Characterization of fracture in adhesively bonded double-lap joints

A broad finite element study was carried out to understand the stress fields and stress intensity factors behavior of cracks in adhesively bonded double-lap joints, which are representative of loading in real aerospace structures. The interaction integral method and fundamental relationships in fracture mechanics were used to determine the mixed-mode stress intensity factors and associated strain energy release rates for various cases of interest. The numerical analyses of bonded joints were also studied for various kinds of adhesives and adherends materials, joint configurations, and thickness of adhesive and different crack lengths. The finite element results obtained show that the patch materials of low stiffness, low adhesive moduli and low tapering angles are desirable for a strong double-lap joint. In the double-lap joint, the shearing-mode stress intensity factor is always larger than that of the opening-mode and both shearing and opening mode stress intensity factors increase as the crack length increases, but their amplitudes are not sensitive to adhesive thickness. Results are discussed in terms of their relationship to adhesively bonded joints design and can be used in the development of approaches aimed at using adhesive bonding and extending the lives of adhesively bonded repairs for aerospace structures.     

Numerical analysis of adhesively bonded T-joints with structural sandwiches and study of design parameters

Adhesively bonded T-joints are extensively used in assembling sandwich structures. The advantage of adhesive bonded joints over bolted or riveted joints is that the use of fastener holes in mechanical joints inherently results in micro and local damages to the composite laminate during their fabrication. One type of adhesive joint in such structures is the T-joint between sandwich panels. The aim of this research paper is to study, by numerical analysis, the effect of fillet geometry and core material of sandwich panels on the performance of T-joints. The base angle of the core triangle (fillet) is the most important geometry parameter of the triangular T-joint. Nine geometrical models with different base angles of the core triangle are made to investigate the effect of the base angle on the performance of the T-joints. It should be mentioned that the base angle in the triangular foam is changed, so that the final volume of the filler is kept constant in all the cases. Different foams with different stiffness are used to model the core of the panels to study the effect of the core material of sandwich panels. To model the adhesive between joint components, contact elements and cohesive zone material models are used. Therefore, failure of adhesive and separation of joint elements can be modeled. Damage and core shear failure of the base panel are modeled by using a written macro-code in the ANSYS finite element method (FEM) program. The ultimate strength of the joint in each case is calculated by modeling adhesive failure and core shear failure of the sandwich panels. Finally, the results of FEM are validated by experimental results available in the literature. In general, the failure load predicted by the FEM is within 5% of the experimental results. The best angle of the core triangle was found to be 45°. Also, the results showed that by changing the core material of the sandwich panel, the joint failure load is also changed.     

A damage zone model for the failure analysis of adhesively bonded joints

The design of structural adhesively bonded joints is complicated by the presence of singularities at the ends of the joint and the lack of suitable failure criteria. Literature reviews indicate that bonded joint failure typically occurs after a damage zone at the end of the joint reaches a critical size. In this paper, a damage zone model based on a critical damage zone size and strain-based failure criteria is proposed to predict the failure load of adhesively bonded joints. The proposed damage zone model correctly predicts the joint failure locus and appears to be relatively insensitive to finite element mesh refinement. Results from experimental testing of various composite and aluminium lap joints have been obtained and compared with numerical analysis. Initial numerical predictions indicate that by using the proposed damage zone model, good correlation with experimental results can be achieved. A modified version of the damage zone model is also proposed which allows the model to be implemented in a practical engineering analysis environment. It is concluded that the damage zone model can be successfully applied across a broad range of joint configurations and loading conditions.     

Understanding and control of adhesive crack propagation in bonded joints between carbon fibre composite adherends II. Finite element analysis

Carbon fibre composites are being widely considered for many classes of heavily loaded components. A common feature of such components is the need to introduce local or global loads into the composite structure. The use of adhesive bonding rather than mechanical fasteners offers the potential for reduced weight and cost. However, such bonded joints must be shown to behave in a predictable and reliable way. A major aspect of this is to demonstrate that the progress of cracks through the bonds is well understood. The simulation work presented here complements the experimental work presented in Part I. The observed failure processes and their sequence are successfully described and modelled.     

Simulation of adhesive joints using the superimposed finite element method and a cohesive zone model

Adhesive joints have been widely used in various fields because they are lighter than mechanical joints and show a more uniform stress distribution if compared with traditional joining techniques. Also they are appropriate to be used with composite materials. Therefore, several studies were performed for the simulation of the bonded joints mechanical behavior. In general for adhesive joints, there is a scale difference between the adhesive and the substrate in geometry. Thus, mesh generation for an analysis is difficult and a manual mesh technique is needed. This task is not efficient and sometimes some errors can be introduced. Also, element quality gets worse.In this paper, the superimposed finite element method is introduced to overcome this problem. The superimposed finite element method is one of the local mesh refinement methods. In this method, a fine mesh is generated by overlaying the patch of the local mesh on the existing mesh called the global mesh. Thus, re-meshing is not required.Elements in the substrate are generated. Then, the local refinement using the superimposed finite element method is performed near the interface between the substrate and the adhesive layer considering the shape of the element, the element size of the adhesive layer and the quality of the generated elements. After performing the local refinement, cohesive elements are generated automatically using the interface nodes. Consequently, a manual meshing process is not required and a fine mesh is generated in the adhesive layer without the need for any re-meshing process. Thus, the total mesh generation time is reduced and the element quality is improved. The proposed method is applied to several examples.     

Geometrically non-linear analysis of adhesively bonded corner joints

When adhesively bonded joints are subjected to large displacements, the small strain-small displacement (linear elasticity) theory may not predict the adhesive or adherend stresses and deformations accurately. In this study, a geometricaly non-linear analysis of three adhesively bonded corner joints was carried out using the incremental finite element method based on the small strain-large displacement (SSLD) theory. The first one, a corner joint with a single support, consisted of a vertical plate and a horizontal plate whose left end was bent at right angles and bonded to the vertical plate. The second corner joint, with a double support, had two plates whose ends were bent at right angles and bonded to each other. The final corner joint, with a single support plus angled reinforcement, was a modification of the first corner joint. The analysis method assumes that the joint members, such as the support, plates, and adhesive layers, have linear elastic properties. Since the adhesive accumulations (spew fillets) around the adhesive free ends have a considerable effect on the peak adhesive stresses, they were taken into account. The joints were analyzed for two different loading conditions: one loading normal to the horizontal plate plane P_y and the other horizontal loading at the horizontal plate free edge P_x. In addition, three corner joints were analyzed using the finite clement method based on the small strain-small displacement (SSSD) theory. In predicting the effect of the large displacements on the stress and deformation states of the joint members, the capabilities of both analyses were compared. Both analyses showed that the adhesive free ends and the outer fibres of the horizontal and vertical plates were subjected to stress concentrations. The peak stresses appeared at the slot corners inside the adhesive fillets and at the horizontal and vertical plate outer fibres corresponding to the locations where the horizontal and vertical adhesive fillets finished. The SSLD analysis predicted that the displacement components and the peak adhesive and plate stress components would show a non-linear variation for the loading condition P_x, whereas the SSSD analysis showed smaller stress variations proportional to the applied load. However, both the SSLD and the SSSD analyses predicted similar displacement and stress variations for the loading condition P_y. Therefore, the stress and deformation states of the joint members are dependent on the loading conditions, and in the case of large displacements, the SSSD analysis can be misleading in predicting the stresses and deformations. The SSLD analysis also showed that the vertical and horizontal support lengths and the angled reinforcement length played an important role in reducing the peak adhesive and plate stresses.     

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.     

Strength prediction of adhesively bonded carbon/epoxy joints

A finite element approach has been used to obtain the stress distribution in some adhesive joints. In the past, a strength prediction method has not been established. Therefore in this study, a strength prediction method for adhesive joints has been examined. First, the critical stress distribution of single-lap adhesive joints, with six different adherend thicknesses, was examined to obtain the failure criteria. It was thought that the point stress criterion, which has been previously used for an FRP tensile specimen with a hole, was effective. The proposed method using the point stress criterion was applied to adhesive joints, such as single-lap joints with short non-lap lengths and bending specimens of single-lap joints. Good agreement was obtained between the predicted and experimental joint strengths.     

Assessing effect of different surface treatments on fracture toughness behaviour of adhesively bonded 8552/AS4 composite joints

Abstract

Adhesive bonding of aeronautical components made of carbon–fibre reinforced plastics is a popular alternative to mechanical fastening. The continuing research is focused on the optimisation of the surface treatments so as to improve the mechanical properties. In this work, the effect of two atmospheric pressure plasma (APP) treatments before bonding on the fracture toughness behaviour of adhesively bonded joints was experimentally investigated. The laminates were in contact with different ancillary materials during the manufacturing process, thus leading to eight different treatment alternatives. For the investigation, a quasi-isotropic layup was subjected to modes I and II fracture toughness test. To support the understanding of the mechanical behaviour observed, non-destructive testing evaluation as well as failure mode analysis at macroscopic level was carried out. As a result, APP showed promising performances regarding surface preparation, revealing an appreciable dependence of the fracture toughness behaviour on the selected alternatives.     

An investigation of fatigue failure prediction of adhesively bonded metal/metal joints

A fracture mechanics-based model for fatigue failure prediction of adhesive joints has been applied in this work. The model is based on the integration of the kinetic law of evolution of defects originated at stress concentrations within the joint. Final failure can be either brittle (fracture toughness-driven) or ductile (tensile/shear strength-driven) depending on the adhesive. The model has been validated against experiments conducted on single-lap shear joints bonded with a structural adhesive. Three different kinds of adhesives, namely a modified methacrylate, a one-part epoxy and a two-part epoxy supplied by Henkel, have been considered and three different overlap lengths have been tested. Fracture toughness and fatigue crack growth properties of the adhesives have been determined with mode I tests. The number of cycles to failure has been successfully predicted in several cases. It is interesting to notice that in the case of joints loaded at the same average shear stress, the shorter the joint, the longer the duration. This fact is also captured by the model.     

An updated review of adhesively bonded joints in composite materials

Continuing interest and more developments in recent years indicated that it would be useful to update Banea and da Silva paper entitled “Adhesively bonded joints in composite materials: an overview”. This paper presents an updated review of adhesively bonded joints in composite materials, which covers articles published from 2009 to 2016. The main parameters that affect the performance of bonded joints such as surface treatment, joint configuration, geometric and material parameters, failure mode etc. are discussed. The environmental factors such as pre-bond moisture, moisture and temperature are also discussed in detail and how they affect the durability of adhesive joints. Lots of shortcomings were resolved during the last years by developing new materials, new methods and models. However, there is still a potential to evaluate and identify the best possible combination of parameters which would give the best performance of composite bonded joints.     

Analysis and design of adhesively bonded corner joints

In this study, the stress and stiffness analyses of corner joints with a single corner support, consisting of two plates, one of which plain and the other bent at right angles, have been carried out using the finite element method. It was assume that the plates and adhesive had linear elastic properties. Corner joints without a fillet at the free ends of the adhesive layer were considered. The joint support was analysed under three loading conditions, two linear and one bending moment. In the stress analysis, it was found that for loading in the y-direction and by bending moment, the maximum stresses occurred around the lower end of the vertical adhesive layer/ vertical plate interface; for loading in the x-direction, the maximum stresses occurred around the right free end of the horizontal adhesive layer/vertical plate interface. The effects of upper support length, support taper length and adhesive thickness on the maximum stresses have been investigated. Since the peel stresses are critical for this type of joint, a second corner joint with double corner support (i.e., one in which the horizontal plate is reinforced by a support that is an extension of the vertical plate) was investigated which showed considerable decreases in the stresses, particularly peel stresses. A third type of corner joint with single corner support plus an angled reinforcement member was investigated as an alternative to the previous two configurations. It was found that increasing the length and particularly the thickness of the angled reinforcement reduced the high peel stresses around the lower free end of the adhesive/vertical plate interface, but resulted in higher compressive stresses. In the stiffness analysis, the effects of the geometry of the joints, relative stiffness of adhesive/adherends and adhesive thickness were investigated under three loading conditions. For three types of corner joint, results were compared and recommended designs were determined based on the overall static stiffness of the joints and on the stress analysis.     

Cohesive and continuum mixed-mode damage models applied to the simulation of the mechanical behaviour of bonded joints

The objective of this work is to discuss the adequacy of cohesive and continuum damage models for the prediction of the mechanical behaviour of bonded joints. A cohesive mixed-mode damage model appropriate for ductile adhesives is presented. The double cantilever beam and the end-notched flexure tests are proposed in order to evaluate the cohesive properties of the adhesive as a thin layer under mode I and mode II, respectively. A new data reduction scheme based on the crack equivalent concept is also proposed to overcome crack-monitoring difficulties during propagation in these fracture characterization tests. An inverse method to determine the cohesive parameters of the trapezoidal softening law is discussed. A continuum mixed-mode damage model is developed in order to better simulate the cases where adhesive thickness plays an important role. The model is applied to evaluate the effect of adhesive thickness on fracture characterization of adhesive joints. Some important conclusions about the advantages and drawbacks of cohesive and continuum damage models are reported.     

On experimental methods to investigate the effect of layer thickness on the fracture behavior of adhesively bonded joints

A number of different experimental methods are used at two independent laboratories to evaluate the influence of layer thickness on the fracture properties of one batch of a crash resistant epoxy adhesive. Both mode I and II are considered. Novel, as well as state of the art methods are used. In mode I, the Double Cantilever Beam (DCB) and two versions of the Tapered Double Cantilever Beam (TDCB) specimens are utilized; in mode II, two versions of the End Notch Flexure (ENF) and the End-Loaded Shear Joint (ELSJ) specimens are used. Good agreement between the test results is achieved for thin layers in both fracture modes. For thicker layers the variation is larger.     

Effects of unbalance on the adhesively bonded composites-aluminium joints

This article presents the experimental and numerical results of adhesively bonded hybrid single-lap joint (SLJ) geometry with different configurations of lower and upper adherends subject to a four-point bending test. AA2024-T3 aluminium alloy and carbon/epoxy composites with different lamina numbers and four different stacking angles as adherend and two-part liquid, structural adhesive DP 125 as paste adhesive were used. In the experimental studies, three different types of SLJs were produced using lower material that had a constant thickness of AA2024-T3 aluminium alloy and upper material of composite material that had different numbers of layers and four different stacking sequences ([0], [0/90], [45/?45], [0/45/?45/90]). In the numerical analysis, stress analyses of the SLJs were performed with a three-dimensional non-linear finite element method and the composite adherends were assumed to behave as linearly elastic materials, while the adhesive and aluminium adherend were assumed to be non-linear. Consequently, the change of stacking sequence and thickness of the composite in adhesively bonded SLJs altered the location of the neutral axis in the joint. This situation substantially influences the load-carrying capacity of the joint.     

Biomechanical three-dimensional finite element analysis of monolithic zirconia crown with different cement thickness

Limited information is available on the optimal cement thickness of monolithic zirconia crowns. This study was designed to evaluate the stress distribution in the posterior monolithic zirconia crowns with different cement thicknesses under masticatory force and maximum bite force using three-dimensional finite element analysis. The prepared and unprepared mandibular right first molar models were scanned and exported to the computer-aided design system. Solid models of monolithic zirconia crowns, which were cemented on prepared teeth were generated. Four models were fabricated applying different cement thicknesses (100 µm, 200 µm, 400 µm, and 600 µm). The solid models were imported into the finite element analysis software and meshed into tetrahedral elements. Four three-dimensional finite element models were simulated under masticatory force and maximum bite force: vertical (axial), angular (45°) and horizontal loads of 280 N at 5 points; vertical load of 700 N at 8 points were loaded, respectively. The stress distribution varied with the different cement thicknesses and directions of applied loads. The monolithic zirconia crowns with cement thicknesses exceeding 200 µm had wider distributions of peak maximum principal stress under the same loading conditions. Monolithic zirconia crowns have more stress concentrations on the occlusal surfaces, while the cement layers have more stress concentrations on the cervical areas. Thicker cement layers were associated with more concentrated stresses on the buccal and lingual cervical areas. The test results show that the cement thickness plays an essential role in the success of monolithic zirconia restorations in terms of reducing cement wash-out. Cement thickness of 100 µm is recommended for monolithic zirconia crowns.     

Characterization and material model definition of toughened adhesives for finite element analysis

Some toughened adhesives used for structural joints are characterised by non-linear behaviour prior to failure that may significantly influence the entire joint response. The determination of appropriate and accurate material models for use in analysis and design phases covering both nonlinearities and final material rupture constitutes one of the main challenges for the utilisation of adhesives and for offering designers the same confidence level as that offered by other joining techniques.The present research proposes the utilisation of both elasto-plastic and continuum damage models as a combination that can fully reproduce the mechanical response of toughened adhesives in finite element (FE) analysis. In this context, the Drucker-Prager exponential model has demonstrated to provide accurate fits with the nonlinearities of these materials, allowing the real plastic behaviour of the adhesives to be adjusted in the computational models with a high degree of correlation. On the other hand, a continuum damage model has been proposed to simulate the final material failure process introducing a displacement-based damage parameter into the constitutive equation of the damaged material. The definition of the parameters associated with the mentioned models has been carried out through the execution of an experimental programme combining traction and torsion tests, described in the present paper as part of the study developed. The research is finally completed with an experimental and FE analysis of a specific bonded joint that allows the operation of the material model to be checked in a real application.