Effects of adhesive thickness on global and local Mode-I interfacial fracture of bonded joints

The interfacial fracture of adhesively bonded structures is a critical issue for the extensive applications to a variety of modern industries. In the recent two decades, cohesive zone models (CZMs) have been receiving intensive attentions for fracture problems of adhesively bonded joints. Numerous global tests have been conducted to measure the interfacial toughness of adhesive joints. Limited local tests have also been conducted to determine the interface traction-separation laws in adhesive joints. However, very few studies focused on the local test of effects of adhesive thickness on the interfacial traction-separation laws. Interfacial toughness and interfacial strength, as two critical parameters in an interfacial traction-separation law, have important effect on the fracture behaviors of bonded joints. In this work, the global and local tests are employed to investigate the effect of adhesive thickness on interfacial energy release rate, interfacial strength, and shapes of the interfacial traction-separation laws. Basically, the measured laws in this work reflect the equivalent and lumped interfacial fracture behaviors which include the cohesive fracture, damage and plasticity. The experimentally determined interfacial traction-separation laws may provide valuable baseline data for the parameter calibrations in numerical models. The current experimental results may also facilitate the understanding of adhesive thickness-dependent interface fracture of bonded joints.     

单搭接胶接接头拉伸剪切性能的数值模拟与实验研究

采用数值模拟和光测技术对单向拉伸载荷作用下单搭接胶接接头中的剪切性能进行分析,研究了不同厚度胶层中切应力的变化规律。用有限元方法(FEM)对不同胶层厚度的试件进行建模,得到了拉伸载荷下胶粘剂中的切应力分布及其统计参数。利用数字图像相关(digitalimage correlation,DIC)方法对试件的变形场进行测量。结果表明,当胶粘剂的厚度较小时,胶粘剂中的切应力的分布统计参数随着其厚度的增加会有显著的变化,但是当厚度超过一定的数值时,统计参数对厚度的变化不再敏感。     

Local Interface Shear Fracture of Bonded Steel Joints with Various Bondline Thicknesses

Interfacial fracture is a critical issue for extensive applications of adhesively bonded structures to a variety of modern industries. Extensive global experimental tests have been conducted to measure the global behavior of adhesively bonded joint, such as ultimate load capacity and toughness. Recently, several studies have also been employed to characterize the local interfacial traction–separation laws. However, very few tests have investigated the dependency of the local interfacial constitutive laws on the adhesive thickness, particularly, under Mode-II loading conditions. In this work, six typical adhesive thicknesses (from 0.1 mm to 1.0 mm) are prepared for the bonded joints with a configuration of end notched flexure (ENF) specimen to realize the Mode-II fracture loading (shear fracture). With a recently developed analytical model, the global energy release rates of the ENF specimens are experimentally measured. Meanwhile, with the image analysis technique, the local slips between the two adherends are obtained. Finally, based on the J-integral theory, the local interfacial constitutive laws at different bondline thicknesses are obtained. Several experimental findings are reported in this work. This work may provide valuable baseline experimental data for the input in cohesive zone model (CZM) based analytical and numerical simulations.     

内聚力模型的形状对胶接结构断裂过程的影响

内聚力模型被广泛应用于粘接结构的断裂数值模拟过程中,为深入分析不同形状内聚力模型与胶黏剂性质和粘接结构断裂之间的关系,本文分别采用脆性和延展性两种类型胶黏剂,对其粘接的对接试件进行了单轴拉伸、剪切实验,以及其粘接的双臂梁试件进行了断裂实验.3种类型的内聚力模型(抛物线型、双线型和三线型)分别模拟了以上粘接结构的断裂过程,并与实验结果进行对比.结果发现:双线型的内聚力模型适用计算脆性胶黏剂的拉伸与剪切的断裂过程;指数型内聚力模型较适合计算延展性胶黏剂的拉伸和剪切的断裂过程,临界应力、断裂能和模型的形状参数是分析拉伸和剪切的重要参数;双臂梁试件的断裂过程模拟结果发现,断裂曲线与胶黏剂性质有关,内聚力模型形状参数也有影响.通过实验与计算结果分析,双线型内聚力模型更适合脆性胶黏剂粘接的双臂梁断裂计算,而三线型更适合计算延展性胶黏剂粘接的双臂梁断裂过程,此研究结果对胶黏剂的使用和粘接结构的断裂分析有很重要意义.     

Thermal effects on adhesively bonded composite repair of cracked aluminum panels

This study introduces the two-dimensional finite element analysis involving three layer technique to investigate the adhesively bonded composite repair of cracked metallic structure under thermo-mechanical loading. The thermal loading involves, in this study, the temperature drop such as seen during the bonding process. Three patch materials having different stiffnesses and coefficients of thermal expansion are investigated to analyze the thermal effects on the damage tolerance of the crack in the repaired structure and of the debond in the adhesive bondline. For the single sided repair, the patch material having the maximum mismatch in the coefficient of thermal expansion with that of the cracked aluminum plate provides the better damage tolerance capability for both the crack in the panel and the debond in the adhesive. On the other hand, for double sided repair, the patch material having the minimal mismatch in the coefficient of thermal expansion with that of the cracked plate provides the better damage tolerance capability.     

复合材料胶接结构有限元分析方法研究进展

胶接结构的强度分析方法可以分为解析法和数值法两类,数值法主要是有限元方法.本文综述了复合材料胶接结构的有限元分析方法,按照胶接结构有限元模型建立的物理机理,将胶接结构力学分析模型分为基于有限元应力分析模型、基于断裂力学模型和基于损伤力学模型3类.详细介绍了这3类模型中的主要有限元建模分析方法:三维应力分析方法、虚拟裂纹闭合技术方法和内聚力模型方法,介绍了每种方法的基本思想、适用范围、优缺点、改进和扩展、有限元建模的实施步骤,以及有限元分析中应用该方法所取得的成果.第五部分从适用范围、应力奇异和破坏判据3个方面对这几种分析模型进行了对比分析.最后,对该领域发展趋势进行了展望.      

Stress analyses of a smart composite pipe joint integrated with piezoelectric composite layers under torsion loading

In order to improve the joint failure strength, an adhesively bonded smart composite pipe joint system has been developed by integrating electromechanical coupling piezoelectric layers with the connection coupler. It has been validated that the integrated piezoelectric ceramic layers can smartly reduce stress concentration in the adhesive layer bond-line under bending or axial tension loads. In this study, piezoelectric particle/fiber reinforced polymer composite was utilized to construct adhesively bonded smart composite pipe joint systems, in order to overcome the brittle characteristic of the piezoelectric ceramic layers and to facilitate joint construction. Since torsion is one of the dominating loading conditions in practice, the behavior of the newly developed smart pipe joint system subjected to torsion loading was investigated in-detail to evaluate the effect of the integrated piezoelectric reinforced polymer composite layer on the joint performance. Firstly, based on the first-order shear deformation theory, the fundamental equations with relevant boundary and continuity conditions were developed to theoretically model the smart pipe joint system subjected to torsion loading. Further, the analytical solutions for the mid-plane displacements and the shear and peel stresses in the adhesive layer were obtained by using the Levy solution and the state-space method. Finally, some numerical examples were presented to evaluate the detailed effect of the stacking sequence and thickness of the integrated composite piezoelectric layers in the connection coupler on reducing the stress concentration in the adhesive layer; the effect of the applied electric fields on shear and peel stresses in the adhesive layer was also illustrated.     

周期激励下单搭接接头强度与振动特性研究

主要研究汽车轻量化粘接结构在周期性振动载荷激励下强度与振动属性的改变。首先,利用实验手段,研究了振动载荷对单搭接接头疲劳特性的影响,分析了疲劳后接头的强度及模态频率的变化;其次,通过仿真分析方法,建立了基于经典双线性内聚力模型(Cohesive Zone Model)的单搭接接头静态及动态仿真模型,对胶接接头的模态频率、振型及加载开裂过程中胶层单元失效扩展进行模拟,与此同时,探讨了疲劳载荷对胶层内聚力模型的弱化效应。最后,利用SEM电镜分析手段,从微观上分析了粘接接头疲劳损伤及断裂机理。     

Quasi-static tensile deformation and fracture behavior of a highly particle-filled composite using digital image correlation method

Polymer bonded explosives (PBXs) are highly particle-filled composite materials. This paper experimentally studies the tensile deformation and fracture behavior of a PBX simulation by using the semi-circular bending (SCB) test. The deformation and fracture process of a pre-notched SCB sample with a random speckle pattern is recorded by a charge coupled device camera. The displacement and strain fields on the observed surface during the loading process are obtained by using the digital image correlation method. The crack opening displacement is calculated from the displacement fields, the initiation and propagation of the crack are analyzed. In addition, the damage evolution and fracture mechanisms of the SCB sample are analyzed according to the strain fields and the correlation coefficient fields at different loading steps.     

Development of a smart composite pipe joint integrated with piezoelectric layers under tensile loading

To actively reduce the stress concentration effect in adhesive layers, a novel smart adhesively bonded composite pipe joint system was developed by integrating piezoelectric layers as sensor/actuator in the connection coupler. In the presently developed smart pipe joint system, the mechanical loading induced structural deformation can be detected and monitored by integrated sensing piezoelectric layers, and then the signal is fed back to the integrated actuating piezoelectric layers to adaptively produce additional forces and moments so as to decrease the maximum peel and shear stresses in the adhesive layer. In order to theoretically predict the efficiency of the developed smart pipe joint system, an electro-mechanical theoretical analytical model was established to investigate the characteristics of the joint system under end tension load in terms of first-order shear deformation theory. Simultaneously, the state-space method was utilized to deduce the final analytical solutions, including the peel and shear stress distributions in the adhesive layer. Finally, some detailed numerical results were obtained to demonstrate the optimal design method of such smart pipe joint system and further validate the integrity of this joint system.     

Design and analysis of a smart composite pipe joint system integrated with piezoelectric layers under bending

Incorporating with the high electro-mechanical coupling performance of piezoelectric materials, design and analysis of an adhesively bonded smart composite pipe joint system were conducted. In this joint system, piezoelectric layers were integrated into the joint coupler in order to reduce stress concentration in the joint adhesive layer. To theoretically verify the composite action and efficiency of the integrated piezoelectric layers, an electro-mechanical model based on the first-order shear deformation theory was established. This model was able to clarify the energetic characteristics of the proposed joint system on the improvement in the joint strength, which was under the action of a bending moment at the joint ends. The state-space method was utilized to obtain the final analytical solutions, including the peel and shear stress distributions in the adhesive layer. Finally, some numerical examples were calculated to evaluate the effect of the detailed stacking sequence and size of the integrated piezoelectric layers on reducing the stress concentration in the adhesive layer as well as the applied electric fields. These numerical results validated the integrity of the developed adhesively bonded smart composite pipe joint system.     

Nondestructive evaluation of model adhesive joints by PVDF piezoelectric film sensors

Metallized poly(vinylidene fluoride) (PVDF) films can be etched into nondestructive evaluation (NDE) sensor devices. Since these sensors are relatively inexpensive, thin and lightweight, they can be attached permanently to adhesively bonded joints, laminated composites, and other structures to measure structural integrity. The present study has addressed techniques to design, attach, and utilize such sensors for adhesive joint and laminated composite applications. PVDF sensors have been successfully used as NDE transducers in pulse-echo, through-transmission, and acousto-ultrasonic techniques to monitor curing, and to detect porosity and crack propagation in different model joint geometries. Feasibility of several applications has been demonstrated, although several problems remain. The potential of using these techniques for practical bonded structures is also suggested.     

Energy release rate and phase angle of delamination in sandwich beams and symmetric adhesively bonded joints

Delamination in sandwich structures along the interface between the face sheet and the core, or along the adherend/adhesive interface in adhesively bonded joints, is one of the most common failure modes of this type of tri-layer structure. This delamination is usually modeled as an interface crack problem, for which the energy release rate and phase angle can be calculated using interface fracture mechanics solutions. Existing interface fracture mechanics solutions, however, ignore the effect of transverse shear deformation, which can be significant for short crack. In an effort to overcome this shortcoming, this study presents new analytical solutions for the energy release rate and for the phase angle of the interface crack in sandwich structures or adhesively bonded joints. Since the new solutions incorporate relative rotation at the tip of the delamination, transverse shear effects are taken into account in this study. Typical delaminated sandwich and adhesively bonded joint specimens are analyzed by using the new solutions, as well as by the existing solutions. The energy release rate predicted by the present model agrees very well with that predicted by FEA, and furthermore it is considerably more accurate relative to existing models. As the existing model neglects the transverse shear force, it underestimates the total energy release rate. A stress field analysis is also conducted in this study in order to clarify some misunderstandings in the literature on the determination of the phase angle of adhesively bonded joints using an interface stress-based method.     

Numerical simulation of debonding of adhesively bonded joint

This paper describes a numerical method to simulate the debonding of adhesively bonded joints. Assuming that the adhesive thickness and the adhesive Young’s modulus are small with respect to the characteristic length of the joint and to the Young’s modulus of the adherents, a simplified model is derived in the case of large displacements using the asymptotic expansion technique. Then, the problem of the crack growth is stated, in the case of a stable growth, as the search of the local minima of the total energy of the joint, sum of the mechanical energy and the Griffith’s fracture energy. This is made using the Newton’s method. To this end, the expressions of the first and second derivatives of the mechanical energy with respect to a crack front displacement are derived analytically. Finally, numerical examples are presented, highlighting the unstable character of the crack growth at initiation.     

Analytical solutions for adhesive composite joints considering large deflection and transverse shear deformation in adherends

This paper presents a novel formulation and analytical solutions for adhesively bonded composite single lap joints by taking into account the transverse shear deformation and large deflection in adherends. On the basis of geometrically nonlinear analysis for infinitesimal elements of adherends and adhesive, the equilibrium equations of adherends are formulated. By using the Timoshenko beam theory, the governing differential equations are expressed in terms of the adherend displacements and then analytically solved for the force boundary conditions prescribed at both overlap ends. The obtained solutions are applied to single lap joints, whose adherends can be isotropic adherends or composite laminates with symmetrical lay-ups. A new formula for adhesive peel stress is obtained, and it can accurately predict peel stress in the bondline. The closed-form analytical solutions are then simplified for the purpose of practical applications, and a new simple expression for the edge moment factor is developed. The numerical results predicted by the present full and simplified solutions are compared with those calculated by geometrically nonlinear finite element analysis using MSC/NASTRAN. The agreement noted validates the present novel formulation and solutions for adhesively bonded composite joints. The simplified shear and peel stresses at the overlap ends are used to derive energy release rates. The present predictions for the failure load of single lap joints are compared with those available in the literature.     

Finite Fracture Mechanics model for mixed mode fracture in adhesive joints

Up to now the failure load assessment of bonded joints is still not fully understood. This work provides a new approach for assessing the crack initiation load of bonded joints. A failure model for single lap joints is proposed that is based on Finite Fracture Mechanics. Only two basic fracture parameters are required: the tensile strength and the fracture toughness of the adhesive. A coupled stress and energy criterion proposed in 2002 by Leguillon is used to model crack initiation in the adhesive layer. The theory of this criterion is outlined in detail, its relationship to other failure criteria is discussed and an overview of applications found in literature is given. An enhanced weak interface model that predicts a linear variation of the shear stresses in the adhesive layer is utilized to model the single lap joint. To compare joint designs and to reveal the limitations of the given approach a dimensionless brittleness number for mixed-mode loading is proposed. Along with a detailed discussion of the results for exemplary joint designs a comparison to experimental results from literature is performed. The two necessary fracture parameters are each taken from standard test results published in literature. A good agreement of the failure load predictions with the experimental results is observed. A remarkable outcome is that the presented failure model renders the adhesive thickness effect correctly. The paper concludes with a discussion of the limitations of the approach and the effect of material parameters.     

Progressive damage modelling of bonded composite repairs

Presented is a three-dimensional progressive damage model that can assess the mechanical behaviour of bonded composite repairs of cracked metallic plates. The model is able to assess the stress intensity factor (SIF) at the crack tip, patch debonding and damage accumulation in the composite patch as functions of the applied load. Considered are the stress analysis, failure analysis and material property degradation. Stress analysis is performed using a three-dimensional detailed parametric finite element (FE) model developed using the ANSYS FE code. Failure analysis is performed using a set of stress-based polynomial failure criteria. Material property degradation of the failed material (patch and adhesive) is performed using appropriate degradation rules. The three model components have been programmed in the ANSYS FE code creating a user-friendly parametric macro-routine, which can be easily applied to bonded repairs of different materials and configuration.     

CFRP-混凝土界面粘结的疲劳性能试验研究

外贴FRP是重要的混凝土结构加固技术,但目前对外贴FRP加固混凝土结构的疲劳性能研究尚不充分,尤其对FRP-混凝土粘结界面的疲劳退化规律和破坏模式的研究更为缺乏。本文采用双面剪切试件,通过2个静载试件和4个疲劳试件的试验研究,考察了粘结长度和胶层厚度等因素对FRP-混凝土界面粘结疲劳性能的影响。通过分析沿粘结长度的FRP应变分布在疲劳循环过程中和疲劳后静载过程中的变化情况,讨论了不同粘结长度和粘结胶层厚度条件下的粘结界面疲劳退化规律和疲劳后静载性能。试验结果表明:胶层树脂-混凝土粘结界面是发生疲劳剥离破坏的薄弱环节;胶层厚度增大时,由于疲劳引起的界面损伤累积发展显著减小,疲劳后静载中胶层厚度较大试件的粘结承载力也更大;粘结长度增大时,界面粘结呈现更为明显的损伤退化,但由于试验粘结长度小于有效粘结长度,疲劳后的静粘结承载力仍更大。     

The fracture behaviour of adhesively-bonded composite joints: Effects of rate of test and mode of loading

The present paper discusses the results of an investigation into the effects of test rate and the mode of loading on the fracture energy, G_c, of adhesively-bonded fibre-composite joints. Various carbon-fibre reinforced-polymer (CFRP) matrix composite substrates have been bonded using two different types of automotive structural epoxy-adhesives. They have been tested via loading the bonded joints in mode I (tensile), mode II (in-plane shear) and mixed-mode I/II from slow rates (i.e., of about 10^?5 m/s) up to relatively high rates of test of about 15 m/s. The high-rate tests were photographed using a high-speed digital video camera to record the deformation of the joint and the fracture behaviour. An analysis strategy has been developed for the various modes of loading (i) to account for the observed fracture behaviour, (ii) to circumvent the problems posed by oscillations in the load traces due to the presence of dynamic effects in the faster tests, and (iii) to account for the kinetic energy associated with the moving specimen arms in the faster tests. Based on the analysis strategy developed, the effect of the test rate on the fracture energy, G_c, for the different loading modes for the joints has been ascertained. Furthermore, various different fracture paths were observed in the tests. They were either cohesive, in the adhesive layer, or interlaminar in the composite substrates. The exact fracture path observed was a function of (i) the type of composite substrate, (ii) the type of adhesive, and (iii) the mode of loading employed. However, the nature of the fracture path was found to be quite insensitive to the test rate. Essentially, it was found that joints subjected to mixed-mode I/II loading were more likely to exhibit an interlaminar fracture path in the composite substrates than when loaded in either pure modes I or II. The propensity for a given joint to exhibit such a fracture path via delamination of the composite substrate has been explained by calculating the transverse tensile stresses induced in the loaded composite arms, and comparing this value to the measured transverse tensile strength of the composite. Following this approach, the underlying reasons for the observed fracture path were identified and could be predicted. Also, the proposed scheme provides a route to design against delamination failure occurring in adhesively-bonded fibre-composite test specimens.