Failure prediction of adhesively bonded CFRP-Aluminum alloy joints using cohesive zone model with consideration of temperature effect

To predict the failure of adhesively bonded CFRP (Carbon Fiber Reinforced Plastics)-aluminum alloy joints applied to High Speed EMU (Electric Multiple Units) more accurately with consideration of temperature influence, a combined experimental-numerical approach is developed in this study. Bulk specimens and adhesive joints, including thick-adherend shear joints(TSJ), scarf joints(SJ) with scarf angle 30°(SJ30°), 45°(SJ45°), and 60°(SJ60°), as well as butt joints(BJ), were manufactured and tested at 23°C (room temperature, RT), 80°C (high temperature, HT) and ?40°C (low temperature, LT). Quadratic stress criteria built at different temperatures were introduced in the cohesive zone mode (CZM) to conduct a simulation analysis. Test results suggest that the effects of HT on mechanical properties of adhesive are more obvious than the effects of LT. It is also found that TSJ show the greatest improvements in failure strengths at LT due to the occurrence of cohesive failure, while SJ and BJ tend to develop fiber tears due to the presence of normal stress. Stress distributions of adhesive layer are found to be symmetrical except for the normal stress of SJ. This simulation analysis shows that the prediction accuracy is related to quadratic stress criteria applied, and that the relative errors of prediction results are less than 7.5% for engineering applications.     

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.     

Strength prediction of epoxy adhesively bonded scarf joints of dissimilar adherends

In this study, strength of epoxy adhesively bonded scarf joints of dissimilar adherends, namely SUS304 stainless steel and YH75 aluminum alloy is examined on several scarf angles and various bond thicknesses under uniaxial tensile loading. Scarf angle, θ=45°, 60° and 75° are employed. The bond thickness, t between the dissimilar adherends is controlled to be ranged between 0.1 and 1.2 mm. Finite element (FE) analysis is also executed to investigate the stress distributions in the adhesive layer of scarf joints by ANSYS 11 code. As a result, the apparent Young's modulus of adhesive layer in scarf joints is found to be 1.5-5 times higher than those of bulk epoxy adhesive, which has been obtained from tensile tests. For scarf joint strength prediction, the existing failure criteria (i.e. maximum principal stress and Mises equivalent stress) cannot satisfactorily estimate the present experimental results. Though the measured stress multiaxiality of scarf joints proportionally increases as the scarf angle increases, the experimental results do not agree with the theoretical values. From analytical solutions, stress singularity exists most pronouncedly at the steel/adhesive interface corner of joint having 45-75° scarf angle. The failure surface observations confirm that the failure has always initiated at this apex. This is also in agreement with stress-y distribution obtained within FE analysis. Finally, the strength of scarf joints bonded with brittle adhesive can be best predicted by interface corner toughness, Hc parameter.     

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.     

Fatigue life prediction of adhesively bonded single lap joints

Better fatigue performance of adhesively bonded joints makes them suitable for most structural applications. However, predicting the service life of bonded joints accurately remains a challenge. In this present study, nonlinear computational simulations have been performed on adhesively bonded single lap ASTM-D1002 shear joint considering both geometrical and material nonlinearities to predict the fatigue life by judiciously applying the modified Coffin-Manson equation for adhesive joints. Elasto-plastic material models have been employed for both the adhesive and the adherends. The predicted life has close agreement in the high cycle fatigue (HCF) regime with empirical observations reported in the literature.     

Strength model of adhesive bonded composite pipe joints under tension

A theoretical model is developed to predict the strain of the pipe, coupling, and adhesive under tensile loading of an adhesive bonded joint. The model is found to be within 10 percent of the experimental pipe and coupling strain. Based on the model, several failure modes and their locations are defined and related to the measured data. In this investigation, delamination is the dominating mode of failure. The delamination stress for each test sample is within 7 percent of the average theoretical delamination stress. In addition, the effect of the coupling length, coupling Young's modulus, adhesive shear modulus, and adhesive thickness on the delamination failure are investigated. The model shows that decreasing the modulus of the coupling improves the delamination failure load; however, the coupling strain at the middle of the joint is increased by this variation. Increasing the shear modulus of the adhesive provides the most significant improvement of the joint delamination failure load. Two geometric factors, the joint length and the adhesive thickness also affect the joint failure load. The joint delamination failure load can only be significantly improved by increasing the bonding length up to a certain limit. Increasing the adhesive thickness increases the delamination failure load, however, a large gap between the pipe and coupling may contribute to misalignment during installation which may result in imposed moments under tensile loading. This study can supply the manufacturers with the appropriate design parameters to improve the joint performance significantly under tensile loading.     

Crack growth in adhesively bonded joints subjected to variable frequency fatigue loading

The main aim of this article is to investigate the effect of frequency on fatigue crack propagation in adhesively bonded joints. Adhesively bonded double-cantilever beam (DCB) samples were tested in fatigue at various frequencies between 0.1 and 10 Hz. The adhesive used was a toughened epoxy, and the substrates used were a carbon fibre-reinforced polymer (CFRP) and mild steel. Results showed that the crack growth per cycle increases and the fatigue threshold decreases as the test frequency decreases. The locus of failure with the CFRP adherends was predominantly in the adhesive layer, whereas the locus of failure with the steel adherends was in the interfacial region between the steel and the adhesive. The crack growth was faster, for a given strain energy release rate, and the fatigue thresholds lower for the samples with steel adherends. Tests with variable frequency loading were also carried out, and a generalised method of predicting crack growth in samples subjected to a variable frequency loading was introduced. The predicted crack growth using this method agreed well with experimental results.     

单搭接胶接接头的拓扑优化

在有限元方法的基础上，利用变密度法对单搭接胶接接头搭接区域的被粘物形状进行了拓扑优化，通过曲线拟舍得到了较为合理的轮廓。拓扑优化的结果表明：在体积减少20％的情况下。胶接结构的强度不会降低；经拓扑优化后，胶层中剪切应力的峰值比优化以前增加不大，约1％。     

Three-parameter,elastic foundation model for analysis of adhesively bonded joints

A novel three-parameter, elastic foundation model is proposed in this study to analyze interface stresses of adhesively bonded joints. The classical two-parameter, elastic foundation model of adhesive joints models the adhesive layer as a layer of normal and a layer of shear springs. This model does not satisfy the zero-shear-stress boundary conditions at the free edges of the adhesive layer due to the inherent flaw of the two-parameter, elastic foundation model, which violates the equilibrium condition of the adhesive layer. To eliminate this flaw, this study models the adhesive layer as two normal spring layers interconnected by a shear layer. This new three-parameter, elastic foundation model allows the peel stresses along the two adherend/adhesive interfaces of the joint to be different, and therefore, satisfies the equilibrium condition of the adhesive layer. This model regains the missing “degree of freedom” in the two-parameter, elastic foundation model of the adhesive layer by introducing the transverse displacement of the adhesive layer as a new independent parameter. Explicit closed-form expressions of interface stresses and beam forces are obtained. The new model not only satisfies all boundary conditions, but also predicts correctly which interface has the strongest stress concentration. The new model is verified by continuum models existing in the literature and finite element analysis. The new three-parameter, elastic foundation model provides an effective and efficient tool for analysis and design of general adhesive joints.     

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.     

Fracture analysis of an adhesively bonded sandwich beam under Mode-I loading

In this paper, an analytical closed-form solution for Mode-I energy release rate of an adhesively bonded sandwich beam is derived from the modified elastic foundation model. For validation purpose, a model based on the finite element method (FEM) was also constructed using the modified crack closure integral technique to calculate the compliance and Mode-I energy release rate of the sandwich beam. Comparison between the closed-form solution and the FEM solution showed a good agreement. The results of calculations also showed a significant effect of the adhesive layer of the sandwich beam on fracture analysis. This means that the effect of the adhesive layer of the sandwich beam cannot be ignored.     

Characterising moisture ingress in adhesively bonded joints using nuclear reaction analysis

The moisture ingress in bonded structures is usually characterised by gravimetric experiments on bulk adhesive samples. This is a relatively economic and convenient method. However, this approach poses a problem as only the total amount of moisture in the specimen can be determined and not the moisture concentration distribution throughout the adhesive layer. In this study, the moisture profile at two different ageing times (43 and 96 h) in a bonded joint has been determined by use of nuclear reaction analysis (NRA). The moisture ingress profile, which was found to be Fickian in the bulk adhesive sample, was dominated by apparent Case II kinetics in the bonded joint specimens. The ingress in the laminates was seen to be much faster than if the moisture transport had been governed by Fickian diffusion.     

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.     

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.     

Composite bonded joints under mode I fatigue loading

Experimental investigation on fatigue behavior of carbon-epoxy composite bonded joints under mode I loading was performed in this work. The objective is to evaluate the performance of different data reduction schemes to obtain the energy release rate (G_I) in the fatigue crack growth (FCG) rate using double cantilever beam (DCB) specimens. This law relates the evolution of the crack along time as a function of the energy release rate (G_I) and is generally composed of three different regions: damage nucleation, stable propagation and abrupt final failure. The second phase corresponding to stable propagation leads to a linear trend on the Paris law representation (log-log scale) and must be well characterized to define the fatigue behavior of the structure. During fatigue tests the classical methods require rigorous monitoring of the crack length during its propagation, which is cumbersome and not easy to perform in some materials. In this work, an alternative data reduction scheme based on specimen compliance and crack equivalent concept is proposed to overcome this difficulty. The results provided by the proposed method, namely Compliance Based Beam Method (CBBM), are compared to the ones obtained from the polynomial and Beam on Elastic Foundation Method (BEFM), both of which require crack monitoring. The first is a compliance calibration method that fits a third-order polynomial curve to the experimental results (compliance (C) versus crack length (a)). The second one uses the beam theory to establish the C=f(a) relationship taking into account the properties of the adhesive. One additional advantage can be pointed to the proposed CBBM relative to the other classical methods. In fact, the equivalent crack is related to the specimen compliance, thus taking into account the influence of fracture process zone on specimen behavior. This issue is particularly important when adhesives with some ductility are being characterized in fatigue tests.     

A numerical study of adhesively bonded lap joints

The two types of joint discussed in this paper are a thick adherend symmetrical lap joint, and a symmetrical double lap joint. The effect of varying adherend and adhesive thicknesses on the stress distribution in the thin adhesive layer is discussed. These analyses were used in the design on a lap shear test to characterize certain aerospace adhesives used in bonded repair of structural components. An alternative analytical approach for the estimation of the load-carrying capacity of the double lap joint is also presented.     

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.     

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.     

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.