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.     

Optimal design of an adhesively-bonded corner joint with single support based on the free vibration analysis

This study investigates the three-dimensional free vibration behaviour of an adhesively-bonded corner joint with single support. The modulus of elasticity, Poisson's ratio and density of adhesive were found to have negligible effects on the first 10 natural frequencies and mode shapes of the corner joint. The effects of the geometrical parameters, such as support length, plate thickness, adhesive thickness and joint length, on the natural frequencies, mode shapes and modal strain energies of the adhesive joint were also investigated using both the finite element method and the back-propagation artificial neural network (ANN) method. The free vibration and stress analyses were carried out for the corner joints with various random geometrical parameters so that a suitable ANN model could be trained successfully. The support length, plate thickness and joint length all played important roles in the natural frequencies, mode shapes and modal strain energies of the corner joint, whereas the adhesive thickness for the range of adhesive thickness studied had only a minor effect. The Genetic Algorithm was also combined with the present ANN models in order to determine the optimum geometrical dimensions which satisfied the maximum natural frequency and minimum modal strain energy conditions for each natural frequency and mode shape of the adhesively-bonded corner joint.     

Free Vibration Analysis and Design of an Adhesively Bonded Corner Joint with Double Support

This study carries out the three dimensional free vibration analysis of an adhesively bonded corner joint and investigates the effect of an additional horizontal support to the adhesive corner joint with single support on the first ten natural frequencies and mode shapes. In the presence of a horizontal support the effects of the vertical support length, the adhesive thickness, the plate thickness, and the joint length on the natural frequencies and modal strain energies of the adhesive joint were also investigated using the back-propagation Artificial Neural Network (ANN) method and the finite element method. The natural frequencies and modal strain energies increased with increasing plate thickness, whereas an adverse effect was observed for increasing joint length. Both horizontal and vertical support lengths exhibited similar effects but the adhesive thickness had a negligible effect. The plate thickness and the joint length are dominant geometrical parameters in comparison with both horizontal and vertical support lengths. The proposed ANN models were combined with the Genetic Algorithm in order to determine the optimal corner joint in which the maximum natural frequency and minimum elastic modal strain energy are achieved for each natural frequency and mode shape of the adhesive corner joint and the optimal dimensions were given versus one geometrical parameter.     

Free Vibration Analysis and Design of an Adhesively Bonded Corner Joint with Double Support

This study carries out the three dimensional free vibration analysis of an adhesively bonded corner joint and investigates the effect of an additional horizontal support to the adhesive corner joint with single support on the first ten natural frequencies and mode shapes. In the presence of a horizontal support the effects of the vertical support length, the adhesive thickness, the plate thickness, and the joint length on the natural frequencies and modal strain energies of the adhesive joint were also investigated using the back-propagation Artificial Neural Network (ANN) method and the finite element method. The natural frequencies and modal strain energies increased with increasing plate thickness, whereas an adverse effect was observed for increasing joint length. Both horizontal and vertical support lengths exhibited similar effects but the adhesive thickness had a negligible effect. The plate thickness and the joint length are dominant geometrical parameters in comparison with both horizontal and vertical support lengths. The proposed ANN models were combined with the Genetic Algorithm in order to determine the optimal corner joint in which the maximum natural frequency and minimum elastic modal strain energy are achieved for each natural frequency and mode shape of the adhesive corner joint and the optimal dimensions were given versus one geometrical parameter.     

Elastic stresses in an adhesively-bonded functionally-graded tubular single-lap joint in tension

In this study, the elastic stress analysis of an adhesively-bonded tubular lap joint with functionally-graded Ni-Al₂O₃ adherends in tension was carried out using a 3D 8-node isoparametric multilayered finite element with 3 degrees-of-freedom at each node. Stress concentrations were observed along the edges of both outer and inner tubes in the overlap region. Thus, the outer tube region near the free edge of the inner tube and the inner tube region near the free edge of the outer tube experienced considerable stress concentrations. Normal σ_zz and shear σ_rz stresses were dominant among the stress components. In addition, both edges of the adhesive layer experience stress concentrations, and the von Mises σ _eqv stress decreases uniformly across the adhesive thickness at the free edge of the outer tube, whereas it increases at the free edge of the inner tube. However, different compositional gradients had only a small effect on the through-the-thickness normal and shear stress profiles of both outer and inner tubes, and the peak von Mises σ _eqv stresses occurred inside the tube walls. As the ceramic phase in the material composition of the outer and inner tubes was increased, peak von Mises σ _eqv stress appeared in the ceramic layer. However, its magnitude was increased 1.75-fold in both tubes. In addition, the peak adhesive stresses appeared at the edge of the outer tube–adhesive interface near the free edge of the inner tube and at the edge of the inner tube–adhesive interface near the free edge of the outer tube. Increasing the ceramic phase in the material composition caused 1.22–1.67-times higher von Mises stresses along the free edges of the adhesivetube interfaces. In addition, with increasing number of layers across the inner and outer tubes the profiles of the normal σ_zz , shear σ_r and von Mises σ _eqv stresses across the tube walls and adhesive layer become similar. Increasing the ceramic phase in the material composition of the tubes causes also evident increases in the normal σ_zz and von Mises stresses while it does not affect their through-the-thickness profiles. However, it affects only shear σ_r and von Mises stresses across the adhesive layer. Finally, the layer number and the compositional gradient do not affect considerably through-the-thickness normal and shear stress profiles but levels in a functionally graded plate subjected to structural loads.     

An efficient analysis model for functionally graded adhesive single lap joints

Employing a functionally graded adhesive the efficiency of adhesively bonded lap joints can be improved significantly. However, up to now, analysis approaches for planar functionally graded adhesive joints are still not addressed well. With this work, an efficient model for the stress analysis of functionally graded adhesive single lap joints which considers peel as well as shear stresses in the adhesive is proposed. Two differential equations of the displacements are derived for the case of an axially loaded adhesive single lap joint. The differential equations are solved using a power series approach. The model incorporates the nonlinear geometric characteristics of a single lap joint under tensile loading and allows for the analysis of various adhesive Young׳s modulus variations. The obtained stress distributions are compared to results of detailed Finite Element analyses and show a good agreement for several single lap joint configurations. In addition, different adhesive Young׳s modulus distributions and their impact on the peel and shear stresses as well as the influence of the adhesive thickness are studied and discussed in detail.     

Optimal Design of the Adhesively-Bonded Tubular Single Lap Joint

In this paper, a method for the optimal design of the adhesively-bonded tubular single lap joint was proposed based on the failure model of the adhesively-bonded tubular single lap joint. The failure model incorporated the nonlinear mechanical behavior of the adhesive as well as the different failure modes in which the adhesive failure mode changed from bulk shear failure, via transient failure, to interfacial failure between the adhesive and the adherend, according to the magnitudes of the residual thermal stresses induced by fabrication.

The effects of the design parameters for the adhesively-bonded tubular single lap joint, such as the thicknesses of adhesive layer and adherends, the bonding length, and the scarfs of adherends, on the torque transmission capability and the efficiency of the adhesive joint were investigated.     

The determination of dynamic strength of single lap joints using the split Hopkinson pressure bar

The current investigation focuses on the determination of the strength of adhesive-bonded single lap joints under impact with the use of a split Hopkinson pressure bar (Kolsky bar). For this, experiments were conducted at different loading rates, for identical metallic adherends bonded by a two-part epoxy adhesive. Four different types of specimens were adopted, all with a given adhesive thickness. The length of overlap and the width of the adherends were varied resulting in four different areas of overlap. It was found that the average strength, as calculated from the readings obtained from a Kolsky bar, increases with decrease of overlap area. An elastodynamic model for the shear strain of the adhesive-bonded single lap joint was developed to investigate this drastic effect of overlap area on the average strength of the joint. The mathematical model was found to be dependent on both the material properties of the adherend and adhesive, as well as the structural properties of the joint, viz. the width and the thickness of the adhesive layer. A combined experimental-numerical technique was used to predict the strain distribution over the length of the bond in the adhesive. It was found that the edges of the adhesive were subjected to maximum strain, while a large part of the adhesive was found to exhibit zero shear strain. The effect of the lap length and the width was studied individually. The cumulative effect of averaging the strain over the entire overlap area, was decreased shear strain for an increased overlap area. The Kolsky bar was identified to give conservative values of the shear strength of an adhesive bonded lap joint under high rates of loading.     

Optimal Design of the Adhesively-Bonded Tubular Single Lap Joint

In this paper, a method for the optimal design of the adhesively-bonded tubular single lap joint was proposed based on the failure model of the adhesively-bonded tubular single lap joint. The failure model incorporated the nonlinear mechanical behavior of the adhesive as well as the different failure modes in which the adhesive failure mode changed from bulk shear failure, via transient failure, to interfacial failure between the adhesive and the adherend, according to the magnitudes of the residual thermal stresses induced by fabrication.

The effects of the design parameters for the adhesively-bonded tubular single lap joint, such as the thicknesses of adhesive layer and adherends, the bonding length, and the scarfs of adherends, on the torque transmission capability and the efficiency of the adhesive joint were investigated.     

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.     

Analysis of tubular adhesive joints with a functionally modulus graded bondline subjected to axial loads

The strength and lifetime of adhesively bonded joints can be significantly improved by reducing the stress concentration at the ends of overlap and distributing the stresses uniformly over the entire bondline. The ideal way of achieving this is by employing a modulus graded bondline adhesive. This study presents a theoretical framework for the stress analysis of adhesively bonded tubular lap joint based on a variational principle which minimizes the complementary energy of the bonded system. The joint consists of similar or dissimilar adherends and a functionally modulus graded bondline (FMGB) adhesive. The varying modulus of the adhesive along the bondlength is expressed by suitable functions which are smooth and continuous. The axisymmetric elastic analysis reveals that the peel and shear stress peaks in the FMGB are much smaller and the stress distribution is more uniform along its length than those of mono-modulus bondline (MMB) adhesive joints under the same axial tensile load. A parametric evaluation has been conducted by varying the material and geometric properties of the joint in order to study their effect on stress distribution in the bondline. Furthermore, the results suggest that the peel and shear strengths can be optimized by spatially controlling the modulus of the adhesive.     

The Effect of Moment and Flexural Rigidity of Adherend on the Strength of Adhesively Bonded Single Lap Joints

In the present study, mechanical properties of different single lap joint configurations derived from adherends with different thicknesses subjected to tensile loading were investigated experimentally and numerically. For this purpose, experimental studies were conducted on two different types of SLJ samples, the first type with identical upper and lower adherend thicknesses and the second with different upper and lower adherend thicknesses. For the first type, five different thickness values were tested. For the second type, the lower adherend thickness was constant while five different upper adherend thickness values were tested. The adhesive was prepared from a two-part paste. After the experimental studies, stress analyses on the SLJs were performed with three-dimensional finite element analysis by considering the geometrical non-linearity and the material non-linearities of the adhesive (DP460) and adherend (AA2024-T3). It was observed that, in single lap joint geometry, variation in the thickness of the adherend and the use of lower and upper adherends with different thickness values changed the stress concentrations at the edges of the overlap regions, affecting the experimental failure load of the joints.     

CRH3高速动车组空调通风口胶接结构设计

通过理论分析和计算确定了动车组空调通风口部件与铝合金车体胶接用胶粘剂的强度指标。介绍了胶粘剂的选择及胶接结构的设计原则,考查了搭接长度、搭接宽度、胶层厚度和被粘接材料厚度等对胶接件粘接强度的影响。结果表明:车体与空调通风口部件的胶接接头选择受剪切应力作用的搭接接头较适宜,并且搭接接头的承载能力随搭接长度或宽度增加呈先快速上升后趋于稳定态势;当搭接长度为10 mm、胶层厚度为6 mm、铝合金板厚度为5 mm且常温湿固化型单组分PU(聚氨酯)胶粘剂的剪切强度超过0.23 MPa时,搭接接头的承载能力相对最大。     

Effect of protrusion at the ends of bondline in single lap joints under tension and bending

In this work, elasto-plastic stress analysis of single lap joints with and without protrusion in adhesive bondline subjected to tension and bending was carried out using 2D non-linear finite element analysis and confirmed experimentally. AA 2024-T3 aluminum adherends were bonded with SBT 9244 film adhesive. The protrusion was obtained by extending the adhesive film by 2?mm from the overlap length at both overlap ends. Three different adherend thicknesses and overlap lengths for each loading and bondline type were used. The joints with and without protrusion, for comparison, were loaded with the same load for each adherend thickness and overlap length. Finally, it was observed that the protrusion reduces the strength in the joint under tension, while the protrusion increases the strength in the joint under bending.     

Modelling of Functionally Graded Adhesive Joints

Nowadays, there is a strong trend towards the use of functionally graded materials, with particular importance for the functionally graded joints. The main objective of this work was to study a functionally modified adhesive in order to have mechanical properties that vary gradually along the overlap of a joint, allowing a uniform stress distribution along the overlap. This allows for a stronger and more efficient adhesive joint and would permit to work with much smaller areas, reducing considerably the weight of the structure which is a key factor in the transport industry. In the proposed joint, the adhesive stiffness varies along the overlap, being maximum in the middle and minimum at the ends of the overlap. The functionally graded joint was found to have a higher joint strength compared to the cases where the adhesive has homogeneous properties along the overlap. A simple analytical model to study the performance of the functionally graded joints was developed. The differential equation of this model was solved by a power series. Numerical modelling by finite element analysis was performed to validate the analytical model developed.     

Static and fatigue behavior of adhesive joints in SMC-SMC composites

This paper discusses the static and fatigue behavior of adhesively bonded single lap joints in SMC-SMC composites. Effects of lap length and adhesive thickness on the static and fatigue strength of SMC-SMC adhesive joints are studied. Effects of SMC surface preparation and test speed on the joint performance are evaluated. Finally, the effect of water exposure on the joint durability is also investigated. Results show that the static behavior of adhesive joints in SMC-SMC composites is significantly influenced by the lap length and adhesive thickness. With an increase in lap length from 12.7 mm to 38.1 mm, the joint failure load increases by 37%. The joint failure load also increases with the adhesive thickness, but it reaches a maximum at an adhesive thickness of 0.33 mm and then decreases. However, lap length and adhesive thickness have negligible effect on the ratio of fatigue strength to static strength. The fatigue strength at 10⁶ cycles is approximately 50% to 54% of the static strength for various adhesive thicknesses and lap lengths investigated in this study. Adhesive failure, fiber tear or combination of these two failure modes are observed during both static and fatigue tests.     

Functionally graded adhesive joints by graded mixing of nanoparticles

The main objective of the present study was to use a functionally modified adhesive in order to have an adhesive with properties that vary gradually along the overlap, allowing a uniform stress distribution along the overlap. This allows for a stronger and more efficient adhesive joint. It is possible to work with much smaller areas, reducing considerably the weight of the structure and obtaining more reliable joints. The adhesive stiffness would vary along the overlap, being maximum in the middle and minimum at the ends of the overlap. The processes tested in this work were dielectric heating using a domestic microwave oven and conventional oven heating. Different amounts of carbon black were used and functionally dispersed along the bondline length in order to obtain a functionally graded joint. The functionally graded joints were found to have a higher joint strength compared to the cases where the carbon black was dispersed uniformly along the overlap or where the adhesive was used without carbon black. An analytical model was used to assist with the prediction and the assessment of the possible effectiveness of a graded joint concept.     

Effect of material,geometry, surface treatment and environment on the shear strength of single lap joints

The single lap joint is the most studied type of adhesive joint in the literature. However, the joint strength prediction of such joints is still a controversial issue as it involves a lot of factors that are difficult to quantify such as the overlap length, the yielding of the adherend, the plasticity of the adhesive and the bondline thickness. The most complicated case is that where the adhesive is brittle and the overlap long. In any case, there is still a problem that is even more difficult to take into account which is the durability. There is a lack of experimental data and design criteria when the joint is subjected to high, low or variable temperature and/or humidity. The objective of this work is to carry out and quantify the various variables affecting the strength of single lap joints in long term, especially the effect of the surface preparation. The Taguchi method is used to decrease the number of experimental tests. The effect of material, geometry, surface treatment and environment is studied and it is shown that the main effect is that of the overlap length.In order to quantify the influence of the adhesive (toughness and thickness), the adherend (yield strength and thickness), the overlap, the test speed, the surface preparation and durability on the lap shear strength, the experimental design technique of Taguchi was used in the present study. An experimental matrix of 18 tests was designed and each test was repeated three times. The influence of the eight previously-mentioned variables could be assessed using the statistical software Statview^®. In this paper a simple predictive equation is proposed for the design of single lap joints.     

Finite element analysis of torsional free vibration of adhesively bonded single-lap joints

Adhesively bonding is a high-speed fastening technique which is suitable for joining advanced lightweight sheet materials that are dissimilar, coated and hard to weld. In this paper, the free torsional vibration characteristics of adhesively bonded single-lap joints are investigated in detail using finite element method. The effectiveness of finite element analysis technique used in the study is validated by experimental tests. The focus of the analysis is to reveal the influence on the torsional natural frequencies and mode shapes of these joints caused by variations in the material properties of adhesives. It is shown that the torsional natural frequencies and the torsional natural frequency ratios of the adhesively bonded single-lap joints increases significantly as the Young′s modulus of the adhesives increase, but only slight changes are encountered for variations of Poisson's ratio. The mode shapes analysis show that the adhesive stiffness has a significant effect on the torsional mode shapes. When the adhesive is relatively soft, the torsional mode shapes at the lap joint are slightly distorted. But when the adhesive is relatively very stiff, the torsional mode shapes at the lap joint are fairly smooth and there is a relatively higher local stiffening effect. The consequence of this is that higher stresses will be developed in the stiffer adhesive than in the softer adhesive.     

Use of artificial neural networks for modelling rate dependent behaviour of adhesive materials

This research work highlights the use of artificial neural networks (ANN) for modelling the rate-dependent response of adhesive materials with the purpose of expanding the established method for modelling the response of adhesively bonded structures, and in particular single lap joints. The motivation for this work comes after a viscoplastic model developed in a previous research work failed to predict the response of single lap joints bonded with a rate dependent adhesive material. The viscoplastic model, however, was successful in replicating both bulk and shear properties of the used adhesive system. Predictions made using the rate-dependent von Mises material model proved to be successful in predicting the behaviour of single lap joints, but it could not model the shear data using the tensile data due to hydrostatic stress sensitivity in the adhesive itself. Accurate predictions of the rate-dependent behaviour using artificial neural networks are possible with the availability of stress and strain data sets from experiments. This is where the neural network constitutive model directly acquires the information on the material behaviour from experimental data sets. Material data defining both the tensile and shear response of the adhesive system was extracted from previous research work. An artificial neural network constitutive model was developed and then used to replicate experimental data and also to generate further data at other strain rates. The available model could be slightly modified and then used to investigate various geometrical parameters, such as overlap length, plate thickness and adhesive thickness on joint strength.