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.     

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.     

Optimization of adhesively-bonded single lap joints by adherend notching

The effect of adherend notching on the strength and deformation behavior of single lap joints was investigated. First, a parametric study was conducted using finite element analysis (FEA). This initial part of the research into the effect of notches on joint behavior involved determination of the optimum notch location and notch dimensions. This was done by using FEA in a series of models with different notch positions and geometries. The results of this parametric study were used to select the most promising lap geometries for further study. Next, more detailed FEA were conducted on the selected lap geometries. These data were compared with the experimental single-lap shear test results to assess the applicability of different failure criteria. Three different model adhesives were used: a rubber toughened film epoxy with nylon carrier, a styrene-butadiene-styrene block copolymer based deformable 'gel' adhesive, and a two-part, metal filled brittle epoxy adhesive. The FEA for single lap joints containing 'top notches' on the unbonded, top side of the adherends, at locations corresponding to the overlap ends, and bonded with the two-part metal filled epoxy provided the best agreement with the experimental results. The experimental results showed a 29% increase in joint strength with the introduction of the notches, which matched very well with the 27% decrease in the peak peel stress observed by the FEA results. For this brittle adhesive, the peel stress is almost certainly the governing failure stress. This was confirmed by matching of the FEA peak peel stress ratios with the experimental load ratios, for both the notched and unnotched specimens.     

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.     

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。     

Non-linear Modeling of Tubular Adhesive Scarf Joints Loaded in Tension

In this paper, a simple analytical model is developed to determine the adhesive shear strain distribution of a tubular adhesive scarf joint loaded in tension. The approach is an extension of the original well-recognized Volkersen's shear lag analysis for a shear loaded joint, which is frequently applied to adhesively-bonded joints. A mathematical representation consisting of linear and exponential functions is employed to model the elastic–plastic behavior commonly observed in structural adhesives. The governing equation is found to be in the form of a non-linear second-degree ordinary differential equation with variable coefficients. A numerical method required for solving this equation is also introduced. Numerical predictions of shear strain distributions are compared with results from non-linear Finite Element Analysis (FEA), utilizing the commercially available software, ANSYS 5.6, a general-purpose software system. It is shown that both the linear and non-linear approximate solutions are closely comparable with the FEA results for a 10°-scarf angle and elastic isotropic adherends. In concurrence with previous work on flat adherends, the present work demonstrates that the scarf joint develops more uniform shear stress and strain distributions with a consequent reduction in peak values than those for the conventional lap joint. In contrast, the conventional lap joint with the equivalent bonded surface area experiences a more substantial elastic trough, which can provide a more stable configuration for, sustained long term loading applications.     

Non-linear Modeling of Tubular Adhesive Scarf Joints Loaded in Tension

In this paper, a simple analytical model is developed to determine the adhesive shear strain distribution of a tubular adhesive scarf joint loaded in tension. The approach is an extension of the original well-recognized Volkersen's shear lag analysis for a shear loaded joint, which is frequently applied to adhesively-bonded joints. A mathematical representation consisting of linear and exponential functions is employed to model the elastic-plastic behavior commonly observed in structural adhesives. The governing equation is found to be in the form of a non-linear second-degree ordinary differential equation with variable coefficients. A numerical method required for solving this equation is also introduced. Numerical predictions of shear strain distributions are compared with results from non-linear Finite Element Analysis (FEA), utilizing the commercially available software, ANSYS 5.6, a general-purpose software system. It is shown that both the linear and non-linear approximate solutions are closely comparable with the FEA results for a 10°-scarf angle and elastic isotropic adherends. In concurrence with previous work on flat adherends, the present work demonstrates that the scarf joint develops more uniform shear stress and strain distributions with a consequent reduction in peak values than those for the conventional lap joint. In contrast, the conventional lap joint with the equivalent bonded surface area experiences a more substantial elastic trough, which can provide a more stable configuration for, sustained long term loading applications.     

Non-linear analysis and optimization of adhesively bonded single lap joints between fibre-reinforced plastics and metals

Non-linear finite element methods are applied in the analysis of single lap joints between fibre-reinforced plastics (FRP) and metals. The importance of allowing for both geometric and material non-linearities is shown. The optimization of single lap joints is done by modifying the geometry of the joint ends. Different shapes of adhesive fillet, reverse tapering of the adherend, rounded edges and denting are applied in order to increase the joint strength. The influence of the joint-end geometry is shown for different metal adherend/FRP adherend/adhesive combinations. The results of the numerical predictions suggest that with a careful joint-end design the strength of the joints can be increased by 90–150%.     

The Effect of PEEK Fibres and Powder on Joints Made with a High Temperature Adhesive

High temperature adhesives typically exhibit low levels of peel strength since they tend to be more brittle than typical toughened adhesives used for lower temperature applications. It was found that incorporating thermoplastic fibres or powder into the bondline of a joint made with a high temperature epoxy-based adhesive resulted in significant improvements in peel strength. Poly(ether ether ketone) (PEEK) fibres and powder were incorporated into the adhesive resin and used in aluminium joints. These were tested in peel and single lap shear using a range of fibre lengths, orientations and volume fractions. It was seen that large increases in peel strength could be achieved but that lap shear strength was degraded with most types of modification. However, some modifications resulted in significant increases in peel strength with limited decrease in lap shear strength. These improved properties have been achieved using physical modifications rather than chemical alteration of the resin.     

Solutions for Clamped Adhesively Bonded Single Lap Joint With Movement of Support End and Its Application to a Carbon Nanotube Junction in Tension

This article presents analytical solutions for a clamped-clamped adhesively bonded single lap joint with movement of supports and its application to studying the failure mechanism of carbon nanotube junctions in a tensile test. In the analytical model, the interface shear and normal stresses, movement of one support end, geometric nonlinearity, and the contact stresses between two cylinders are considered. Analytical solutions are derived for a clamped-clamped single lap joint with movement of one support end first, and then geometrically nonlinear finite element analysis is conducted to verify the present analytical solutions. An equivalent two-dimensional model is presented for a junction self-assembled by two carbon nanotubes, and the failure mechanism of the carbon nanotube junction is then studied by using the present analytical solutions. Structural performance of single lap joints with movement of support ends as boundary conditions is also investigated.     

Single and dual adhesive bond strength analysis of single lap joint between dissimilar adherends

The emerging trends for joining of aircraft structural parts made up of different materials are essential for structural optimization. Adhesively bonded joints are widely used in the aircraft structural constructions for joining of the similar and dissimilar materials. The bond strength mainly depends on the type of adhesive and its properties. Dual adhesive bonded single lap joint concept is preferred where there is large difference in properties of the two dissimilar adherends and demanding environmental conditions. In this work, Araldite-2015 ductile and AV138 brittle adhesives have been used separately between the dissimilar adherends such as, CFRP and aluminium adherends. In the dual adhesive case, the ductile adhesive Araldite-2015 has been used at the ends of the overlap because of high shear and peel strength, whereas in the middle of the bonded region the brittle adhesive AV138 has been used at different dimensions. The bond strength and corresponding failure patterns have been evaluated. The Digital Image Correlation (DIC) method has been used to monitor the relative displacements between the dissimilar adherends. Finite element analysis (FEA) has been carried-out using ABAQUS software. The variation of peel and shear stresses along the single and dual adhesive bond length have been captured. Comparison of experimental and numerical studies have been carried-out and the results of numerical values are closely matching with the experimental values. From the studies it is found that, the use of dual adhesive helps in increasing the bond strength.     

A numerical and experimental study of preformed angle in the lap zone on adhesively bonded steel single lap joint

The effect of a preformed angle in the lap zone of steel adherends on the stress distribution in adhesively bonded single lap joints was investigated using an elasto-plastic finite element analysis (FEA). The ultimate loads of the joints were determined by shear tests and the failure surfaces of the lap zone were analyzed using scanning electron microscopy (SEM). The results from the numerical simulation showed that all the peak stresses in the mid-bondline of the adhesively bonded single lap joint were reduced as the preformed deflection angle was increased from 0° to 15°. The highest value of the average ultimate load of the experimental joints occurred when the preformed angle was equal to 7° (about 64% higher than the standard one). The SEM images also indicated that the failure mode in the overlap zone of the joint changed from that of a mainly adhesion one to a mixed one as the preformed angle increased.     

Analysis of tubular adhesive joints with a functionally modulus graded bondline subjected to axial loads

The strength and lifetime of adhesively bonded joints can be significantly improved by reducing the stress concentration at the ends of overlap and distributing the stresses uniformly over the entire bondline. The ideal way of achieving this is by employing a modulus graded bondline adhesive. This study presents a theoretical framework for the stress analysis of adhesively bonded tubular lap joint based on a variational principle which minimizes the complementary energy of the bonded system. The joint consists of similar or dissimilar adherends and a functionally modulus graded bondline (FMGB) adhesive. The varying modulus of the adhesive along the bondlength is expressed by suitable functions which are smooth and continuous. The axisymmetric elastic analysis reveals that the peel and shear stress peaks in the FMGB are much smaller and the stress distribution is more uniform along its length than those of mono-modulus bondline (MMB) adhesive joints under the same axial tensile load. A parametric evaluation has been conducted by varying the material and geometric properties of the joint in order to study their effect on stress distribution in the bondline. Furthermore, the results suggest that the peel and shear strengths can be optimized by spatially controlling the modulus of the adhesive.     

Increasing strength of single lap joints of metal adherends by taper minimization

The effect of tapering the ends of the adherend on the joint strength and joint deformation behavior of a single lap joint geometry was studied. The joints were geometrically modeled using finite element (FE) techniques involving linear, as well as nonlinear (bilinear) material behavior. The FEA results were then compared with the experimental results for different single lap configurations, which had aluminum and steel adherends with different surface etch conditions, bonded using two different adhesives. The FEA results were found to be consistent with the experimental results with the normal and shear stresses significantly decreasing in the modified (tapered) geometries over those in unmodified geometries. The joint strength increased with decreasing taper angle, reaching a maximum at the smallest value considered (~10°).     

Effect of Adherend Recessing on the Tensile Strength of Single Lap Joints

Bonded joints are gaining importance in many fields of manufacturing owing to a significant number of advantages to the traditional methods. The single lap joint (SLJ) is the most commonly used method. The use of material or geometric changes in SLJ reduces peel and shear peak stresses at the damage initiation sites. In this work, the effect of adherend recessing at the overlap edges on the tensile strength of SLJ, bonded with a brittle adhesive, was experimentally and numerically studied. The recess dimensions (length and depth) were optimized for different values of overlap length (L _O), thus allowing the maximization of the joint's strength by the reduction of peak stresses at the overlap edges. The effect of recessing was also investigated by a finite element (FE) analysis and cohesive zone modelling (CZM), which allowed characterizing the entire fracture process and provided joint strength predictions. For this purpose, a static FE analysis was performed in ABAQUS® considering geometric nonlinearities. In the end, the experimental and FE results revealed the accuracy of the FE analysis in predicting the strength and also provided some design principles for the strength improvement of SLJ using a relatively simple and straightforward technique.     

Structural shape optimization of bonded joints using the ESO method and a honeycomb-like mesh

This work presents an application of the evolutionary structural optimization (ESO) method to optimize two of the most common bonded joints – the single lap joint and the double lap joint. The ESO method was used to shape the adherends contour to reduce peak stresses at the overlap ends. The shape optimization was performed under a von Mises rejection criterion. The von Mises stress was evaluated using the finite element model for both types of joints. It is proposed here to utilize a honeycomb-like mesh using hexagonal elements to minimize stress concentration problem. Additionally, the use of a honeycomb mesh in the ESO method led to a smoother adherend contour. Numerical results show how the stress distributions for both shear and peel stresses are improved after the application of this optimization method.     

Analysis and design of adhesively bonded joints for fatigue and fracture loading: a fracture-mechanics approach

An experimental–computational fracture-mechanics approach for the analysis and design of structural adhesive joints under static loading is demonstrated by predicting the ultimate fracture load of cracked lap shear and single lap shear aluminum and steel joints bonded using a highly toughened epoxy adhesive. The predictions are then compared with measured values. The effects of spew fillet, adhesive thickness, and surface roughness on the quasi-static strength of the joints are also discussed. This fracture-mechanics approach is extended to characterize the fatigue threshold and crack growth behavior of a toughened epoxy adhesive system for design purposes. The effects of the mode ratio of loading, adhesive thickness, substrate modulus, spew fillet, and surface roughness on the fatigue threshold and crack growth rates are considered. A finite element model is developed to both explain the experimental results and to predict how a change in an adhesive system affects the fatigue performance of the bonded joint.     

胶瘤中嵌入金属对单搭接接头的影响

研究了在胶瘤中嵌入金属对单搭接接头强度的影响,结果表明,金属嵌入后均能显著提高接头的强度.但随三角形锲块入射角度的增大,接头强度提高幅度逐渐降低.有限元数值分析的结果显示,三角形金属楔块使端部应力峰值和平均应力均大大降低,剥离应力降低明显.     

Moisture durability of four moisture cure urethane adhesives

Moisture durability of four low modulus adhesives was examined. The four low modulus adhesives all had the same basic moisture cure polymer but contained different fillers and additives. Hot-dipped galvanized steel was bonded to random fiber-reinforced unsaturated polyester and aged in two moisture environments for various durations. Adherend surface wipes included acetone, isopropyl alcohol and a typical surface contamination for galvanized steel (an organic lubricant). Diffusion coefficients, moisture uptake and modulus changes due to moisture environment were determined for the adhesives and the fiber-reinforced plastic (FRP). The moisture cure adhesive with clay and poly(vinyl chloride) (PVC) as fillers (adhesive 252) had the highest retained lap joint strengths. Initially, adhesive 252 had single lap joint strengths of 1.47 ± 0.08 MPa for acetone-wiped joints and 1.39 ± 0.33 MPa for organic lubricant-wiped joints. After accelerated aging in a cataplasma environment for 9 weeks, lap joint strengths fell to 0.61 ± 0.08 MPa for acetone-wiped joints and to 0.65 ± 0.11 MPa for organic lubricant-wiped joints. Environmental scanning electron microscopy (ESEM) and energy-dispersive spectrometry (EDS) showed that the actual failure locus was through a corroded zinc layer and between the adhesive and the zinc surface after aging. Dynamic mechanical analysis (DMA) showed that the modulus for adhesive 252 dropped from 21.7 to 13.9 MPa after cataplasma aging. From finite element analysis (FEA), this modulus drop corresponded to a drop in normal stress concentration from 0.75 to 0.57, and a drop in shear stress concentration from 1.41 to 1.36 at a point 0.5 mm from the end of the single lap joint overlap.