Elasto-plastic stress distributions in adhesively bonded double lap joints

Elasto-plastic stress analysis is an important solution for a used ductile adhesive in single or double lap solutions. After loading, the joint strength can be increased by residual stresses. In this study, an elasto-plastic stress analyses of the shear and peel stresses are carried out in a double-lap joint. The adhesive material is chosen as a ductile material which is DP460. Elasto-plastic solution of the shear stress is obtained in a simple and accurate form in one dimensional case. Then, the solution of the peel stress is performed by considering the shear stress in the elasto-plastic form. In this solution, the boundary conditions are satisfied by the Newton–Raphson method. A good agreement is obtained between these analytical and numerical (ANSYS 10) solutions. The values are calculated highest at the ends of the adhesive.     

The analysis of elastic adhesive stresses in bonded lap joints in FRP structures

Numerous publications provide the closed form solution for adhesive stress distribution in bonded lap joints. However, in order to render these solutions tractable the authors invariably impose simplifications, one of the most restrictive being that the adherends are identical. This is unrealistic for bonded joints in most practical structures where a variety of dissimilar components may be assembled.This paper presents two analytical techniques, namely the classical and the finite element theories, which are used to determine the elastic adhesive stress distribution for the single, double and tubular lap configurations. The generality for dissimilar adherends is included. The governing differential equations obtained when using the classical approach necessitate a numerical solution and in this paper a procedure is described which uses the finite difference method. Example solutions are presented as case studies.     

Analysis of adhesive bonded composite lap joints with transverse stitching

The effect of transverse stitching on the stresses in the adhesive is investigated using an adhesive sandwich model with nonlinear adhesive properties and a transverse stitching model for adhesive bonded composite single-lap and double-lap joints. Numerical results indicate that, among all stitching parameters, thread pretension and stitch density have significant effect on the peel stresses in the adhesive; increase in the thread pretension and the stitch density leads to a decrease in peel stress in the adhesive, while an increase in other parameters generally results in a negligible reduction in peel stress. The effect of stitching was found to be negligible on the shear stresses in the adhesive. Thus it is concluded that stitching is effective for the joints where peel stresses are critical and ineffective for those where shear stresses are critical.     

The investigation of effect of adherend thickness on scarf lap joints

In this paper, the mechanical behavior of the Scarf Lap Joints (SLJs) bonded with adhesive under a tensile load was analyzed. The effects of adherend thickness at the interface stress‐strain distributions of SLJs were examined. The stress‐strain analyses were performed by Finite Element Method (3D‐FEM). The 3D‐FEM code was employed with Ansys (Ver.12.0.1). Experimental results were compared with the 3D‐FEM results and were found quite reasonable. It was concluded that both experimental and 3D‐FEM failure loads were increased with increased adherend thickness. The results indicated that the maximum failure loads were determined at t=8 mm in all joints. The analysis of the SLJs under tensile load showed that the stress and strain concentrations occurred around the edges of the joints.     

Parametric study of the creep failure of double lap adhesively bonded joints

In this paper the influence of adhesive thickness and adhesive fillet on the creep deformation and creep life time of the adhesively bonded double lap joint have been studied experimentally. Also finite element modeling was used to simulate creep behavior of bonded joints and the results are compared with those obtained from experimental tests. The adhesive used in this research was Araldite 2015 which is an epoxy based adhesive. Research procedure is carried out in two major stages. Firstly, uniaxial creep tests were conducted in 63 °C to obtain the creep characteristics and constitutive equation parameters of the adhesive at 63 °C. An empirical based rheological model based on Maxwell and Zener’s model is proposed to simulate the creep behavior of the adhesive and it is used to predict the creep behavior of the bonded joint using finite element method. Numerical results show good agreement with experimental data. It was observed that applying fillet increases creep life and decreases joint creep deformation, however increasing adhesive thickness has slight effect on the creep life time of the joint.     

Computational analysis of geometric nonlinear effects in adhesively bonded single lap composite joints

It is well known that geometric nonlinear effects have to be taken into account when the ultimate strength of single lap composite joints are studied. In the present paper we investigate for which level of loads or prescribed end displacements nonlinear effects become significant and how they appear. These aspects are studied by comparing finite element results obtained from geometric nonlinear models with the results from the linear ones. The well-known software package ANSYS is applied in the numerical analysis together with a self-implemented module in the C++ library Diffpack. Some of the results are also compared with classical analytical theories of idealized joints showing significant differences.The joints examined are made of cross-ply laminates having 0 or 90° surface layers. A combined cross-ply/steel joint and an isotropic joint made of steel are also studied. All the models except the all-steel one are assembled with adhesives, while the latter is welded.Through the investigation a considerable departure from linear behavior has been detected for a large regime of prescribed end displacements or external loads. Geometric nonlinear effects begin to develop for external loads that produces stresses which are far below ultimate strength limits and for average longitudinal strains that are less than 0.5%. It has also been detected that the distribution of materials within the joint has some influence on the nonlinear behavior. Thus, geometric nonlinear methods should always be applied when single lap (or other non-symmetric) composite joints are analyzed.     

Failure prediction and strength improvement of uni-directional composite single lap bonded joints

A methodology is presented for the failure prediction of the composite single lap bonded joints considering both the composite adherend and the bondline failures. An elastic-perfectly plastic model of the adhesive and a delamination failure criterion were used in the methodology. The failure predictions using the finite element analysis and the proposed methodology were performed. The failure prediction results such as failure mode and strength showed very good agreements with the test results for the joint specimens with various bonding methods and parameters. Based on the numerical investigation, the optimal joint strength condition was found and a new joint strength improvement technique was suggested. The suggested technique was verified to have a significant effect on the joint strength improvement.     

Failure load evaluation and prediction of hybrid composite double lap joints

Hybrid joints are a combination of adhesive bonding and mechanical fastening and are known to combine the advantages of both joint types. In this paper, we evaluate and compare the strengths of mechanical joints, adhesive joints and hybrid composite joints. We manufactured and tested 10 hybrid joint specimens with different width-to-diameter (w/d) ratios, edge-to-diameter (e/d) ratios and adherend thicknesses. Additionally, the strengths of the hybrid joints were predicted using the Failure Area Index (FAI) method and the damage zone method, and we compared our theoretical predictions with our experimental results. From these data, we were able to predict hybrid joint strengths to within 23.0%.     

Three-dimensional singularities in double lap joints

A 3-dimensional numerical analysis of a double lap joint specimen is presented. It is focused on the stress field on the interface plane where delamination would probably start. Combinations of isotropic and orthotropic layers are studied. It is shown that the most favorable point for delamination onset according to the linear fracture mechanics (LFM) approach lies near the 3-D corner, where all three modes of fracture are present, for all cases checked. The shear energy, which represents the tendency for yielding, is at the corner itself. The singular region for common combinations of adhesives-adherents is so small that regular continuum mechanics tools may be limited in failure predictions. The special features of the 3-D singularity at the comer point is discussed. Limitations of LFM for delamination onset prediction may lead to an extended type of failure criteria which is based on the shear energy state of the adhesive as well as the regular stress intensity factors. Two-dimensional solutions would show higher critical loads for the same problem.     

Ultimate behaviour of adhesively bonded FRP lap joints

This paper deals with a numerical investigation on double-lap and symmetrical single-lap joints subjected to shear/bending moment and axial force. The analysis has been developed using the theoretical model proposed by the author in [Ascione F. Mechanical behaviour of FRP adhesive joints: a theoretical model; 2007].The mechanical behavior of the adhesive is modeled through two sets of independent interfacial springs capable of characterizing the normal and transversal interactions, respectively. The adherents are modeled following the hypotheses of the beam technical theory. The mathematical model is based on two fundamental hypotheses: the possibility to separate the shear-flexure problem from the extensional one; the total fracture energy is additionally broken down in a term relative to mode I of fracture (opening) and in a term relative to mode II of fracture (sliding).Five dimensionless parameters which influence the design problem of the joints are identified. Several examples of the ultimate domains of the interface between the adherents are also presented as well as comparisons with some results reported in literature.     

Fatigue de-bond growth in adhesively bonded single lap joints

The fatigue de-bond growth studies have been conducted on adhesively bonded lap joint specimens between aluminium and aluminium with Redux-319A adhesive with a pre-defined crack of 3 mm at the bond end. The correlations between fracture parameters and the de-bond growth data are established using both numerical and experimental techniques. In the numerical method, geometrically non-linear finite element analyses were carried out on adhesively bonded joint specimen for various de-bond lengths measured from the lap end along the mid-bond line of the adhesive. The finite element results were post processed to estimate the SERR components G _I and G _II using the Modified Virtual Crack Closure Integral (MVCCI) procedure. In experimental work, specimens were fabricated and fatigue de-bond growth tests were conducted at a stress ratio R = − 1. The results obtained from both numerical analyses and testing have been used to generate de-bond growth curve and establish de-bond growth law in the Paris regime for such joints. The de-bond growth rate is primarily function of mode-I SERR component G _I since the rate of growth in shear mode is relatively small. The value of Paris exponent m is found to be 6.55. The high value of de-bond growth exponent in Paris regime is expected, since the adhesive is less ductile than conventional metallic materials. This study is important for estimating the life of adhesively bonded joints under both constant and variable amplitude fatigue loads.     

Failure mode and strength of uni-directional composite single lap bonded joints with different bonding methods

Failure process, mode and strength of unidirectional composite single lap bonded joints were investigated experimentally with respect to bonding methods, that is, co-curing with or without adhesive and secondary bonding. The co-cured joint specimen without adhesive had the highest failure strength. Progressive failures along an adhesive layer occurred in the secondary bonded specimen. In the co-cured specimen with adhesive film, delamination failure occurred and the joint strength was lower than that of secondary bonded specimens. Delamination failure did not occur in the secondary bonded specimen because of early crack growth and progressive failure in the adhesive layer. Therefore, The failure strength of composite bonded joint is not always proportionate to adhesion strength of adhesive due to the weakness of delamination in composite materials. The influences of surface roughness, bondline thickness and fillets in the secondary bonded specimens were also studied.     

Investigation of prepreg bonded composite single lap joint

Adhesive bonded single lap joint has been used extensively in laminated composite structures. Using neat resin adhesives, however, the joint strength is comparatively low and the fabrication time is long. In order to increase the joint strength and reduce the fabrication time, two types of fiber pre-impregnated (prepreg) composites were used to bond composite single lap joints. Test specimens were prepared per ASTM D 3165-95 standard. Ninety days of accelerated conditioning using seawater and ultraviolet radiation were conducted to investigate the long-term performance of prepreg bonded single-lap joint in an offshore environment. The shear strength of various specimens was obtained using tension tests. Two types of neat resin bonded specimens were also used for comparisons. Finite element analysis was implemented to justify test results. Parameters affecting the load carrying capacity of prepreg bonded composite single lap joints were investigated based on finite element analysis results.     

Influence of disbond on notch crack behaviour in single bonded lap joints

The behaviour of the adhesive bonded joints due to the imposed eccentric loading generates a very complex distribution of the stress in the structure. Good adhesion between substrate and adhesive ensures a successful and lasting assembly. In this study the finite element method is used to analyze the behaviour of a bonded lap joint of dissimilar materials. The effects of the mechanical properties of the joints on the shear stress variation with and without presence of a circular notch are investigated. The results show that the maximum shear stresses are located at a distance of about 18% that of the lap length whatever the type of material used. In addition, the stress intensity factor is amplified by the presence of the negative effect of disband whose increase is linearly proportional to the square of the stress intensity factor. It reached its maximum value for a crack length equal to two-fifths of the notch radius.     

Fatigue behaviour of composite adhesive lap joints

This paper is concerned with a fatigue study of composite adhesive lap joints produced from a bi-directional woven E-glass fibres and polypropylene. The adhesive used was a Bostik 7452 (Rubber & Plastics Grade) ethyl cyanoacrylate type. The effects of layer orientation, lap joint length and water immersion on the fatigue behaviour were studied. The specimens were immersed in water during periods until ninety days for controlled temperatures of 20, 40 and 70 °C. The results are presented in the form of curves of stress amplitude versus number of cycles to failure and also in the form of number of cycles to failure against time to exposure in water for fixed stress amplitudes. The fatigue damage and failure mechanisms were analysed and discussed. The joint shows that creep deformation within the temperature range of this study was probably the mainly cause of the dynamic stiffness reduction observed.     

Evaluation of fatigue strength of adhesively bonded single and single step double lap joints based on stress singularity parameters

Most adhesively bonded joints have stress singularity points at the corners of the adhesive/adherend interface. Recently, stress singularity parameters, i.e. the intensity of stress singularity, K, and the order of stress singularity, λ, have been used to evaluate the strength of adhesively bonded joints. However, in many cases, stress singularity fields of adhesive joints cannot be formulated strictly by using constant values of K and λ. To apply these parameters to evaluate the strength of an adhesive joint, it is necessary to determine a key stress component and characteristic range for calculating the apparent singularity parameters K_app and λ_app. In this study, the endurance limits of adhesively bonded single lap, cracked single lap and single step double lap joints are evaluated using the stress singularity parameters. The results indicate that fatigue failure criterion for these joints can be obtained by using the apparent singularity parameters K_app and λ_app which are calculated by the least square method for the maximum principal stress distributions in the range from 0.05 to 0.5 mm from the singularity point.     

Mixed-mode fracture of adhesively-bonded pultruded composite lap joints

The fracture behavior of adhesively-bonded double- and stepped-lap joints composed of pultruded glass fiber-reinforced polymer composite laminates and subjected to axial tension was experimentally investigated and numerically modeled. Two methods were used for the calculation of the strain energy release rate: the experimental compliance method and the virtual crack closure technique. Their results showed good agreement for stepped-lap joints, while significant deviations were observed for double-lap joints due to small stiffness changes. The experimental compliance method results were sensitive to these small changes and the virtual crack closure technique accuracy was affected by the inability of the finite element analysis to accurately model the behavior before visual crack initiation. The dominant fracture mode changed from Mode I to Mode II in the case of stepped-lap joints, while an almost constant mode ratio was retained for double-lap joints in the applied loading range. A non-convex mixed-mode fracture criterion was established for crack initiation and propagation based on the virtual crack closure technique results. Both the experimental compliance method and the virtual crack closure technique proved applicable for the interpretation of the fracture mechanics data of the structural joints examined, provided that stiffness degradation can be accurately described.     

Fatigue performance of a bonded wavy composite lap joint

A novel wavy lap joint design was further studied. Our previous studies using cross‐ply composite adherends showed that the new design was indeed much stronger than the conventional flat joint. In order to fully demonstrate advantage of the new wavy lap joint over the conventional single lap joint, comparative fatigue tests were performed to determine the durability performance of the wavy joint. In this study, a comparative static strength test of the conventional flat joint and the wavy joint was first carried out using unidirectional composite adherends. Then fatigue tests at different load levels and load frequencies were conducted. The test results showed that the wavy lap joint had a much longer fatigue life than the conventional lap joint.     

Elasto-static and elasto-plastic stress analysis of adhesive bonded tubular lap joints

The problem of an adhesive bonded lap joint between two dissimilar orthotropic circular cylindrical laminated shells is considered. The principal directions of orthotropy do not have to coincide with the principal directions of curvature, and the external loads are allowed to be of non-axisymmetric type. The adhesive layer is modelled in two ways. The first approach assumes the adhesive layer to behave as a linear elastic material. The second, more realistic approach takes into account the predominantly inelastic behaviour of many polymeric adhesives, and it is shown that the non-linear behaviour affects the adhesive stress distribution even at low levels of external loading. The developed numerical solution procedures have been used to conduct a parametric study, and a few general design recommendations are given.