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

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

Strength of adhesively bonded joints under mixed axial and shear loading

This study aims at optimising adhesive properties in an aluminium/structural epoxy assembly for different conditions of surface pre-treatment. We consider the mechanical behaviour and failure under proportional, multi-axial loading using an instrumented, Arcan-type test. Values of fracture strength were found to be dispersed (even for a given surface treatment). Typically dispersion was of the order of 15%. This statistical behaviour, also observed with a simple tensile test, seems to be related to the heterogeneous nature of the microstructure of the adhesive bond, which contains voids, as well as mineral particles for reinforcement. A statistical analysis is suggested for use in conjunction with a strength envelope in practical design, for cases when the stress distribution is significantly heterogeneous. It is believed that this approach may be developed in order to understand the well-known scatter of adhesion strength results, and thus contribute to better reliability assessment.     

Strength prediction of adhesively bonded carbon/epoxy joints

A finite element approach has been used to obtain the stress distribution in some adhesive joints. In the past, a strength prediction method has not been established. Therefore in this study, a strength prediction method for adhesive joints has been examined. First, the critical stress distribution of single-lap adhesive joints, with six different adherend thicknesses, was examined to obtain the failure criteria. It was thought that the point stress criterion, which has been previously used for an FRP tensile specimen with a hole, was effective. The proposed method using the point stress criterion was applied to adhesive joints, such as single-lap joints with short non-lap lengths and bending specimens of single-lap joints. Good agreement was obtained between the predicted and experimental joint strengths.     

Strength prediction of epoxy adhesively bonded scarf joints of dissimilar adherends

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

Failure behavior of adhesively bonded joints with a rubber modified epoxy adhesive under tensile-shear combined cyclic loading

Rubber-modified epoxy adhesives are used widely as structural adhesive owing to their properties of high fracture toughness. In many cases, these adhesively bonded joints are exposed to cyclic loading. Generally, the rubber modification decreases the static and fatigue strength of bulk adhesive without flaw. Hence, it is necessary to investigate the effect of rubber-modification on the fatigue strength of adhesively bonded joints, where industrial adhesively bonded joints usually have combined stress condition of normal and shear stresses in the adhesive layer. Therefore, it is necessary to investigate the effect of rubber-modification on the fatigue strength under combined cyclic stress conditions. Adhesively bonded butt and scarf joints provide considerably uniform normal and shear stresses in the adhesive layer except in the vicinity of the free end, where normal to shear stress ratio of these joints can cover the stress combination ratio in the adhesive layers of most adhesively bonded joints in industrial applications.

In this study, to investigate the effect of rubber modification on fatigue strength with various combined stress conditions in the adhesive layers, fatigue tests were conducted for adhesively bonded butt and scarf joints bonded with rubber modified and unmodified epoxy adhesives, wherein damage evolution in the adhesive layer was evaluated by monitoring strain the adhesive layer and the stress triaxiality parameter was used for evaluating combined stress conditions in the adhesive layer. The main experimental results are as follows: S–N characteristics of these joints showed that the maximum principal stress at the endurance limit indicated nearly constant values independent of combined stress conditions, furthermore the maximum principal stress at the endurance limit for the unmodified adhesive were nearly equal to that for the rubber modified adhesive. From the damage evolution behavior, it was observed that the initiation of the damage evolution shifted to early stage of the fatigue life with decreasing stress triaxiality in the adhesive layer, and the rubber modification accelerated the damage evolution under low stress triaxiality conditions in the adhesive layer.     

Predicting the strength of adhesively bonded joints of variable thickness using a cohesive element approach

One major characteristic of bonded structures is the highly localised nature of deformation near sharp corners, ply-terminations, and ends of joints where load transfer occurs. This paper presents an investigation of the use of a cohesive zone model in predicting the strong effects of stress concentration due to varying adherend thickness on the pull-off strength measured by the Pneumatic Adhesion Tensile Testing Instrument. A comparison is made with the point-strain-at-a-distance criterion, where the plastic deformation of the adhesive is analysed using a modified Drücker–Prager/cap plasticity material model. The fracture properties of the cohesive zone model were determined using double-cantilever and end-notch flexural specimens, and the cohesive strengths were measured using tensile and lap shear tests. Comparisons with experimental results reveal that the cohesive zone model with perfectly plastic (or non-strain-softening) cohesive law provides accurate predictions of joint strengths.     

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.     

A damage zone model for the failure analysis of adhesively bonded joints

The design of structural adhesively bonded joints is complicated by the presence of singularities at the ends of the joint and the lack of suitable failure criteria. Literature reviews indicate that bonded joint failure typically occurs after a damage zone at the end of the joint reaches a critical size. In this paper, a damage zone model based on a critical damage zone size and strain-based failure criteria is proposed to predict the failure load of adhesively bonded joints. The proposed damage zone model correctly predicts the joint failure locus and appears to be relatively insensitive to finite element mesh refinement. Results from experimental testing of various composite and aluminium lap joints have been obtained and compared with numerical analysis. Initial numerical predictions indicate that by using the proposed damage zone model, good correlation with experimental results can be achieved. A modified version of the damage zone model is also proposed which allows the model to be implemented in a practical engineering analysis environment. It is concluded that the damage zone model can be successfully applied across a broad range of joint configurations and loading conditions.     

Fatigue life prediction of adhesively bonded single lap joints

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

An improved model for adhesively bonded DCB joints

An improved analytical model is proposed for characterizing the fracture behavior of an adhesively bonded double cantilever beam joint under Mode I loading. Novel interfacial normal stress distribution function is used with a key parameter c that is determined using continuum mixture theory. In addition to the mechanical and sectional properties of the adherends, crack length, and overlap area, the model also incorporates the adhesive thickness and material properties as well as the crack tip rotation. Model prediction of the fracture toughness of the joint is entered into finite element analysis to simulate crack propagation under peel loading. The effect of various parameters on the joint fracture properties is discussed. Results show that the proposed model provides better correlation with published experimental data.     

Analysis of cohesive failure in adhesively bonded joints with the SSPH meshless method

Adhesives have become the method of choice for many structural joining applications. Therefore, there is a need for improved understanding of adhesive joint performance, especially their failure, under a variety of loading conditions. Various numerical methods have been proposed to predict the failure of adhesive bonded material systems. These methods generally use a cohesive zone model (CZM) to analyze crack initiation and failure loci. The CZM incorporates a traction–separation law which relates the jump in surface tractions with the jump in displacements of abutting nodes of the cohesive segment; the area under the curve relating these jumps equals the energy release rate which is determined from experimental data. Values of parameters in the CZM are usually obtained through the comparison of results of numerical simulations with the experimental data for pure mode I and mode II deformations. Here a numerical approach to simulate crack initiation and propagation has been developed by implementing CZM in the meshless method using the symmetric smoothed particle hydrodynamics (SSPH) basis functions, and using the design of experiments technique to find optimal values of CZM parameters for mode I failure. Unlike in the finite element method where a crack generally follows a path between element boundaries, in the meshless method a crack can follow the path dictated by the physics of the problem. The numerical technique has been used to study the initiation and propagation of a crack in a double cantilever beam under mode I and mixed mode in-plane loadings. Computed results are found to agree well with the corresponding experimental findings. Significant contributions of the work include the determination of optimum values of CZM parameters, and simulating mode I, mode II and mixed mode failures using a meshless method with the SSPH basis functions.     

Comparison of cohesive zone and continuum damage approach in predicting the static failure of adhesively bonded single lap joints

The paper presents a comparison of the cohesive zone model (CZM) and the continuum damage mechanics approach in predicting the static failure of a single lap joint (SLJ). The effect of mesh size and viscosity were studied to give more understanding on the failure load and computational time. Both the load–displacement response and the backface strain technique were utilised to compare the validity of predictions. Peel and shear stress and damage distributions along with the damage progression are compared to understand the behaviour of the models in predicting the static failure response. In general, both approaches show good accuracy in predicting the failure load; however, the cohesive zone approach requires shorter computation time than the continuum damage approach. The continuum damage approach shows some mesh-dependency particularly for elements with high aspect ratios, whereas the cohesive zone approach is not. The continuum damage approach is less sensitive than the cohesive zone approach to the artificial damping required to achieve convergence. Another interesting finding is using the same ultimate stress level of damage in the continuum damage approach at the peak load is much lower than that in the cohesive approach; but the failure process in this approach is faster.     

Strength model of adhesive bonded composite pipe joints under tension

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

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

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

单搭接胶接接头的拓扑优化

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

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

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

An investigation of fatigue failure prediction of adhesively bonded metal/metal joints

A fracture mechanics-based model for fatigue failure prediction of adhesive joints has been applied in this work. The model is based on the integration of the kinetic law of evolution of defects originated at stress concentrations within the joint. Final failure can be either brittle (fracture toughness-driven) or ductile (tensile/shear strength-driven) depending on the adhesive. The model has been validated against experiments conducted on single-lap shear joints bonded with a structural adhesive. Three different kinds of adhesives, namely a modified methacrylate, a one-part epoxy and a two-part epoxy supplied by Henkel, have been considered and three different overlap lengths have been tested. Fracture toughness and fatigue crack growth properties of the adhesives have been determined with mode I tests. The number of cycles to failure has been successfully predicted in several cases. It is interesting to notice that in the case of joints loaded at the same average shear stress, the shorter the joint, the longer the duration. This fact is also captured by the model.     

Analysis and design of adhesively bonded joints for fatigue and fracture loading: a fracture-mechanics approach

An experimental–computational fracture-mechanics approach for the analysis and design of structural adhesive joints under static loading is demonstrated by predicting the ultimate fracture load of cracked lap shear and single lap shear aluminum and steel joints bonded using a highly toughened epoxy adhesive. The predictions are then compared with measured values. The effects of spew fillet, adhesive thickness, and surface roughness on the quasi-static strength of the joints are also discussed. This fracture-mechanics approach is extended to characterize the fatigue threshold and crack growth behavior of a toughened epoxy adhesive system for design purposes. The effects of the mode ratio of loading, adhesive thickness, substrate modulus, spew fillet, and surface roughness on the fatigue threshold and crack growth rates are considered. A finite element model is developed to both explain the experimental results and to predict how a change in an adhesive system affects the fatigue performance of the bonded joint.     

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

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