Mixed-mode crack initiation at a v-notch in presence of an adhesive joint

The failure criterion for v-notched specimens developed for mixed-mode loadings by Yosibash et al. [Yosibash, Z., Priel, E., Leguillon, D., 2006. A failure criterion for brittle elastic materials under mixed mode loading. Int. J. Fract. 141(1), 289–310.] is generalised in order to consider the influence of the shear stresses and the mode-dependence of the toughness. This is demonstrated to be important in some cases with adhesive joints under complex loadings for instance. The original criterion assumes that an abrupt onset of a crack with a finite extension occurs when two conditions are fulfilled simultaneously: first the normal traction all along the presupposed crack path reaches a critical value, and second the onset is energetically allowed. The influence of the shear stresses is now considered through a mixed law involving critical shear and tensile stresses as well as the mode-dependent toughness introducing a new equivalent SIF. This extended criterion is applied to the simulation of an Arcan test on v-notched compact tension shear (CTS) specimens made of two parts bonded together along the geometric plane of symmetry of the specimen. The competition between two modes of failure is studied: crack initiation along the weak joint which may constitute a privileged fracture surface and initiation in the homogeneous material at an optimum angle that minimizes the critical load to failure.     

On flaw size and distribution in lap joints

By using adhesive as the bonding substance between metals or polymeric materials, simple structural joints can be made to bear relatively high loads. Applications have increasingly been made in substituting adhesive joints for conventional mechanical fastenings, especially in the aircraft and aerospace industries where weight is a predominant factor. In order to design a most effective adhesive-bonded joint, an understanding of the stress distribution along the joint is as important as the physical properties of the bonding agent. One of the most common and widely used adhesive joints is the single lap joint.Recent investigations using various analytical models have revealed that the cause of failure in an idealized ‘defect free’ lap joint is primarily due to the localized effect of high stress concentration at the lap ends. With the presence of flaw like defects in the adhesive layer, the load transfer from adherend to adhesive is expected to be different from the idealized joint. In addition, localized stress concentrations induced by irregular adhesive defects that may be found in practical engineering applications can further reduce fracture strength of such an imperfect joint.This paper is intended to describe an investigation into the effect of internal adhesive flaw size and distribution on the fracture behaviour of adhesive-bonded lap joints. The finite element method is used to gain a quantitative understanding of the localized shear stress distributions due to the presence of the internal flaws along the bonding layer. It is observed that the reduction in the fracture strength is relatively small when a flaw is located in the central portion of the bonding length. However, a flaw located near the lap ends of the adhesive joint can cause marked reduction in the fracture strength, due to its interaction with the high stress concentration at the lap ends.     

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。     

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.     

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.     

Constant amplitude and variable load history fatigue test results and predictions for cruciform and lap welds

Cruciform and lap welds were fatigue tested under constant amplitude axial load and SAE Bracket spectrum load conditions. For the cruciform joints, fatigue cracks generally initiate at the root but may initiate at the toe if higher bending stresses are induced by joint distortion. For lap welds, the stress ratio ($\text{R}$) and weld shape are the major factors influencing the fatigue crack initiation site.The fatigue test results were compared with predictions made using an analytical model developed by the authors, and good agreement between experiment and theory was observed. The model for the predictions assumes that the fatigue crack initiation period, which is the number of cycles for the initiation of a fatigue crack and its early growth and coalescence into a dominant fatigue crack, is the main portion of the total fatigue life at long lives.     

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.     

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.     

平面编织复合材料胶螺混合连接接头拉伸性能分析

对平面编织复合材料胶螺（单排螺钉）混合连接结构拉伸性能进行了试验研究,分析了螺钉直径为4mm和6mm两种情况下连接结构的破坏形式。基于ANSYS平台建立了胶螺混合连接三维损伤扩展模型,其中融入了非线性接触问题,数值计算的结果与试验结果吻合良好。研究发现,机械连接可以通过分担部分载荷而起着加强胶接连接的作用;如果机械连接工艺稳定的话,应该有螺钉直径越大,其加强效果越明显的规律;对于胶接与多钉混合连接复合材料结构的拉伸性能分析和计算确实存在很大困难,应该谨慎使用。研究结果与分析方法可以为今后的复合材料胶螺混合连接接头的设计提供一定的依据与技术支撑。     

EFFECT OF Z-PINS＇ DIAMETER, SPACING AND OVERLAP LENGTH ON CONNECTING PERFORMANCE OF CMC SINGLE LAP JOINT

The effect of through-thickness reinforcement by composite pins （Z-pins） on the static tensile strength and failure mechanisms of the joints made from ceramic matrix composite （CMC） is investigated. Overlap length of the single lap joint is 15 mm, 20 mm, 23 mm, 37 mm, and 60 mm, respectively. The experimental results indicate that the final failure modes of the joints can be divided into two groups, （a） the bond-line stops debonding until crack encounters Z-pins; and then the adherends break at the location of Z-pins, when overlap length is more than 20 mm; （b） the bond-line detaches entirely and Z-pins are drawn from adherends, when overlap length is equal to 15 mm. A simple efficient computational approach is presented for analyzing the benefit of through-thickness pins for restricting failure in the single lap joints. Here, the mechanics problem is simplified by representing the effect of the pins by tractions acting on the fracture surfaces of the cracked bond-line. The tractions are prescribed as functions of the crack displacement, which are available in simple forms that summarize the complex deformations to a reasonable accuracy. The resulting model can be used to track the evolution of complete failure mechanisms, for example, bond-line initial delamination and ultimate failure associated with Z-pin pullout, ultimate failure of the adherends. The paper simulates connecting performance of the single lap joints with different Z-pins＇ diameter, spacing and overlap length; the numerical results agree with the experimental results; the numerical results indicate enlarging diameter and decreasing spacing of Z-pins are in favor of improving the connecting performance of the joints. By numerical analysis method, the critical overlap length that lies between two final failure modes is between 18 mm and 19 mm, when Z-pins＇ diameter and spacing are 0.4 mm, 5 mm, respectively.     

EFFECT OF Z-PINS'' DIAMETER, SPACING AND OVERLAP LENGTH ON CONNECTING PERFORMANCE OF CMC SINGLE LAP JOINT

The effect of through-thickness reinforcement by composite pins (Z-pins) on the static tensile strength and failure mechanisms of the joints made from ceramic matrix composite (CMC) is investigated.Overlap length of the single lap joint is 15 mm,20 mm,23 mm,37 mm,and 60 mm,respectively.The experimcntal results indicate that the final failure modes of the joints can be divided into twó groups,(a) the bond-line stops debonding until crack encounters Z-pins;and then the adherends break at the location of Z-pins,when overlap length is more than 20 mm;(b) the bond-line detaches entirely and Z-pins are drawn from adherends,when overlap length is equal to 15 mm.A simple efficient computational approach is presented for analyzing the benefit of through-thickness pins for restricting failure in the single lap joints.Here,the mechanics problem is simplified by representing the effect of the pins by tractions acting on the fracture surfaces of the cracked bond-line.The tractions are prescribed as functions of the crack displacement,which are available in simple forms that summarize the complex deformations to a reasonable accuracy.The resulting model can be used to track the evolution of complete failure mechanisms,for example,bond-line initial delamination and ultimate failure associated with Z-pin pullout,ultimate failure of the adherends.The paper simulates connecting performance of the single lap joints with different Z-pins' diameter,spacing and overlap length;the numerical results agree with the experimental results;the numerical results indicate enlarging diameter and decreasing spacing of Z-pins are in favor of improving the connecting performance of the joints.By numerical analysis method,the critical overlap length that lies between two final failure modes is between 18 mm and 19 mm,when Z-pins' diameter and spacing are 0.4 ram,5 ram,respectively.     

Process zone in the Single Cantilever Beam under transverse loading - Part II: Experimental

This paper describes an experimental arrangement to evaluate stress/strain fields in the process zone of asymmetric adhesively bonded joints. A transparent polycarbonate flexible beam was bonded to an aluminium alloy rigid block with an epoxy adhesive in a Single Cantilever Beam (SCB) configuration. The flexible adherend was loaded in the direction parallel to the initial crack front at constant rate. To monitor strains induced by bending and shear along the beam, electric strain gauges were attached to the upper surface of the flexible adherend. Thus strain distribution was measured above the bonded surface, which could be used to monitor crack propagation and investigate stress redistribution in the process zone. A Timoshenko beam lying on a Pasternak elastic foundation model was used for the analysis of experimental findings. Subsequently, the Digital Image Correlation technique was used to measure the flexible substrate in-plane displacement field in the vicinity of the crack front and to assess the specimen kinematics. We found that strain gauge instrumentation of the fracture mechanics specimen was a very sensitive technique for experimental analysis of crack propagation under complex loading, offering fine investigation of stress distribution in the cohesive zone.     

Nonlinear interface shear fracture of end notched flexure specimens

The nonlinear analytical solutions of an end notched flexure adhesive joint or fracture test specimen with identical or dissimilar adherends are investigated. In the current study, a cohesive zone model (with arbitrary nonlinear cohesive laws) based analytical solution is obtained for the interface shear fracture of an end notched flexure (ENF) specimen with sufficiently long bond length. It is found that the scatter and inconsistency in calculating Mode II toughness may be significantly reduced by this model. The present work indicates that the Mode II toughness G_IIc under pure shear cracking condition is indeed very weakly dependent on the initial crack length. And this conclusion is well supported by the experimental results found in the literature. The parametric studies show that the interface shear strength is the most dominant parameter on the critical load. It is also interesting to note that with very short initial crack length and identical interface shear strength, higher Mode II toughness indeed cannot increase the critical load. Unlike the high insensitivity of critical load to the detailed shape of the cohesive law for Mode I peel fracture, the shape of the cohesive law becomes relatively important for the critical load of joints under pure Mode II fracture conditions, especially for joints with short initial crack length. The current study may help researchers deepen the understanding of interface shear fracture and clarify some previous concepts on this fracture mode.     

Stress-function variational method for interfacial stress analysis of adhesively bonded joints

High interfacial stresses at the free edges of adherends are responsible for the debonding failure of adhesively bonded joints (ABJs). In this paper, a general stress-function variational method is formulated to determinate the interfacial shear and normal (peeling) stresses in ABJs in high accuracy. By extending authors’ prior work in stress analysis of bonded joints (Wu and Jenson, 2011), all the planar stress components in the adherends and adhesive layer of an ABJ are expressed in terms of four unknown interfacial stress functions, which are introduced at the upper and lower surfaces of the adhesive layer. A set of governing ordinary differential equations (ODEs) of the four interfacial stress functions is obtained via minimizing the complimentary strain energy of the ABJ, which is further solved by using eigenfunctions. The obtained semi-analytic stress field can satisfy all the traction boundary conditions (BCs) of the ABJ, especially the stress continuity across the bonding lines and the shear-free condition at the ends of adherends and adhesive layer. As an example, the stress field in an adhesively single-sided strap joint is determined by the present method, whose numerical accuracy and reliability are validated by finite element method (FEM) and compared to existing models in the literature. Parameter studies are performed to examine the dependencies of the interfacial stresses of the exemplified ABJ upon the geometries, moduli and temperature change of the adherends and adhesive layer, respectively. The present method is applicable for scaling analysis of joint strength, optimal design of ABJs, etc.     

Strength scaling of adhesive joints in polymer–matrix composites

The fracture of adhesive joints between two glass-fibre laminates was studied by testing double cantilever beam test specimens loaded by uneven bending moments. A large-scale fracture process zone, consisting of a crack tip and a fibre bridging zone, developed. The mixed mode fracture resistance increased with increasing crack length, eventually reaching a steady-state level (R-curve behaviour). The steady-state fracture resistance level increased with increasing amount of tangential crack opening displacement. Cohesive laws, obtained from fracture resistance data, were used for prediction the load carrying capacity of 2-m long “medium size” adhesive joint specimens subjected to four point flexure. Medium size specimens were manufactured and tested. A good agreement was found between the predicted and measured strength values of the medium-size specimens. Thus, the scaling from small specimens to medium-size specimens was successfully achieved.     

含缺口试件疲劳全寿命预测一种建议的方法

传统的研究含缺口构件的疲劳的方法是将疲劳启裂和疲劳裂纹扩展两个过程完全独立起来,用不同的方法来模拟,相互间并没有定量的关系。本文是基于最新发展的多轴疲劳损伤理论,建立了一种适用于各种载荷条件下的疲劳启裂和裂纹扩展的普适方法。根据从弹塑性分析中得到的应力应变,确定疲劳损伤模型,建立能够预测疲劳启裂、裂纹扩展速率和扩展方向的新方法。整个模拟可以分为两步:弹-塑性应力分析得到材料的应力应变分布;再运用一个通用的疲劳准则预测疲劳裂纹启裂和裂纹扩展。通过对1070号钢含缺口试件的疲劳全寿命预测,得到了与实验非常吻合的模拟结果。     

Pressure-sensitive ductile layers – I. Modeling the growth of extensive damage

Polymeric adhesives sandwiched between two elastic substrates are commonly found in multi-layers and IC packages. The non-elastic deformation and flow stress of such adhesive joints are highly pressure-sensitive. In this work, we study the effects of pressure-sensitivity, α, and plastic dilatancy, β, on void growth and coalescence ahead of a crack in ductile adhesive joints. To this end, a single layer of discrete voids is placed ahead of the crack in a pressure-sensitive dilatant adhesive sandwiched between two elastic substrates. The adhesive joint is subjected to small-scale yielding conditions. Using an associated flow rule (α = β), we show that pressure-sensitivity not only intensifies damage levels but also increases its spatial extent several fold. The damage level as well as its spatial extent is found to be even greater when a non-associated flow rule (β < α) is deployed. A reduction in the damage process zone’s thickness further increases the voiding activity in the adhesive, thereby resulting in brittle-like failure. This work also examines the fracture toughness trends using a material failure criterion for crack growth.     

Balanced and unbalanced patching of cracked lap joints using weighted adhesive plate element

First order shear deformation theory is applied to analyze the behavior of one-side (unbalanced) and two-side (balanced) patched lap joints containing initial through cracks. The joints are made of adherends bonded together by adhesives. An adhesive interface plate element is introduced; it consists of an adhesive layer weighted by influence of the adherend. The thin adhesive layer is assumed to behave elastically and modelled as a simple tension-shear spring. The mathematical model contains layers of adherend and weighted adhesive layer.Finite elements are employed to model the adherend with an 8-node isoparametric plate element and interface layer with a 16-node plate element. Numerical results are obtained for one-side and two-side patches the width of which could be narrower or wider than the crack length. The former leads to bulging and possible peeling while the latter provides better bonding. Stresses and crack-tip stress intensity factors are calculated for different patch thickness. Effectiveness of the weighted adhesive layer model is exhibited by comparing the present results with those found in previous work where the adhesive is modelled as an individual layer.     

Interfacial mixed-mode fracture of adhesive bonds undergoing large deformation

Interfacial fracture of adhesive bonds undergoing large-scale yielding is studied using a combined experimental/finite-element approach. The full range of in-plane mode mixity is produced over bond thickness ranging from 30 to 500 μm using the scarf and the ENF joint geometries. Novel techniques for introducing pre-cracks and surface decoration, together with in situ observations, facilitate accurate determination of the bond-average and the local shear strains at the crack tip during the onset as well as the rest of the crack propagation event. The crack generally grew along one of the two interfaces of the bond, although the failure was always fully cohesive. The local shear strain at the crack tip is independent of the bond thickness, and, under quasi-static conditions, it remains constant throughout the growth, which make it a viable fracture parameter. This quantity strongly depends on the mode mixity, the sign of the phase angle (i.e., shearing direction) and the crack speed, however.A finite-element analysis is used to obtain the crack tip deformation field for an interface crack in adhesively bonded scarf and ENF joints. Large-strain and quasi-static conditions are assumed. A distinct material model in the fracture process zone that allows for volume change in the post-yield regime is incorporated into the analysis. The local deformation is characterized by a pair of bond-normal and tangential displacements corresponding to the nodal points adjacent to the crack tip. The critical values of these quantities are obtained when the FEM bond-average shear strain at the crack tip becomes equal to its experimental counterpart. The so defined critical local displacements, after an appropriate normalization, seem to conform to a single-valued, linear type interrelationship over the entire range of mode mixity. The fact that this relationship is independent of the bond thickness, and furthermore it encompasses both cases of positive and negative phase angles, makes it a viable candidate for characterizing mixed-mode interfacial fracture under large-deformation conditions.