. In addition, both edges of the adhesive layer experience stress concentrations, and the von Mises σ _eqv stress decreases uniformly across the adhesive thickness at the free edge of the outer tube, whereas it increases at the free edge of the inner tube. However, different compositional gradients had only a small effect on the through-the-thickness normal and shear stress profiles of both outer and inner tubes, and the peak von Mises σ _eqv stresses occurred inside the tube walls. As the ceramic phase in the material composition of the outer and inner tubes was increased, peak von Mises σ _eqv stress appeared in the ceramic layer. However, its magnitude was increased 1.75-fold in both tubes. In addition, the peak adhesive stresses appeared at the edge of the outer tube–adhesive interface near the free edge of the inner tube and at the edge of the inner tube–adhesive interface near the free edge of the outer tube. Increasing the ceramic phase in the material composition caused 1.22–1.67-times higher von Mises stresses along the free edges of the adhesivetube interfaces. In addition, with increasing number of layers across the inner and outer tubes the profiles of the normal σ_zz , shear σ_r and von Mises σ _eqv stresses across the tube walls and adhesive layer become similar. Increasing the ceramic phase in the material composition of the tubes causes also evident increases in the normal σ_zz and von Mises stresses while it does not affect their through-the-thickness profiles. However, it affects only shear σ_r and von Mises stresses across the adhesive layer. Finally, the layer number and the compositional gradient do not affect considerably through-the-thickness normal and shear stress profiles but levels in a functionally graded plate subjected to structural loads.     

单搭接接头峰值应力数值模拟的正交法分析

运用正交试验法研究了几个主要力学和几何参数如泊松比,弹性模量和被粘物厚对单搭接接头Von Mises等效应力的影响。有限元分析结果的极差分析、方差分析和最优方案的工程平均等结果表明:被粘物厚对单搭接接头Von Mises等效应力影响最大,弹性模量次之,泊松比影响程度最小。分析可知:高的泊松比、低弹性模量和被粘物厚的增大会使得Von Mises等效应力值显著降低。     

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.     

Thin membranes loaded with adhesive lap joints

Adhesive joints in which load is transfered from a relatively small lap onto a large membrane have been studied using finite element analysis. The effects of loading mode and lap geometry on the stress state in the membrane and adhesive and on the shear stresses at the adhesive/membrane interface have been examined. The results show that the load capacity of the joint, as well as the possible failure origin, depends on the mode of loading and the shape of the lap, with higher load capacities being achieved for wider and shorter laps. Application of the concentrated load at the central region of the lap produces a more favourable state stress in the membrane.     

Investigating the performances of stepwise patched double lap joint

An adhesive-bonded double-lap composites joint with stepwise attachments was proposed and investigated experimentally and numerically in this study. For the conventional double lap joint (DLJ), the high shear stress and peel stress taking place in the adhesive layer near the patch termination significantly influenced the joint strength. In order to diminish the amount of the stresses, a new design of stepwise patch was introduced in the fabrication of the double-lap joint. Based on the finite element stress analysis (FEA), it was found that both shear stress and peel stress within the adhesive layer were reduced appreciably by the employment of the stepwise attachment. In addition, experimental results illustrated that the double lap joint with stepwise patch exhibited not only higher joint strength, but also it showed longer fatigue life than the conventional double lap joints.     

Progressive failure and experimental study of adhesively bonded composite single-lap joints subjected to axial tensile loads

Experimental tests and finite element method (FEM) simulation were implemented to investigate T700/TDE86 composite laminate single-lap joints with different adhesive overlap areas and adherend laminate thickness. Three-dimensional finite element models of the joints having various overlap experimental parameters have been established. The damage initiation and progressive evolution of the laminates were predicted based on Hashin criterion and continuum damage mechanics. The delamination of the laminates and the failure of the adhesive were simulated by cohesive zone model. The simulation results agree well with the experimental results, proving the applicability of FEM. Damage contours and stress distribution analysis of the joints show that the failure modes of single-lap joints are related to various adhesive areas and adherend thickness. The minimum strength of the lap with defective adhesive layer was obtained, but the influence of the adhesive with defect zone on lap strength was not decisive. Moreover, the adhesive with spew-fillets can enhance the lap strength of joint. The shear and normal stress concentrations are severe at the ends of single-lap joints, and are the initiation of the failure. Analysis of the stress distribution of SL-2-0.2-P/D/S joints indicates that the maximum normal and shear stresses of the adhesive layer emerge on the overlap ends along the adhesive length. However, for the SL-2-0.2-D joint, the maximum normal stress emerges at the adjacent middle position of the defect zone along the adhesive width; for the SL-2-0.2-S joint, the maximum normal stress and shear stress emerge on both edges along the adhesive width.     

Direct Measurement of Longitudinal Strains and Stresses within Single Lap Shear Adhesive Joints Using Neutron Diffraction

The neutron diffraction technique has been used to investigate the longitudinal stresses in the adherend produced as a result of cure and due to the application of a tensile load in a single lap shear joint. A comparison has also been made between the stress distributions in loaded “aged” and “unaged” joints. The neutron diffraction technique is the only viable method of investigating these stresses within metal adherends and enables comparisons between predicted and measured stresses to be made. The results of these experiments cast doubt on some of the predictions from finite element modelling of adherend stress levels.     

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

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

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

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

预偏角对单搭接接头强度的影响

研究了在被粘物搭接区顸偏转角度对钢单搭接拉伸接头剪切强度的影响,并用弹性有限元法分析了预偏角变化时单搭接接头上胶层中的应力分布情况。数值分析的结果表明：当预偏角从0°增加到12°时,结构钢单搭接接头胶层中的所有应力峰值分量均显著下降。而在所采取实验条件下,接头的剪切强度最高值出现在预偏角为6°时。因而在进一步研究预偏角对单搭接接头承载能力的作用时,应将外载作用下接头的本征偏转情况考虑在内。     

Geometric Factors Impacting Adhesive Lap Joint Strength and Design

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

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%.