Application of interface finite elements to three-dimensional progressive failure analysis of adhesive joints

ABSTRACT The paper presents a new model for three‐dimensional progressive failure analysis of adhesive joints. The method uses interface elements and includes a damage model to simulate progressive debonding. The interface finite elements are placed between the adherents and the adhesive. The damage model is based on the indirect use of fracture mechanics and allows the simulation of the initiation and growth of damage at the interfaces without considering the presence of initial flaws. The application of the model to single lap joints is presented. Experimental tests were performed in aluminium/epoxy adhesive joints. Linear elastic and elastoplastic analyses were performed and the predicted failure load for the elastoplastic case agrees with experimental results.     

Mode II fracture energy characterization of brittle adhesives using compliance calibration method

The end‐notched flexure (ENF) test is widely used for measuring the Mode II critical strain energy release rate of adhesively bonded joints (ABJs). Unstable crack growth in ENF joints with brittle adhesives is a common phenomenon. Classic data reduction methods like the direct beam theory (DBT) and the compliance‐based beam method (CBBM) usually result in unacceptable scatter when crack grows unstable. In this study, the application of a compliance calibration method (CCM) for ENF adhesive joints with a brittle adhesive is experimentally investigated. For this purpose, ENF specimens were manufactured and tested. Different data reduction methods were considered for treating the results. Afterwards, the obtained fracture energies were used as an input parameter in a finite element (FE) analysis with a cohesive zone model to evaluate the validity of the experimental data. It is shown that the fracture loads obtained by the CCM have the best agreement with the experimental ones comparing with the other data reduction approaches. To study the effect of geometry on the CCM results, ENF specimens with different adhesive thicknesses, substrate thicknesses and span lengths were also considered in this study, and some general conclusions are made about the geometrical parameters effect on the Mode II fracture energy.     

Effect of thermal residual stress on the crack path in adhesively bonded joints

Mode I fracture behaviour of adhesively bonded double and cantilever beam (DCB) compact tension (CT) joints was studied using a rubber-modified epoxy (Araldite® GY260) as the adhesive. Adherends were prepared from a carbon fibre (CF)/epoxy composite or aluminium alloys. The crack path in the joints was studied based on the sign of the non-singularT-stress ahead of the crack tip by calculating the thermal residual stress in the joints using finite element analysis. The results indicate that the type of adherend materials influence the level of the thermal residual stress in the adhesive layer, which consequently causes different crack paths in the joints, i.e. a uniformly smooth fracture surface in both CT and DCB aluminium joints and a wavy crack growth in the DCB CF/epoxy composite joints. However, the fracture energies of different types of adhesive joints were almost identical to each other for bond thicknesst<0.2 mm, and a somewhat higher fracture resistance was obtained for the CF/epoxy DCB joints with large bond thickness.     

Application of two‐state M‐integral for analysis of adhesive lap joints

With the aid of the two‐state M‐integral and finite element analysis, the asymptotic solution in terms of the complete eigenfunction expansion is obtained for adhesive lap joints. The notch stress intensity is introduced to characterize the singular stress field near the notch vertex of adhesive lap joints. The proposed scheme enables us to extract the intensity of each eigenfunction term from the far field data without resort to special singular elements at the vertex. It turns out that a weak stress singularity is not negligible around the vertex when it exists in addition to the major singularity. For a thin adhesive layer, there exist two asymptotic solutions: one is the inner solution approaching the eigenfunction solution for the vertex at which the adherend meets with the adhesive and the other is intermediate solution represented by the eigenfunction series that would be obtained in the absence of the adhesive layer. An appropriate guideline for choosing the geometric parameters in designing the adhesive lap joints, particularly the overlap length or the size of the adhesive zone, is suggested from the viewpoint of minimizing the notch stress intensity. Copyright © 2001 John Wiley & Sons, Ltd.     

Energy release rate and mode-mixity of adhesive joint specimens

Fracture behaviour of adhesive joints under mixed mode loading is analysed by using the beam/adhesive-layer (b/a) model, in which, the adherends are beamlike and the adhesive is constrained to a thin flexible layer between the adherends. The adhesive layer deforms in peel (mode I), in shear (mode II) or in a combination of peel and shear (mixed mode). Macroscopically, the ends of the bonded part of the joints can be considered as crack tips. The energy release rate of a single-layer adhesive joint is then formulated as a function of the crack tip deformation and the mode-mixity is defined by the shear portion of the total energy release rate. The effects of transversal forces and the flexibility of the adhesive layer are included in the b/a-model, which can be applied to joints with short crack length as well as short bonding length. The commonly used end-loaded unsymmetric semi-infinite joints are examined and closed-form solutions are given. In comparison to the singular-field model in the context of linear elastic fracture mechanics, the b/a-model replaces the singularity at the crack tip with a stress concentration zone. It is shown that the b/a-model and the singular-field model yield fundamentally different mode-mixities for unsymmetric systems. The presented closed-form b/a-model solutions facilitates parametric studies of the influence of unbalance in loading, unsymmetry of the adherends, as well as the flexibility of the adhesive layer, on the mode mixity of an adhesive joint.     

胶粘剂在粘接接头内热分解动力学的计算

为了研究粘接接头内胶粘剂的耐热性能,采用X射线能谱分析确定了不同条件下粘接接头内胶粘剂的元素组成及其变化行为,利用X射线能谱计算了胶粘剂的热失重率,进而计算出聚酰亚胺薄膜粘接接头内胶粘剂的热分解动力学,并与空气环境下胶粘剂热分解活化能进行了比较.计算结果表明,粘接接头内胶粘剂的热分解速率低于空气环境下胶粘剂热分解速率,这种分析测试方法为原位表征粘接接头内胶粘剂耐热性能提供了一种新的分析方法.     

Experimental and numerical investigations of mixed mode crack growth resistance of a ductile adhesive joint

Polymeric adhesive joints are extensively employed in various industrial and technological applications. It has been observed that in ductile adhesive joints, interface fracture is a common mode of failure which may involve stable crack propagation followed by catastrophic growth. The objectives of this paper are to investigate the effects of bondline thickness and mode mixity on the steady state energy release rate J_ss of such a joint. To this end, a combined experimental and numerical investigation of interfacial crack growth is carried out using a modified compact tension shear specimen involving two aluminium plates bonded by a thin ductile adhesive layer. A cohesive zone model along with a simple traction versus separation law is employed in the finite element simulations of crack growth. It is observed that J_ss increases strongly as mode II loading is approached. Also, it enhances with bondline thickness in the above limit. These trends are rationalized by examining the plastic zones obtained from the numerical simulations. The numerically generated J_ss values are found to agree well with the corresponding experimental results.     

Shape optimization of bonded patch to cylindrical shell structures

Adhesive bonding has been widely used to join or repair metallic and composite structural components to achieve or restore their designated structural stiffness and strengths. However, current analysis methods and empirical databases for composite bonded patch repairs or joints are limited to flat structures, and there exists a very limited knowledge on the effect of curvature on the performance and durability of composite bonded joints and repairs. Recently, a novel finite element formulation was presented for developing adhesive elements for conducting 2.5‐D simplified stress analysis of bonded repairs to curved structures. This paper presents the work on optimal shape design of a bonded curved composite patch using the newly developed adhesive element. The Sequential Linear Programming (SLP) method is employed as the optimization algorithm in conjunction with a fully implemented mesh generation algorithm into which new features have been incorporated. The objective of shape optimization is to minimize the maximum stress in the entire adhesive layer to ensure that the bonded patch effectively works together with the parent structure in service. Several different objective functions, related to possible failure mechanisms of the adhesive layer, are proposed to optimize the shape of a bonded patch. Copyright © 2003 John Wiley & Sons, Ltd.     

Adhesive interface element for bonding of laminated plates

An isoparametric adhesive interface element is used in the stress analysis of adhesive-bonded structures. The model assumes that transverse shear and peel stresses prevail in the adhesive layer. The analyses articulate separate responses of the plate, overlays and the adhesive. The stress distribution in the adhesive layer, obtained for lap joints, is found to be in agreement with those obtained by previous authors. To extend the use of bonded joints, the deflection of patched plates under transverse loading and the stress concentration in a plate having a center hole reinforced by a ring patch are also analyzed. The present element, together with the eight-node isoparametric plate element based on first order shear deformation theory used to model the plate and overlay patch, is found to have an advantage in solving problems of adhesive-bonded structures.     

Fatigue life estimation of adhesive bonded shaft joints

Fatigue tests and analytical investigation of adhesive bonded shaft joints were conducted to propose the estimation method of fatigue strength. Two kinds of adhesive bonded joints were studied: one, shaft joints connected with adhesive coupling, the other, adhesive joints of thin wall tubes to obtain standard fatigue strength. Both pulsating tensile and torsional fatigue tests were conducted with each adhesive joint. Furthermore, the stress distributions under tensile and torsional load conditions were analyzed by finite element method. Based on the analytically computed maximum normal shear stress in the adhesive layer, fatigue strength of the shaft joints was tandardized and compared with that of adhesive joints of thin wall tubes. As a result, it is confirmed that the maximum normal and shear stresses are key parameters for estimating fatigue strength under pulsating tensile and forsional load conditions, respectively. Furthermore, this study indicates an improved method of estimating fatigue strength by using tapered coupling order to reduce the stress concentration at the end of the adhesive layer.     

Fracture and yield behavior of adhesively bonded joints under triaxial stress conditions

Most of adhesively bonded joints are under complicatedly distributed triaxial stress in the adhesive layer. For the estimating of the strength of adhesively bonded joints, it is crucial to clarify behavior of yield and failure of the adhesives layer under triaxial stress conditions. Two types of the adhesively bonded joints were used in this study: One is the scarf joint which is under considerably uniform normal and shear stresses in the adhesive layer, where their combination ratio can be varied with scarf angle. The other is the butt joint with thin wall tube in which considerably uniform pure shear can be realized in the adhesive layer under torsional load conditions. These joints can cover the stress triaxiality in adhesive layers of most joints in industrial application. The effect of stress triaxiality on the yield and fracture stresses in the adhesive layer were investigated using the joints bonded by three kinds of adhesives in heterogeneous and homogeneous systems. The results showed that both the yield and failure criterion depend on the stress triaxiality and that the fracture mechanism of the homogeneous adhesive is different from that of the heterogeneous one. From these experimental results, a method of estimating the yield and failure stresses was proposed in terms of a stress triaxiality parameter.     

Influence of root curvature on the fracture energy of adhesive layers

Previously performed experiments to study the mode I behavior of an adhesive layer revealed an apparent increase in the fracture toughness when the adherends deformed plastically. Attempts to simulate the experiments are made; both with elastically and plastically deforming adherends. Thus, effects of the size of the process zone and the deformation of the adherends are revealed. The adhesive layer is modeled using finite elements with different approaches; cohesive elements and representative volume elements. The adherends are modeled with solid elements. With a long process zone, all models give good results as compared to the experiments. However, only the model with representative volume elements gives good agreement for large root curvatures and correspondingly short process zones. The results are interpreted by analyzing the deformation and mechanisms of crack propagation in the representative volume elements. It is shown that with large root curvature of the adherends, the in-plane stretching of the adhesive layer gives a substantial contribution to the fracture energy. A simple formula is derived and shown to give an accurate prediction of the effects of the root curvature. This result indicates the limits of conventional cohesive zone modeling of an adhesive layer of finite thickness.     

胶层网格尺寸与性能参数相关性的反演研究

在使用内聚力模型对复合材料胶层进行有限元失效分析时,为了保证计算结果的准确性和收敛性,胶层网格尺寸应小于1 mm。然而当使用内聚力模型对飞机上的大型复合材料结构进行有限元分析时,模型将会产生上百万的有限元单元,这将耗费大量的计算资源。本文在研究胶层参数对胶层失效分析影响的基础上,通过对不同网格尺寸下胶层参数进行反演,提出了一种修改胶层参数的方法以适用于不同网格尺寸下胶层失效分析。使用此方法对不同网格尺寸的混合型弯曲(MMB)有限元模型和复合材料圆壳模型进行了有限元仿真。结果表明:所提出的方法能够大幅降低模型的网格数量,减小计算规模,快速准确地计算出混合加载条件下胶层损伤演化和破坏情况。      

Temperature dependence of cohesive laws for an epoxy adhesive in Mode I and Mode II loading

The influence of the temperature on the cohesive laws for an epoxy adhesive is studied in the glassy region, i.e. below the glass transition temperature. Cohesive laws are derived in both Mode I and Mode II under quasi-static loading conditions in the temperature range $-30\le T \le 80^{\,\circ }$ C. Three parameters of the cohesive laws are studied in detail: the elastic stiffness, the peak stress and the fracture energy. Methods for determining the elastic stiffness in Mode I and Mode II are derived and evaluated. Simplified bi-linear cohesive laws to be used at any temperature within the studied temperature range are derived for each loading mode. All parameters of the cohesive laws are measured experimentally using only two types of specimens. The adhesive has a nominal layer thickness of 0.3 mm and the crack tip opening displacement is measured over the adhesive thickness. The derived cohesive laws thus represent the entire adhesive layer as having the present layer thickness. It is shown that all parameters, except the Mode I fracture energy, decrease with an increasing temperature in both loading modes. The Mode I fracture energy is shown to be independent of the temperature within the evaluated temperature span. At $80^{\,\circ }$ C the Mode II fracture energy is decreased to about 2/3 of the fracture energy at $-30^{\,\circ }$ C. The experimental results are verified by finite element analyses.     

Mixed Mode cohesive law with interface dilatation

Experimental investigations of adhesive joints and fibre composites have shown that under Mode II cracking, the fracture process induces a displacement normal to the fracture plane. This effect can be attributed e.g. to roughness of the fracture surface under dominating tangential crack face displacements. As the crack faces displace relatively to each other, the roughness asperities ride on top of each other and result in an opening (dilatation) in the normal direction. Furthermore, the interaction of the crack surfaces in the contact zone gives rise to compressive normal stresses and frictional shear stresses opposing the crack face displacements. A phenomenological Mixed Mode cohesive zone law, derived from a potential function, is developed to describe the above mentioned fracture behaviour under monotonic opening. The interface dilatation introduces two new lengths. The cohesive law is implemented in the commercial finite element program Abaqus. The model is validated and tested against experimental results under various mode mixities.     

Strength analysis of metallic bonded joints containing defects

Finite element simulation has been utilized to study the overall strength of metallic single lap joints with defects in their adhesive layers. Three types of defects are taken into account respectively, which are local debonding, weak bonding and void. For the first two types of defects, a developed numerical method using the cohesive zone model modified by user-defined subroutines is carried out as to consider the influences of the defect size and location. Furthermore, a modified-Gurson model is employed to simulate the adhesive layer with voids, considering the influence of the void size. The results show that the overall strength of the joints diminishes as the defect size is increased. Especially, the adhesive fracture properties and the size of the weak bonding region have combined influences on the strength of the joints.     

基于响应面法的自冲铆-粘接复合接头强度预测

为建立可快速预测铆接参数对自冲铆-粘接复合接头力学性能影响的模型,基于响应面法对AA5182、AA5052和AL1420三种铝合金板材开展了自冲铆-粘接复合连接工艺实验研究。以板材硬度、胶层厚度及刺穿压强为自变量,失效载荷值和能量吸收值为响应值,建立各因素与优化目标的响应面回归模型,并通过实验验证模型的可靠性。研究结果表明：该回归模型预测结果值与实验结果误差小于10%,即模型显著性较高,可用来预测自冲铆-粘接复合接头的静力学性能。在单因素作用下,失效载荷值受各因素影响顺序为：板材硬度>刺穿压强>胶层厚度,各因素对能量吸收值影响情况为：板材硬度>胶层厚度>刺穿压强。板材硬度对失效载荷值与能量吸收值的影响最为显著,并且随板材硬度的增加,两者皆呈先增加后减小的变化趋势。在交互作用下,板材硬度和胶层厚度对失效载荷值影响最大,刺穿压强与胶层厚度对能量吸收值影响最显著。通过对模型预测结果分析可得：在确保接头质量的情况下,适当增大刺穿压强可有效提高接头能量吸收值。使用粘接剂时,胶层厚度须控制在0.5～0.9 mm才能与其余两因素相互配合,达到最好的铆接效果。     

A convenient way to represent fatigue crack growth in structural adhesives

The present paper examines crack growth in a range of aerospace and automotive structural adhesive joints under cyclic‐fatigue loadings. It is shown that cyclic‐fatigue crack growth in such materials can be represented by a form of the Hartman–Schijve crack‐growth equation, which aims to give a unique and linear ‘master’ representation for the fatigue data points that have been experimentally obtained, as well as enabling the basic fatigue relationship to be readily computed. This relationship is shown to capture the experimental data representing the effects of test conditions, such as R‐ratio and test temperature. It also captures the typical scatter often seen in the fatigue crack‐growth tests, especially at low values of the fatigue crack‐growth rate. The methodology is also shown to be applicable to both Mode I (opening tensile), Mode II (in‐plane shear) and Mixed‐Mode I/II fatigue loadings. Indeed, it has been demonstrated that the fatigue behaviour of structural adhesives under both Mode I and Mode II loadings may be described by one unique ‘master’ linear relationship via the Hartman–Schijve approach.     

Accurate evaluation of 3D stress fields in adhesive bonded joints via higher-order FE models

Abstract

The accurate representation of the 3D stress fields at the bonded areas of adhesive joints is essential for their design and strength evaluation. In the present study, higher-order beam models developed in the framework of the Carrera Unified Formulation are employed to reduce the complexity and computational cost of numerical simulations on adhesive joints. The different components of the adhesive joint, i.e. adherends and adhesive, are modeled as beams with independent kinematics based on the Hierarchical Legendre Expansion (HLE). HLE models make use of a hierarchical polynomial expansion over the cross-section of the beam, thus allowing for the control of the accuracy of the stress solutions via the polynomial expansion. Recalling the Finite Element method, the beam axis is discretized by means of 1D elements. In this manner, generic geometries of the adhesive bonded joints can be studied. The proposed model is assessed through comparison against numerical and analytical references from the literature for single lap and double lap joints. Finally, a detailed 3D analysis is performed on the single lap joint problem, showing that the stress gradients along the adhesive are correctly and efficiently described if the proposed methodology is employed.