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.     

Direct determination of a new mode-dependent cohesive zone model to simulate metal-to-metal adhesive joints

In this paper, a new mode-dependent cohesive zone model for the simulation of metal to metal adhesive joints is directly determined. Three consecutive steps have been taken into account for this end. First, double cantilever beam (DCB) and end-notched flexure (ENF) specimens are utilized for the direct experimental extraction of the traction-separation laws (TSLs) for adhesive bonded joints subjected to pure mode I and mode II, respectively. Next, the results are implemented to obtain the relative cohesive zone parameters for defining the simplified Park-Paulino-Roesler cohesive zone model (S-PPR CZM). Finally, mixed-mode characteristics parameters are derived for an arbitrary mode-mixity ratio based on pure mode TSLs. The model is further implemented in ABAQUS® commercial software to be verified against the experimental results of pure mode loadings which leads to the direct extraction of TSLs. The experiments conducted on the strength of single lap joint (SLJ) and scarf joint (SJ) specimens, commonly tested for mixed-mode loading, confirm the accuracy of the developed mixed-mode S-PPR model for different mode-mixity conditions.     

Comparison of cohesive zone elements and smoothed particle hydrodynamics for failure prediction of single lap adhesive joints

This research investigates the use of a meshless smoothed particle hydrodynamics (SPH) method for the prediction of failure in an adhesively bonded single lap joint. A number of issues concerning the SPH based finite element modelling of single lap joints are discussed. The predicted stresses of the SPH finite element model are compared with the results of a cohesive zone based finite element model. Crack initiation and crack propagation in the adhesive layer are also studied. The results show that the peel stresses predicted by the SPH finite element model are higher and the shear stresses are lower than those predicted by the cohesive zone finite element model. The crack initiation and propagation response of the two models is similar, however, the SPH finite element model predicted a lower failure load than the cohesive zone finite element model. It is concluded that the current implementation of SPH method is a promising method for modelling cohesive failure in bonded joins but requires further development to allow for interfacial crack growth and better stress prediction under tensile loading to compete with existing methods.     

Modeling of cohesive failure processes in structural adhesive bonded joints

This paper presents an approach to predicting the strength of joints bonded by structural adhesives using a finite element method. The material properties of a commercial structural adhesive and the strength of single-lap joints and scarf joints of aluminum bonded by this adhesive were experimentally measured to provide input for and comparison with the finite element model. Criteria based on maximum strain and stress were used to characterize the cohesive failure within the adhesive and adherend failure observed in this study. In addition to its simplicity, the approach described in this paper is capable of analyzing the entire deformation and failure process of adhesive joints in which different fracture modes may dominate and both adhesive and adherends may undergo inelastic deformation. It was shown that the finite element predictions of the joint strength generally agreed well with the experimental measurements.     

Predicting environmental degradation of adhesive joints using a cohesive zone finite element model based on accelerated fracture tests

A framework was developed to predict the fracture toughness of degraded adhesive joints by incorporating a cohesive zone finite element (FE) model with fracture data of accelerated aging tests. The developed framework addresses two major issues in the fracture toughness prediction of degraded joints by significant reduction of exposure time using open-faced technique and by the ability to incorporate the spatial variation of degradation with the aid of a 3D FE model. A cohesive zone model with triangular traction-separation law was adapted to model the adhesive layer. The degraded cohesive parameters were determined using the relationship between the fracture toughness, from open-faced DCB (ODCB) specimens, and an exposure index (EI), the time integration of the water concentration. Degraded fracture toughness predictions were done by calculating the EI values and thereby the degraded cohesive parameters across the width of the closed joints. The framework was validated by comparing the FE predictions against the fracture experiment results of degraded closed DCB (CDCB) joints. Good agreement was observed between the FE predictions and the experimental fracture toughness values, when both ODCB and CDBC were aged in the same temperature and humidity conditions. It was also shown that at a given temperature, predictions can be made with reasonable accuracy by extending the knowledge of degradation behavior from one humidity level to another.     

Modelling of furniture experiments with zone models

The Harvard Computer Fire Code Mark V has been used to simulate full-scale furniture fires. Simulations were run with one sofa burning in the open and another burning in a small room. To obtain better agreement between experiment and simulation, changes were made in the code to include heating of the lower surfaces in the room. A simulation of a mattress test, conducted at NBS, is included. Comparison with a zone model using a different plume equation is also presented.     

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.     

Accuracy of cohesive laws with different shape for the shear behaviour prediction of bonded joints

The use of adhesive bonding as a joining technique is increasingly being used in many industries because of its convenience and high efficiency. Cohesive Zone Models (CZM) are a powerful tool for the strength prediction of bonded joints, but they require an accurate estimation of the tensile and shear cohesive laws of the adhesive layer. This work evaluated the shear fracture toughness (J_IIC) and CZM laws of bonded joints for three adhesives with distinct ductility. The End-Notched Flexure (ENF) test geometry was used. The experimental work consisted of the shear fracture characterization of the bond by the J-integral. Additionally, by this technique, the precise shape of the cohesive law was defined. For the J-integral, digital image correlation was used for the evaluation of the adhesive layer shear displacement at the crack tip during the test, coupled to a Matlab sub-routine for extraction of this parameter automatically. Finite Element Method (FEM) simulations were carried out in Abaqus® to assess the accuracy of triangular, trapezoidal and linear-exponential CZM laws in predicting the experimental behaviour of the ENF tests. As output of this work, fracture data is provided in shear for the selected adhesives, allowing the subsequent strength prediction of bonded joints.     

A Bayesian framework for the calibration of cohesive zone models

Adhesively bonded joints are used in several industrial sectors. Cohezive Zone Modes can be used to predict the adhesive mechanical behaviour. This work presents an approach to calibrate Cohesive Zone Models (CZM) by means of Statistical Inverse Analysis. The Bayesian framework for Inverse Problems is used to infer about the CZM model parameters. The solution corresponds to the exploration of the posterior probability density function of the model parameters. The exploration of the posterior density is performed by means of Markov Chain Monte Carlo (MCMC) methods mixing Population-Based MCMC with Adaptive Metropolis (AD) strategies. The assessment of the approach is performed using measured data from a single-lap shear experimental set-up. Measured data from 5 test-specimens is used for calibration and measured data from five other test-specimens is used for model validation. It is proposed a stochastic effective model for the CZM parameters. The predictions of maximum force and maximum displacement that are provided by the effective model are in accordance with measured data that is used for validation.     

Cohesive/adhesive failure interaction in ductile adhesive joints Part I: A smeared-crack model for cohesive failure

This paper proposes a new methodology for the finite element (FE) modelling of failure in adhesively bonded joint. Unlike current methods, cohesive and adhesive failures are treated separately. Initial results show the method׳s ability to give accurate prediction of failure of adhesive joints subjected to thickness-induced constraint and complex multi-axial loading using a single set of material parameters. The present paper (part I), focuses on the development of a smeared-crack model for cohesive failure. Model verification and validation are performed comparing the model predictions with experimental data from 3 point bending End Notched Flexure (3ENF) and Double Cantilever Beam (DCB) fracture tests conducted on adhesively bonded composite panels of different adhesive thicknesses.     

Estimation of static strength of adhesively bonded single lap joints with an acrylic adhesive under tensile shear condition based on cohesive zone model

In this study, the tensile shear and bending tests of adhesively bonded single lap joints with the acrylic adhesive was evaluated experimentally and numerically. In the previous paper, the traction-separation laws in mode 1 and mode 2 for an acrylic adhesive were directly obtained from the observation of failure process using Arcan type adhesively bonded specimens: simultaneous measurements of the J-integral and the opening displacements in the directions normal, δ_n and tangential to the adhesive layer, δ_s respectively. The experimental results were compared with numerical simulations conducted in ABAQUS including cohesive damage model. The cohesive laws obtained in the previous paper were simplified to trapezoidal shape from the experimentally obtained ones which were indicated in the previous paper. A good agreement was found between the experimental and numerical results. Then, to investigate the damage evolution in the adhesive layer for some lap joints, microscopic video observation was conducted near the end of the adhesive layer, and the video image have been compared with the contours of damage variable obtained by FEM corresponding to the video images. The observed damage evolution also agrees with the trend of damage variable.     

单搭接胶接接头胶层的拓扑优化

利用有限元法,对单搭接胶接接头胶层进行拓扑优化,寻求胶粘剂最佳分配.结果表明,合理的胶粘剂分配能够在不影响接头整体力学性能的前提下,极大限度地减少胶粘剂的用量,且使胶粘剂中剪切应力分布更为均匀.     

Evaluation of different modelling conditions in the cohesive zone analysis of single-lap bonded joints

Cohesive Zone Models (CZM) are widely used for the strength prediction of adhesive joints. Different simulation conditions, such as damage initiation and growth criteria, are available for use in CZM analyses to provide the mixed-mode behaviour. Thus, it is highly relevant to understand in detail their influence on the simulations’ outcome. This work studies the influence of different conditions used in CZM simulations to model a thin adhesive layer in single-lap joints (SLJ) under a tensile loading, for an estimation of their influence on the strength prediction under diverse geometrical and material conditions. Validation with experimental data is considered. Adhesives ranging from brittle to highly ductile and overlap lengths (L_O) between 12.5 and 50 mm were considered. Different studies were considered: Variation of the elastic stiffness of the cohesive laws, different mesh refinements, study of the element type, and evaluation of several damage initiation and growth criteria. The analysis carried out in this work confirmed the known suitability of CZM for static strength prediction of bonded joints and pointed out the best set of numerical conditions for this purpose. Inaccurate results can be obtained if the choice of the modelling conditions is not the most suitable for the problem.     

Analysis of adhesively-bonded T-joints by experimentation and cohesive zone models

Within the scope of adhesively-bonded joints, one of the joint types having industrial application is the T-joint, for example, in marine applications (joining of panels to the hull and connecting the glass-fibre composite hull with anti-flood panels) and aeronautical applications (wing panels, fuselage sections). This work aims to experimentally and numerically study, by cohesive zone models (CZM), the behaviour of T-joints under peel loads. The experimentally evaluated adhesives are the Araldite^® AV138 (high ultimate strength but brittle) and Araldite^® 2015 (less stress to failure but ductile and more flexible). The joint strength is evaluated with different L-shaped adherends’ thickness (t_P2). With the numerical analysis, the stress distributions, damage evolution and strength are studied. Additionally, a purely numerical study compared joints with or without adhesive filling at the curvature of the L-shaped adherends, and an extremely ductile adhesive (Sikaforce^® 7752) was additionally evaluated. The experimental tests validated the numerical results and showed that CZM is an accurate technique for the study of T-joints. It was also shown that the geometry of the L-parts, the presence of filler adhesive and the type of adhesive have a direct influence on the joint strength. In fact, in this particular joint configuration, the ductile but with lower ultimate strength adhesive Sikaforce^® 7752 clearly outperforms the two adhesives with higher mechanical properties but less ductility.     

胶层局部缺陷对胶接接头承载能力的影响研究

针对汽车车身中应用日益广泛的钢板胶接结构,通过实验得到了不同胶层局部缺陷对接头承载能力的影响规律,进而采用接头的三维弹塑性有限元模型,解释了实验结果,并提出了接头承载危险系数(K)的概念。研究结果表明,胶层为四角缺陷时,接头处的危险系数随缺陷面积的增加而增大(从0.66增加到0.91),接头的断裂强度由8640N降低到8121N;胶层为中央缺陷时,接头处的危险系数随中央缺陷面积的增加增幅较小,接头承载能力基本不变。     

Environmental effect on the fatigue degradation of adhesive joints: A review

ABSTRACT

Environmental factors, such as temperature and moisture, are known to have a degrading effect on the mechanical properties and performance of adhesive joints, which may be perceived as a non-problem because various works have shown that the static response of an adhesive is normally unaffected by slight moisture and temperature variations that occur in real-world applications. While this may be true, performance under purely static conditions is rarely found in commercial uses and most adhesive joints are subjected to cyclic loadings throughout their life. Interestingly, not much work has been done on the effects of the environment on cyclically loaded adhesive joints, but the consensus is that the fatigue response is much more affected by environmental changes than the static response, which is arguably the most important analysis. The general trend is that hygrothermal ageing decreases the number of cycles the joint can withstand and also decreases the threshold fracture toughness value, which translates to cracks initiating sooner, but exceptions to these behaviours also exist.     

The effect of primers on adhesive properties and strength of adhesive joints made with polyurethane adhesives

The paper presents selected aspects of the effect of primers on adhesive properties and strength of aluminium sheet adhesive joints, made using polyurethane adhesives. The strength of adhesive joints was determined based on two cure time variants: 15 and 64 h. It was found that the longer cure time at a humidity of 33% is more desired, as it leads to a substantial increase in strength of the tested adhesive joints. In addition, two variants of surface preparation were applied: degreasing and degreasing followed by the application of a primer (a pro-adhesive agent). It was observed that the primer application prior to the application of an adhesive leads to a significant increase in strength compared to the variant where the adhesive application is preceded only by degreasing. Moreover, the aluminium sheet surface that was subjected to cataphoretic painting and priming exhibits better adhesive properties. It has a higher value of both surface free energy and its dispersion and polar components compared to the surface that was only subjected to degreasing.     

A 3D ductile constitutive mixed-mode model of cohesive elements for the finite element analysis of adhesive joints

In this paper, a new traction–separation law is developed that represents the constitutive relation of ductile adhesive materials in Modes I, II, and III. The proposed traction–separation laws model the elastic, plastic, and failure material response of a ductile adhesive layer. Initially, the independent-mode proposed laws (loading and fracture in Modes I, II, and III) are mathematically described and then introduced in a developed formulation that simulates the interdependency of the mixed-mode coupled laws. Under mixed-mode conditions, damage initiation is predicted with the quadratic stress criterion and damage propagation with the linear energetic fracture criterion. For verification and validation purposes of the proposed laws and mixed-mode model, steel adherends have been adhesively bonded with a structural ductile adhesive material in order to fabricate a series of single and double strap adhesive joint configurations. The specimens have been tested under uni-axial quasi-static load and the respective force and displacement loading history have been recorded. Corresponding numerical and experimental results have been compared for each joint case, respectively. Additionally, the developed stress fields (peel, in-plane, and out-of-plane shear) are presented as they evolve during the loading of both joint cases.     

Behavior and failure of adhesive bonds in pin fin heat sinks using cohesive zone model

Adhesive bonding is a versatile material joining method that tends to distribute the load over the bonded area and provide more flexibility in selecting the base material without worrying about the joining process and its effects. To improve the performance of heat sinks, polymer composite pin fin are used to improve the thermal conductivity. Adhesives are usually used in bonding composite fins to their metal base plate. In this work we provide a methodology for estimating the fatigue life of the adhesive joint. A thermo-mechanical cohesive zone model (CZM) is used at the interfaces to measure the softening of the bond under thermal cyclic loading which in turn decreases the critical stress for failure. A summary of the fatigue crack initiation (FCI) life prediction model is presented before a qualitative study is performed to estimate the effect of convection environment on the life and behavior of the adhesive bond.