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 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.     

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

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

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.     

Two-dimensional stress analysis of adhesive butt joints subjected to cleavage loads

This paper deals with the two-dimensional stress analysis of adhesive butt joints subjected to cleavage loads. The purpose of the paper is to contribute to the establishment of fracture criteria of adhesive joints. Similar adherends and an adhesive bond are replaced with finite strips in the analysis. Stress distributions in adhesive joints are analysed using the two-dimensional theory of elasticity. The effects of the ratio of Young's modulus of adherends to that of an adhesive and the thickness of the adhesive bonds on the stress distributions are shown by numerical calculations. For verification, strains produced on adherends are experimentally measured and a photoelastic experiment is carried out. The analytical results are in fairly good agreement with experiment.     

Stress analysis and strength evaluation of single-lap band adhesive joints of dissimilar adherends subjected to external bending moments

Single-lap band adhesive joints of dissimilar adherends subjected to external bending moments are analyzed as a four-body contact problem using a two-dimensional theory of elasticity (plane strain state). In the analysis, the upper and lower adherends and the adhesive which are bonded in two regions are replaced by finite strips. In the numerical calculations, the effects of the ratio of Young's moduli of the adherends, the ratio of the adherend thicknesses, and the ratio of the band length to the half lap length on the stress distributions at the interfaces are examined. A method for estimating the joint strength is proposed using the interface stress and strain obtained by the analysis. An elasto-plastic finite element analysis (EP-FEA) was conducted for predicting the joint strength more exactly. Experiments to measure strains and the joint strength were also carried out. The results show that the strength of a single-lap band adhesive joint is almost the same as that of a single-lap adhesive joint in which the two adherends are completely bonded at the interfaces. Thus, the single-lap band adhesive joints are useful in the design of single-lap joints.     

Three-dimensional finite element analysis of 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.     

A two-dimensional stress analysis of single-lap adhesive joints of dissimilar adherends subjected to tensile loads

Single-lap adhesive joints of dissimilar adherends subjected to tensile loads are analyzed as a three-body contact problem using the two-dimensional theory of elasticity. In the numerical calculations, the effects of Young's modulus ratio between different adherends, the ratio of the adherend thicknesses, the ratio of the adherend lengths, and the adhesive thickness on the contact stress distributions at the interfaces are examined. As a result, it is found that (1) the stress singularity occurs near the edges of the interfaces and it increases at the edge of the interface of an adherend with smaller Young's modulus; (2) the stress singularity increases at the edge of the interface of an adherend with thinner thickness; (3) the singular stresses increase at the edges of the two interfaces as the ratio of the upper adherend length to the lower one decreases; and (4) the singular stresses increase at the edges of the two interfaces as the adhesive thickness decreases when the adhesive is thin enough, and they also increase as the adhesive thickness increases when the adhesive is thick enough. In addition, the singular stresses obtained from the present analysis are compared with those obtained by Bogy. Fairly good agreement is seen between the present analysis and the results from Bogy. Strain measurement and finite element analysis (FEA) were carried out. The analytical results are in fairly good agreement with the measured and the FEA results.     

A 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.     

The two-dimensional adhesive contact problem in the theory of couple stress elasticity

Abstract

The adhesive contact problem of a half-space indented by a rigid cylindrical punch in the theory of couple-stress elasticity is investigated. Both the size effect and adhesion are considered to analyze the two-dimensional frictionless contact problem. The method of Mindlin’s stress function and the technology of Fourier transform are applied to reduce the mixed boundary value problem to the singular integral equations. Efficient computational techniques is used to obtain the influence of the size effect and adhesion parameter on the adhesive contact behavior. Results indicated that the size effect play an important role in contact with adhesion and can help understanding the mechanism of adhesion.     

Closed-form solutions for elastic stress-strain analysis in unbalanced adhesive single-lap joints considering adherend deformations and bond thickness

A theoretical model is developed for the stress analysis in adhesive-bonded single-lap joints under tension, for which the two adherends could have different thicknesses and consist of different materials. A two-dimensional (2D) elasticity theory is adopted in the analysis, which simultaneously incorporates the complete strain-displacement and the complete stress-strain relationships for the adherends and adhesive. The approach provides a unified treatment for any possible adhesive layer flexibility and capable of satisfying the stress-free condition at the ends of the bondline. An explicit closed-form analytical solution is formulated for upper and lower adherends/adhesive stresses (strains) and tensile, shear and bending loads acting on the adherends along the overlap and then simplified for practical applications, and simple design formulae for adhesive stresses are produced. The results predicted by the present full and simplified solutions were compared with the previously theoretical solution by Bigwood and Crocombe (1989) [35], and the 2D geometrically nonlinear finite element model using MSC/NASTRAN. The agreement validates the present formulation and solutions for unbalanced bonded joints. The effects of the stiffness unbalanced parameters on the adhesive stress distributions were also discussed.     

Study of the singular term in mixed adhesive joints

In the numerical modelling of mixed adhesive joints, where different materials are disposed along the bond-lines, trimaterial singularities may arise at the adhesive bands transition points, resulting in mesh-dependent models. This work is focused on the study, characterization and treatment of these type of singularities. Firstly, the selection of an intermediate adhesive material for generating a tailored transition between bands is addressed, using analytical solutions and then corroborating by means of a novel technique for determining the influence distance of the singularity with the finite element method as calculation tool. Furthermore, it is proved how a continuum material field transition between bands produces a convergent finite element solution applying the considerations of this framework (analytical asymptotic solutions). Finally, in order to achieve the best numerical convergence rate in the models, the optimum material transition function is obtained and checked through FEM.     

Stress analysis at the interface of metal-to-metal adhesively bonded joints subjected to 4-point bending: Finite element method

This paper presents a study of stress states in two-dimensional models of metal-to-metal adhesively bonded joints subjected to 4-point flexural loading using the finite element (FE) method. The FE simulations were carried out on adhesive bonded joints of high support span to specimen thickness ratio undergoing extensive plastic deformations. Two different adhesive types with eight different adhesive layer thicknesses each varying between 50 μm and μm were considered. The lower interfaces in the brittle adhesive were observed to be under a lower stress state because of the constraint exerted by a relatively stiff lower adherend. The ductile adhesive layers were under a lower state of stress as a result of the lower elastic modulus. It is concluded that the degree of plastic deformation in the adhesive is dictated by the adherend stiffness and the load transfer along the interface. The effect of load and support pins is noticeable at all adhesive thicknesses. High stress localisation exists in the vicinity of the load pins. The constraint exerted by the adherends dictates the deformation gradient through thickness of the adhesive layer. Adhesive joint behaviour as determined by the adhesive properties is investigated and also experimentally validated. Conclusions were drawn by correlating the adhesive and adherend stress states.     

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.     

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

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

Dynamic analysis of single-lap,adhesively bonded composite-titanium joints subjected to solid projectile impact

The transient stress in a single-lap, adhesively bonded composite-titanium joints subjected to solid projectile impact is analyzed using the three-dimensional finite element method. This method is constructed based on the progressive failure features of the composite adherend and the elastic-plastic property of the titanium adherend and adhesive. The effects of the thickness and overlap length of the adhesive layer, the solid projectile size and its velocity, and the strain-rate effect on the dynamic stress of the joints are examined. It is shown that the stress evolution with certain amplitude exists in the joint. During the impact process, compressive stress concentration is imparted at the point of the contact. Furthermore, experiments are carried out for measuring the strain responses of the adhesively bonded joints. A fairly good agreement is observed between the numerical and measured results.     

Three-dimensional finite element stress analysis of single-lap adhesive joints of dissimilar adherends subjected to impact tensile loads

The stress-wave propagations and stress distributions in single-lap joints of dissimilar adherends were analyzed using an elastic three-dimensional finite-element method (DYNA3D). An impact tensile load was applied to the single-lap adhesive joint by dropping a weight. One end of the upper adherend in the single-lap adhesive joint was fixed and the other adherend (lower adherend) which was connected to a bar was impacted by the weight. The effects of Young's modulus and the thickness of each adherend on the stress wave propagations and stress distributions at the interfaces were examined. It was found that the maximum value of the maximum principal stress occurred near the edge of the interface of the fixed adherend. The maximum principal stress increased as Young's modulus of the fixed adherend increased. It was also observed that the maximum principal stress increased as the fixed adherend thickness decreased. In addition, strain responses in the single-lap adhesive joints of dissimilar adherends subjected to impact tensile loads were measured using strain gauges. Fairly good agreements were found between the FEM calculations and the experimental measurements.     

Three-dimensional stress analysis of adhesive butt joints with disbonded areas and spew fillets

This paper deals with three-dimensional stress analysis of adhesive butt joints subjected to tensile loads, to help establish fracture criteria. In this analysis, the adherends and adhesive bond are replaced with finite solid culinders. Stress distributions in adhesive joints are analysed using a three-dimensional theory of elasticity. The effects of a disbonded area and a spew fillet on the principal stress distributions are shown by numerical calculation. Where a joint has a disbonded area, the stress singularity increases with a decrease in the diameter of the spew fillet, and the stress singularity decreases with an increase in the diameter of the adhesive. The analytical result is compared with that obtained by an experiment concerning the strain produced on the adherends in the case of a disbonded area. Both results are satisfactorily consistent.     

Finite element analysis of adhesively bonded composite joints subjected to impact loadings

The main concern of this paper is to explore the geometrical and material effects on composite double lap joints (DLJ) subjected to dynamic in-plane loadings. Thus, three-dimensional finite element analyses were carried out at quasi-static and impact velocities. The DLJ alone was used for quasi-static case while an output bar was added for impact case. Elastic behavior was assumed for both adhesive and adherends. Average shear stress and stress homogeneity were extracted and compared. It was observed that the adhesive shear stiffness increases the average shear stress. Moreover, it makes the stress heterogeneity more important. On the other hand, higher values of the substrates longitudinal stiffness make the average shear stress higher; whereas, the stress homogeneity in the joint is better achieved for lower substrates’ shear stiffness.     

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.