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.     

Two dimensional analysis for an adhesively bonded composite single-lap joint based on flexible interface theory

An improved two-dimensional model based on flexible interface theory is proposed for an adhesively bonded composite single-lap joint. In the modified model, the adherends are treated as a Timoshenko beam, and the adhesive layer is assumed to be an Euler–Bernoulli beam. The peel stress and shear stress across the adhesive thickness varied. Additionally, the zero shear stress condition at the free end of the adhesive layer was satisfied. Based on the displacement compatibility condition of a flexible interface, the governing differential equations for the internal forces are derived. The stress distributions of the adhesive layer can be obtained by solving the governing differential equations. A comparison of the results between the modified model, existing classical models, and finite element results indicate that the improved two-dimensional model can determine the stress distribution of the adhesive with high accuracy. Finally, the effects of the thickness ratio, Young’s modulus ratio, and interfacial compliance on the stress distribution of the adhesive are studied using the improved model.     

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％。     

An alternative solution for the edge moment factors of the unbalanced adhesive single-lap joint in tension

An evaluation of the existing theoretical solutions and a proposal of an improved one for edge moment factors of the unbalanced adhesive single-lap joint are performed. Firstly, the existing classical solutions are reviewed and studied in detail. The scope of applications and limitations related to the classical solutions are identified. Meanwhile, the determination for the long and short unbalanced single-lap joint (SLJ) is performed. Then, through removing disadvantages of the existing theoretical solutions, an improved theoretical solution considering the effect of large deflection for overlap is proposed. Meanwhile, the adherends of the overlap regions are treated as individual beams in the improved theoretical solution. The fully-coupled nonlinear formulations for determining adherend displacements (includes axial deformation and transverse deformation) in the overlap and edge moment factors are constructed using the improved theoretical solution. Finally, the results of the existing solutions and the improved theoretical solution are compared with the results of the finite element analysis.     

Optimization of smart adhesively bonded single-strap composite joint

In order to reduce the stress concentration and improve the failure strength of adhesively bonded joint structures, a smart adhesively bonded joint structure has been developed by integrating piezoelectric layers into the adherends. For better design guide, a combined theoretical model and multi-objective optimization approach is employed to optimize the smart joint in this study. Firstly, the first-order shear deformation theory is utilized to model and analyze the detailed peel and shear stresses distribution in the adhesive layer. Further, considering the characteristics of the stress distribution, the interface debonding failure criterion is used to set up the objective; optimization variables are considered as the stacking sequence, geometries and applied electric fields of the integrated piezoelectric layer. Thus, with the aid of the Mathematica software, the optimal smart adhesively bonded joint system can be determined. Finally, some detailed examples are analytically solved to show the considerable difference between the preoptimized and optimized smart joint systems, which validate that the developed theoretical model and multi-objective optimization approach can be used to enhance adhesively bonded joint failure strength.     

胶层尺寸对单搭胶接接头性能的影响研究

针对汽车车身中应用日益广泛的钢板胶接结构,通过试验得到了不同胶层尺寸对胶接接头承载能力的影响规律,建立了钢板单搭接头的三维弹塑性有限元模型,分析了胶层尺寸对胶接接头应力分布的影响.研究结果表明:随着胶层厚度的增加,胶接件的承载能力呈先升后降的趋势,合理的胶层厚度应为0.3-0.5 mm;无论胶层厚度为多少,增加搭接区域胶层的长度或宽度.均会提高胶接件的承载能力.     

Improved one-dimensional beam model for unbalanced composite single-lap joint

An analytical nonlinear solution was provided for unbalanced composite single-lap joint (CSLJ) using an improved one-dimensional beam model, which incorporated the effect of bending–tension coupling. The bending–tension coupling stiffness was introduced to characterize the coupling bending and tension behavior induced by the un-symmetric stacking sequence of composite laminates. The governing differential equations captured the bending–tension coupling behavior and the geometrically nonlinear features were constructed based on the displacement compatibility conditions of flexible interface. The transverse deformation in overlap region, edge moment factors and adhesive stress distributions for the unbalanced CSLJ with inflexible, intermediate flexibility and flexible adhesive can be determined by the present one-dimensional beam model. The accuracy of the present model was validated by the comparison with nonlinear finite element model. The effect of bending–tension coupling on edge moment factors and peak values of adhesive stresses was shed light on with the present model.     

Increasing single-lap joint strength by adherend curvature-induced residual stresses

Single-lap joint (SLJ) geometry is the most widely used type of adhesive joint geometry. In this joint, peel stresses occur at the overlap ends due to load eccentricity and the presence of shear-free adhesive termination surfaces. These peel stresses, along with the transverse tensile stresses which occur along the overlap longitudinal axes, and adhesive shear stresses, ultimately cause joint failure. Obviously, reductions in these stresses should result in higher joint strength and increased load capacity. To this end, we exploited elastic spring-back capability of (steel) metal adherends by initially forming curved segments of varying arc lengths and radii at overlap ends. These adherends with curved-end sections were then bonded in single-lap configuration, simply by applying sufficient bonding pressure to elastically flatten the curved segments to result in typically flat overlap sections subsequent to adhesive cure and the removal of bonding pressure. Since the elastic adherend overlap ends tend to revert back to their initial curved form, they exert compressive residual stresses on the adhesive layer in the overlap end regions. We determined that the compressive residual stresses induced in this fashion considerably increased the load capacity of SLJs subjected to tension.     

固化工艺对HT1012铜粉导电胶剪切强度的影响

研究了固化工艺参数对由HT1012型铜粉导电胶制备的单搭接接头剪切强度的影响。结果表明，在所采取的研究条件下，随着晾置时间的推移，导电胶剪切强度起初增加但随后减小；当固化温度为60℃、晾置时间取定为10min时，固化时间为3h所对应的剪切强度较高；当变动固化温度时，固化温度提高会引起剪切强度下降。     

Free vibration analysis of an adhesively bonded functionally graded double containment cantilever joint

In this study, Genetic Algorithms (GAs) combined with the proposed neural networks were implemented to the free vibration analysis of an adhesively bonded double containment cantilever joint with a functionally graded plate. The proposed neural networks were trained and tested based on a limited number of data including the natural frequencies and modal strain energies calculated using the finite element method. GA evaluates a value generated iteratively by an objective function and this value is calculated by the finite element method. The iteration process restricts us apparently to use directly the finite element method in our multi-objective optimisation problem in which the natural frequency is maximised and the corresponding modal strain energy is minimised. The proposed neural networks were used accurately to predict the natural frequencies and modal strain energies instead of calculating directly them by using the finite element method. Consequently, the computation time and efforts were reduced considerably. The adhesive joint was observed to tend vertical bending modes and torsional modes. Therefore, the multi-objective optimisation problem was limited to only the first mode which appeared as a bending mode. The effects of the geometrical dimensions and the material composition variation through the plate thickness were investigated. As the material composition of the horizontal plate becomes ceramic rich, both natural frequency and modal strain energy of the adhesive joint increased regularly. The plate length and plate thickness were more effective geometrical design parameters whereas the support length and thickness were less effective. However, the adhesive thickness had a small effect on the optimal design of the adhesive joint as far as the natural frequencies and modal strain energies are concerned. The distributions of optimal solutions were also presented for the adhesive joints with fundamental joint lengths and material compositions in reference to their natural frequencies and corresponding modal strain energies.     

A two-dimensional stress analysis of single-lap adhesive joints subjected to external bending moments

The stress distributions in single-lap adhesive joints of similar adherends subjected to external bending moments have been analyzed as a three-body contact problem using a two-dimensional theory of elasticity (plain strain state). In the analysis, both adherends and the adhesive were replaced by finite strips. In the numerical calculations, the effects of the ratio of Young's moduli of the adherends to that of the adhesive and the adhesive thickness on the stress distribution at the interfaces were examined. It was found that the stress singularity occurs at the edges of the interfaces and that the peel stress at the edges of the interfaces increases with decreasing Young's modulus of the adherends. It was noticed that the singular stress decreases at the edges of the interfaces as the adherend thickness increases. In addition, photoelastic experiments and FEM (finite element method) calculations were carried out and fairly good agreement was found between the analytical and the experimental results.     

胶层中间隙长度及位置对接头剪切强度的影响

研究了在单搭接接头上、胶缝中预留的不同长度间隙对接头剪切强度和剪切应力分布的影响。结果表明，随着间隙长度的增加，接头的承栽能力趋于减小，但接头的实际剪切强度却持续上升．当间隙长度再继续增加时，接头的实际强度趋于下降。研究中还发现间隙所处的位置对接头的剪切强度有较大的影响，胶层端部预留间隙使接头的承载能力和实际强度均显著下降。有限元数值分析的结果表明，间隙长度超过某特定值后，胶层中的应力集中系数会急剧上升，间隙位于端部时胶层中的应力集中程度明显高于位于中部处。     

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

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

外加磁场对粘接接头剪切强度的影响

采用自制的装置研究了磁场对由环氧胶层连接的钢制单搭接接头剪切强度的影响，结果表明．在所采取的试验条件下．试样叠合后立即施加的磁场可显著影响接头的强度；垂直于胶层的磁场提高接头的剪切强度效果高于平行磁场，磁场处理的时间以4h左右为宜。     

Interfacial failure analysis of functionally graded adhesively bonded double supported tee joint of laminated FRP composite plates

This paper deals with three-dimensional non-linear finite element analyses to assess the structural behavior of adhesively-bonded double supported tee joint of laminated FRP composites having embedded interfacial failures. The onset of interfacial failures is predicted by using Tsai–Wu coupled stress failure criterion with pre-determined stress values. The concept of fracture mechanics principle is utilized to study the sustainability of the tee joint having interfacial failures pre-existed at the critical locations. Individual modes of the strain energy release rates (SERR) G_I, G_II and G_III, are considered as the damage growth parameters and, are evaluated using the Modified crack closure integral (MCCI) technique based on the concept of linear elastic fracture mechanics (LEFM). Based on the stress analyses, it has been observed that the interfacial failures in tee joint structure trigger at the interface of base plate and adhesive layer from both ends of base plate. Depending on the SERR magnitudes, it has been noticed that the interfacial failure propagates under mixed mode condition. Therefore total SERR (G_T) is considered as the governing parameter for damage propagation. Furthermore, efforts have been made to retard damage propagation rate by employing functionally graded adhesive (FGA) instead of monolithic adhesive material. Series of numerical simulations have been performed for varied interfacial failure length in functionally graded adhesively bonded double supported tee joint structure in order to achieve the significant effect of FGA with various modulus ratios on SERR. Material gradation of adhesive indicates significant SERR reduction at the incipient stage of failure which necessitates the use of functionally graded adhesive for the tee joint and prolong the service life of the structure.     

Progressive failure and experimental study of adhesively bonded composite single-lap joints subjected to axial tensile loads

Experimental tests and finite element method (FEM) simulation were implemented to investigate T700/TDE86 composite laminate single-lap joints with different adhesive overlap areas and adherend laminate thickness. Three-dimensional finite element models of the joints having various overlap experimental parameters have been established. The damage initiation and progressive evolution of the laminates were predicted based on Hashin criterion and continuum damage mechanics. The delamination of the laminates and the failure of the adhesive were simulated by cohesive zone model. The simulation results agree well with the experimental results, proving the applicability of FEM. Damage contours and stress distribution analysis of the joints show that the failure modes of single-lap joints are related to various adhesive areas and adherend thickness. The minimum strength of the lap with defective adhesive layer was obtained, but the influence of the adhesive with defect zone on lap strength was not decisive. Moreover, the adhesive with spew-fillets can enhance the lap strength of joint. The shear and normal stress concentrations are severe at the ends of single-lap joints, and are the initiation of the failure. Analysis of the stress distribution of SL-2-0.2-P/D/S joints indicates that the maximum normal and shear stresses of the adhesive layer emerge on the overlap ends along the adhesive length. However, for the SL-2-0.2-D joint, the maximum normal stress emerges at the adjacent middle position of the defect zone along the adhesive width; for the SL-2-0.2-S joint, the maximum normal stress and shear stress emerge on both edges along the adhesive width.     

Strain energy release rate based damage analysis of functionally graded adhesively bonded tubular lap joint of laminated FRP composites

Strain energy release rate (SERR) based damage analyses of functionally graded adhesively bonded tubular lap joints of laminated fiber reinforced plastic (FRP) composites under varied loadings have been studied using three-dimensional geometrically non-linear finite element (FE) analyses. FE simulations have been carried out when a tubular joint is subjected to axial and pressure loadings. SERR is utilized as the characterizing and governing parameter for assessing damages emanating from the critical location. Individual and total SERR over the damage front have been computed using modified crack closure integral (MCCI) based on the concept of linear elastic fracture mechanics. Results reveal that damage initiation locations in tubular joints subjected to axial and pressure loadings are entirely different. Furthermore, modes responsible for propagation of such damages in tubular joints under axial and pressure loadings are also different. Based on the FE simulations, tubular joints under pressure loading are found to be more vulnerable for damage initiation and its propagation. Furthermore, the damage propagation behavior of tubular joints with pre-embedded damages at the critical location has been compared between conventional mono-modulus adhesives and functionally graded adhesives with appropriate material gradation profile. Results indicate that material gradient profile of the adhesive layer offers excellent reduction in SERR for shorter interfacial failure lengths in tubular joints under axial loading which is desired to delay the damage growth. Improved crack growth resistance in the joint enhances the structural integrity and service life of the tubular joint structure. However, considerable reduction in SERR has not been noticed in the said joint when subjected to pressure loading. Hence, the use of functionally graded adhesive along the bond layer is recommended for the designer/technologist while designing tubular joint under general loading condition.     

Elasto-plastic analysis of bonded joints with macro-elements

The Finite Element (FE) method could be able to address the stress analysis of bonded joints. Nevertheless, analyses based on FE models are mainly computationally cost expensive and it would be profitable to develop simplified approaches, enabling extensive parametric studies. Firstly, a one-dimensional 1D-bar and 1D-beam simplified models for the bonded joint stress analysis, assuming a linear elastic adhesive material, are presented. These models derive from an approach, inspired by the FE method using a formulation based on a four-node macro-element, which is able to simulate an entire bonded overlap. Moreover, a linear shear stress variation in the adherend thickness is included in the formulation. Secondly, a numerical procedure is then presented to introduce into both models an elasto-plastic adhesive material behavior, while keeping the previous linear elastic formulation. Finally, assuming an elastic perfectly plastic adhesive material behavior, the results produced by simplified models are compared with the results predicted by FE using 1D-bar, plane stress, and three-dimensional (3D) models. Good agreements are shown.     

Shear and peel stress analysis of an adhesively bonded scarf joint

The shear and peel stress distributions in a scarf joint made of two isotropic adherends with blunt adherend tips are analysed using a linear elastic analysis. The limits of the analysis with respect to adherend tip thickness have been investigated. A finite difference method is used to solve the differential equations for the shear and peel stress distributions over the joint. The boundary conditions used limit the analysis to the two adherends having the same thicknesses, lengths, and material properties. The adherends are modelled as plates with extensional and bending stiffnesses bonded together with an elastic interlayer. The stresses across the adhesive layer are assumed to be constant. The current analysis applied to cases known from the literature shows good agreement with the shear stresses but the peel stresses are overestimated.     

折曲单搭接胶接接头应力分布探讨

在同轴单搭接胶接接头的基础上,设计了一种新型折曲单搭接胶接接头。通过有限元方法研究了折曲胶接接头和同轴胶接接头的应力分布规律。研究结果表明:折曲单搭接胶接接头搭接区两端的应力峰值下降幅度均超过40%,并使搭接区出现应力峰值的位置从搭接区端部转移到中部,从而显著地提高接头的承载能力。当L1=7.5 mm时,胶层中应力分布较为理想,各应力呈对称分布,是一种优于普通同轴的胶接接头形式。