A review of finite element analysis of adhesively bonded joints

The need to design lightweight structures and the increased use of lightweight materials in industrial fields, have led to wide use of adhesive bonding. Recent work relating to finite element analysis of adhesively bonded joints is reviewed in this paper, in terms of static loading analysis, environmental behaviors, fatigue loading analysis and dynamic characteristics of the adhesively bonded joints. It is concluded that the finite element analysis of adhesively bonded joints will help future applications of adhesive bonding by allowing system parameters to be selected to give as large a process window as possible for successful joint manufacture. This will allow many different designs to be simulated in order to perform a selection of different designs before testing, which would currently take too long to perform or be prohibitively expensive in practice.     

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.     

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.     

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％。     

Mechanism of ultrasonic vibration effects on adhesively bonded ceramic matrix composites joints

Ultrasonic vibration treatment is being utilized to improve adhesive bonding performance, but the mechanisms remain unclear. Moreover, few studies have been carried out on improvement of adhesive bonding of ceramic matrix composites (CMCs) by ultrasonic vibration. In this work, a mathematical model based on fluid mechanics and capillary rise theory is developed to determine the adhesive penetration ability. The effect of ultrasonic vibration on adhesive bonding performance of CMCs is studied. Based on the experimental results, a good agreement is found with respect to measurements of hydraulic force and pressure. Ultrasonic vibration-assisted processing can improve interfacial adhesion strength due to adhesive has high wettability and penetration ability. Furthermore, it is found that delamination and ply-delamination are the main failure modes for all conditions, but porous areas are reduced by ultrasonic treatment.     

Numerical design and multi-objective optimisation of novel adhesively bonded joints employing interlocking surface morphology

A novel concept for joining materials is presented which employs adhesive joints with interlocking bond-surface morphology formed on the surfaces of male and female adherends that mechanically interlock in shear when brought together. In the present work, miniature, single-lap joint specimens with a single truncated square pyramid interlocking profile, centred in the bond area, are investigated. The performance of the concept is assessed through finite element analysis (FEA) by incorporating yield criteria representing plasticity in the adherends and a cohesive zone model to represent damage in the adhesive layer. This allows for effective simulation of the joint response until ultimate failure and thus, full assessment of the concept's performance. Various interlocking geometries are explored and refined through an adaptive surrogate modelling design optimisation procedure coupled with FEA. The results indicated that significant improvements in work to failure, of up to 86.5%, can be achieved through the more progressive failure behaviour observed compared to that of a traditional adhesively bonded joint. Improvements in the joint's ultimate failure load can also be achieved with a relatively ductile adhesive system.     

Experimental and numerical investigations of adhesively bonded CFRP single-lap joints subjected to tensile loads

In this study, both experimental tests and numerical simulation are implemented to investigate the tensile performance of adhesively bonded CFRP single-lap joints (SLJs). The study considers 7 different overlap lengths, 5 adherend widths and 3 stacking sequences of the joints. Three-dimensional (3D) finite element (FE) models are established to simulate the tensile behavior of SLJs. The failure loads and failure modes of SLJs are investigated systematically by means of FE models and they are in good agreement with those of experiments, proving the accuracy of finite element method (FEM). It is found that increasing the adherend width can improve the load-carrying capacity of the joint better than increasing the overlap length does. Moreover, choosing 0° ply as the first ply is also beneficial for upgrading joint's strength. With respect to failure modes, cohesive failure in adhesive and delamination in adherend take dominant, while matrix cracking and fiber fracture only play a small part. With overlap length increasing or adherend width decreasing, cohesive failure takes up a smaller and smaller proportion of whole failure area, but the opposite is true for delamination. SLJs bonded with [0/45/-45/90]_3S adherends are prone to cohesive failure, and [90/-45/45/0]_3S adherends are easy to appear delamination. Both shear and peel stress along the bondline indicate symmetrical and non-uniform distributions with great stress gradient near the overlap ends. As the load increases, the high stress zone shifts from the end to the middle of the bondline, corresponding to the damage initiation and propagation in the adhesive layer.     

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.     

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.     

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.     

Low-speed bending impact behavior of adhesively bonded single-lap joints

This study addresses the low-speed impact behavior of adhesively bonded single-lap joints. An explicit dynamic finite element analysis was conducted in order to determine the damage initiation and propagation in the adhesive layers of adhesive single-lap joints under a bending impact load. A cohesive zone model was implemented to predict probable failure initiation and propagation along adhesive–adherend interfaces whereas an elasto-plastic material model was used for the adhesive zone between upper and lower adhesive interfaces as well as the adherends. The effect of the plastic deformation ability of adherend material on the damage mechanism of the adhesive layer was also studied for two aluminum materials Al 2024-T3 and Al 5754-0 having different strength and plastic deformation ability. The effects of impact energy (3 and 11 J) and the overlap length (25 and 40 mm) were also investigated. The predicted contact force-time, contact force-central displacement variations, the damage initiation and propagation mechanism were verified with experimental ones. The SEM and macroscope photographs of the adhesive fracture surfaces were similar to those of the explicit dynamic finite element analysis.     

Stress analysis of adhesively bonded double strap joints with or without intermediate part subjected to tensile loading

Accidents in the industry, especially in the field of aerospace, are quite common. Damages like tears cracks and holes occur especially when small sand particles present in the airfield collide with the body and wings of an airplane during takeoff and landing. This torn, cracked, or pierced region should be repaired gently. Damaged parts are frequently small regions for which repair is more suitable than complete replacement as workmanship; cost and time are an important concept in today’s world.

A gap occurs between the patches if double-bonded patches are used in the repair of the damaged parts. In this study, the region between patches in a joint with and without intermediate parts was modeled and its effect on strength was examined numerically and experimentally. The effects of patch thickness, overlap length, adherent thickness, and gap length on the strength of the joints with and without intermediate part was compared. The results show that the intermediate part does not have any influence on the strength of the lap joint such that double strap joints without intermediate part have higher failure load. Additionally, it is seen that the failure load decreased with increasing patch thickness and increased with the thickness of the adherent.     

Stress concentration coefficient in a composite double lap adhesively bonded joint

The main target of this paper is to investigate the effect of peak stress at the extremities of the adhesive layer of a bonded assembly subjected to dynamic shear impact. It is known, that under both static and dynamic loadings such joints endure at their extremities high level of stresses, an aspect known as edge effects. Double lap joint assembly was considered with unidirectional carbon–epoxy substrates and Araldite 2031 adhesive. To quantify this edge effect, a specific coefficient, named coefficient of stress concentration was defined: it is the ratio of the maximum shear stress to the average shear stress. This coefficient helps to calculate maximum strength of the joint since experimentally, only average shear stress could be measured. A numerical analysis at the midplane of the joint was carried out to investigate the effect of geometrical and material parameters on this stress concentration factor. It was found that this factor is constant with the time once the equilibrium is established. Moreover, this stress concentration coefficient decreases with higher Young's modulus of the adherents, lower Young's modulus of the adhesive, thicker and shorter adhesive layer. A unified parameter involving geometrical and mechanical parameters of the specimen was established to quantify this stress concentration factor.     

Multivariate analysis of high through-put adhesively bonded single lap joints

The goal of this research was to experimentally demonstrate the correlations between processing variables (adhesive type, bondline thickness, adherend thickness, surface pretreatment, overflow fillet) and effective strength in adhesively bonded single lap joints. While generalizations between effective strength and individual joint design parameters have been assumed for decades, the multifaceted interplay between parameters is complex and remains difficult to understand. Traditionally reported studies of the adhesive bond strength of single lap joints are often limited in the sample size populations needed to statistically probe concurrent design variables. To overcome sample size limitations a test matrix of 1200 single lap joints, partitioned by 96 unique fabrication conditions, was processed and tested using a workflow protocol orchestrated through a relational database. The enhanced pedigree and integrity enabled by using a relational database centered workflow allowed for multivariate principal component analysis of the joint design parameters, with all experimental data input available for peer audit. The results of this study revealed that the adhesive type biases the remaining joint configuration variables towards more influence with respect to either mechanical load or displacement to failure.     

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.     

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.     

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.     

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.