Damage modelling of adhesively bonded joints

A cohesive zone model (CZM) has been used in conjunction with both elastic and elasto– plastic continuum behaviour to predict the response of a mixed mode flexure and three different lap shear joints, all manufactured with the same adhesive. It was found that, for a specific dissipated CZM energy (Γ₀) there was a range of CZM tripping tractions (σ_u) that gave a fairly constant failure load. A value of σ_u below this range gave rise to global damage throughout the bonded region before any crack propagation initiated. A value above this range gave rise to a discontinuous process zone, which resulted in failure loads that were strongly dependent on σ_u. A discontinuous process zone gives rise to mesh dependent results. The CZM parameters used in the predictions were determined from the experimental fracture mechanics specimen test data. When damage initiated, a deviation from the linear load–displacement curve was observed. The value for σ _uwas determined by identifying the magnitude that gave rise to the experimentally observed deviation. The CZM energy (Γ ₀) was then obtained by correlating the simulated load-crack length response with corresponding experimental data. The R-curve behaviour seen with increasing crack length was successfully simulated when adhesive plasticity was included in the constitutive model of the adhesive layer. This was also seen to enhance the prediction of the lap shear specimens. Excellent correlation was found between the experimental and predicted joint strengths.     

双斜接修补复合材料层合板的拉伸行为及影响因素双斜接修补复合材料层合板的拉伸行为及影响因素

基于试验和有限元数值方法对双斜接修补碳纤维增强聚合物（CFRP）复合材料层合板在拉伸载荷作用下的力学行为开展研究。通过试验分析了两种不同厚度的双斜接修补复合材料结构的承载能力和失效形式。结果表明,对于不同厚度的双斜接修补复合材料结构,失效强度接近,主要破坏形式均以胶层内聚破坏为主,伴随局部的90°基体开裂。利用连续介质损伤力学模型和内聚力模型分别对复合材料和胶层失效进行描述,通过数值方法开展双斜接修补结构的强度预测和损伤演化分析。数值结果与试验吻合较好,并且指出复合材料基体开裂起始早于胶层失效。通过有限元模型讨论了附加层、双斜接内部尖端所处位置和修补胶层参数对修补性能的影响。      

Fatigue crack growth acceleration due to intermittent overstressing in adhesively bonded CFRP joints

Double cantilever beam joints were used to investigate cohesive and interlaminar crack growth in bonded composite joints under constant and variable amplitude (VA) loading. Numerical crack growth integration was used to predict the VA fatigue life using constant amplitude data. This underestimated the fatigue crack growth rate for interlaminar cracks, indicating crack growth acceleration due to load interactions. This was also the case for cohesive cracks subjected to a moderate initial strain energy release rate (G_max). An unstable crack growth regime was also identified for the case of high initial G_max cohesive crack propagation. This behaviour is attributed to the development of a damage zone ahead of the crack tip.     

Characterisation of moisture-dependent cohesive zone properties for adhesively bonded joints

Structural adhesives are being widely used in the aerospace and automobile industries. However, in many applications, aggressive environments damage the adhesive systems and degrade the structural performance of bonded members. Cohesive zone models are often employed in the numerical analysis of adhesively bonded structural joints. To accurately model these bonded joints, the characterisation of the cohesive zone properties for different environmental conditions is important. In this regard, an experimental-numerical approach was developed to characterise the environment-dependent cohesive zone properties based on a miniature cantilever peel test. As moisture is a commonly encountered aggressive environment, the current methodology was implemented to characterise the moisture-dependent cohesive zone properties for an Al 2024-T3 and FM73 system.     

基于粘聚区模型的含填充区复合材料接头失效数值模拟

建立了Ⅰ型与Ⅱ型失效模式耦合的粘聚单元本构模型, 并通过模拟双悬臂梁实验进行了验证。将粘聚单元插入填充区任何2 个实体单元之间, 预测填充区的随机裂纹, 模拟了接头在拉伸载荷下的失效。计算了复合材料基体、界面胶膜、填充物3 者不同强度、填充区半径、填充物刚度等多种情况下接头的拉伸失效。计算结果表明: 复合材料基体、界面胶膜、填充物3 者的强度显著影响接头的承载能力与失效模式; 随着填充区半径增大, 结构承载能力也随之提高。试验结果验证了模拟结果。      

Modelling the tensile fracture behaviour of CFRP scarf repairs

An experimental and numerical study concerning the tensile behaviour of adhesively-bonded carbon–epoxy scarf repairs is presented, using scarf angles ranging from 2° to 45°. A mixed-mode cohesive damage model adequate for ductile adhesives was used to simulate the adhesive layer. The cohesive laws of the adhesive layer, composite interlaminar and composite intralaminar (in the transverse and fibre directions) in pure modes I and II, necessary to simulate numerically the experimental failure paths, were previously characterized using an inverse method. Validation of this methodology was accomplished in terms of repair initial stiffness, maximum load and the corresponding displacement, as well as the failure mode. A good agreement between the numerical predictions and the experiments showed that the proposed methodology can be successfully applied to joints or repairs bonded with ductile adhesives.     

A two-dimensional in situ fatigue cohesive zone model for crack propagation in composites under cyclic loading

In this paper a two-dimensional fatigue cohesive zone model (CZM) for crack propagation in composites under cyclic loading has been formulated and validated through successful predictions of fatigue crack growth under pure and mixed mode conditions for several different composites. The proposed fatigue CZM assumes simple power-law functions for fatigue damage accumulation of which the damage parameters can be calibrated from simple fatigue tests under pure mode I and mode II conditions. The model relies solely on the in situ cohesive responses for fatigue damage rate calculation, enabling the differentiation of the local elemental load history from the global load history. An effective cycle jump strategy for high-cycle fatigue has also been proposed. It has been demonstrated that once calibrated, the fatigue CZM can predict the Paris laws for the pure modes. Furthermore, it can predict the Paris laws of any mixed-mode conditions without the need of additional empirical parameters. This is of significant practical importance because it leads to greatly reduced experimental needs for mixed mode crack propagation widely observed in composites under cyclic loads.     

交变载荷对CFRP复合材料-铝合金粘接接头剩余强度的影响

为了给碳纤维增强聚合物（CFRP）复合材料粘接结构的安全设计及应用提供参考,针对CFRP复合材料-铝合金对接接头,研究了拉-拉交变载荷作用下的疲劳寿命特性及剩余强度变化规律。设计专用夹具,完成接头的制作及固化,并测试其拉伸、剪切准静态失效强度,在此基础上进行不同载荷水平下的疲劳寿命测试。选取特定载荷水平,测试不同循环次数后的接头剩余强度,并对失效形式进行观察分析。结果表明:CFRP复合材料-铝合金对接接头强度-寿命（S-N）曲线在单对数坐标上符合线性函数规律;随着交变载荷循环周期的增加,接头剩余强度呈先慢后快的下降趋势,而且在较大的载荷水平下,下降幅度更为明显;经历交变载荷循环前、后接头失效形式发生改变,由局部CFRP复合材料表层撕裂转变为局部界面破坏。结合试验测试所获得的初始失效准则,并引入疲劳退化因子,建立内聚力模型对交变载荷作用下的粘接接头强度衰减进行数值模拟,结果表明所建立模型能够有效预测交变载荷作用下的接头剩余强度。      

Durability of metal joints bonded with aluminium powder filled epoxy adhesive

Abstract

Durability of the metal joints bonded with aluminium powder filled epoxy adhesive was investigated by measuring the joint strength by the single lap shear test before and after exposure to distilled water and the hot and humid Arabian Gulf atmosphere. Fractured specimens were examined by photography. The epoxy adhesive retained its strength with as much as 50 wt-% addition of aluminium filler. Moreover, varying the Al filler content in the adhesive did not have a significant effect on adhesive behaviour in either of the two environments studied. Exposure to atmosphere for as long as 6 months did not cause a deterioration of strength for metal joints bonded with aluminium powder filled epoxy. They failed almost completely within the adhesive, similar to the cohesive mode of unexposed specimens. However, a significant strength decrease was observed in adhesive joints after exposure to distilled water for 6 months. The joints failed in more than a single mode. The interior part of the adhesive lap area failed in cohesive mode while an adhesion failure mode was observed near the edges of the adhesive lap area, which is believed to be a result of moisture diffusion through the edges.     

Cohesive zone modelling of interface fracture near flaws in adhesive joints

A cohesive zone model is suggested for modelling of interface fracture near flaws in adhesive joints. A shear-loaded adhesive joint bonded with a planar circular bond region is modelled using both the cohesive zone model and a fracture mechanical model. Results from the models show good agreement of crack propagation on the location and shape of the crack front and on the initial joint strength. Subsequently, the cohesive zone model is used to model interface fracture through a planar adhesive layer containing a periodic array of elliptical flaws. The effects of flaw shape are investigated, as well as the significance of fracture process parameters. The results from simulations of fracture in a bond containing circular flaws show that localization of crack propagation in the vicinity of a flaw has significant effect on the joint strength and crack front shape. The localization effects are highly dependent on the fracture process zone width relative to the flaw dimensions. It is also seen that with increasing fracture process zone width, the strength variation with the flaw shape decreases, however, the strength is effected over a wider range of propagation.     

Fracture load prediction of lead-free solder joints

Continuous and discrete SAC305 solder joints of different lengths were made between copper bars under standard surface mount (SMT) processing conditions, and then fractured under mode-I loading. The load-displacement behavior corresponding to crack initiation and the subsequent toughening before ultimate failure were recorded and used to calculate the critical strain energy release rates. The fracture of the discrete solder joints was then simulated using finite elements with two different failure criteria: one in terms of the critical strain energy release rate at initiation, G_ci, and another based on a cohesive zone model at the crack tip (CZM). Both criteria predicted the fracture loads reasonably well. In addition, the CZM was able to predict accurately the overall load-displacement behavior of the discrete joint specimen. It could also predict the load sharing that occurred between neighboring solder joints as a function of joint pitch and adherend stiffness. This has application in the modeling of the strength of solder joint arrays such as those found in ball grid array packages.     

A semi-analytical solution method for problems of cohesive fracture and some of its applications

Cohesive zone models are extensively used for the failure load estimates for structure elements with cracks. This paper focuses on some features of the models associated with the failure load and size of the cohesive zone predictions. For simplicity, considered is a mode I crack in an infinite plane under symmetrical tensile stresses. A traction–separation law is prescribed in the crack process zone. It is assumed by the problem statement that the crack faces close smoothly. This requirement is satisfied numerically by a formulation of the modified boundary conditions. The critical state of a plate with a cohesive crack is analyzed using singular integral equations. A numerical procedure is proposed to solve the obtained systems of integral equations and inequalities. The presented solution is in agreement with other published results for some limiting cases. Thus, an effective methodology is devised to solve crack mechanics problems within the framework of a cohesive zone model. Using this methodology, some problems are solved to illustrate the (i) influence of shape parameters of traction–separation law on the failure load, (ii) ability to account for contact stress for contacting crack faces, (iii) influence of getting rid of stress finiteness condition in the problem statement.     

Analysis of automotive mixed‐adhesive joints weakened by moist conditions: Experimental characterization and numerical simulation using cohesive zone model

This paper is mostly concerned with an experimental and numerical study to clarify the behaviour and failure in the mono‐adhesive joints and mixed‐adhesive joints under different environmental conditions (dry [E₀], 75.3% relative humidity [E₁], 84.2% relative humidity [E₂], and submerged in tap water [E₃] at 25°C) and different strain rates (1 and 100 mm/min). Experimental investigations are compared with the numerical analysis, which is carried out by bilinear cohesive zone model (CZM). Through this work, degradations of cohesive parameters are calculated by using open‐faced double cantilever beam (DCB) and end notch flexure (ENF) specimens. The experimental data show that the cohesive parameters of Araldite 2015 have negative correlation to moisture content. Although Araldite AV138 parameters experience a decrease in mode I, in mode II, its cohesive parameter increases. First, it is found that the decrease in experimental failure load of mixed‐adhesive joints with regard to the dry condition is recorded as 32.6%, 54%, and 59.1% for E₁, E₂, and E₃ conditions, respectively. Following this further, single lap joint (SLJ) that has non‐uniform moisture content distribution is modelled by engaging specific CZM parameters related to the specific moisture content. The results show a good agreement between experimental and numerical data.     

The effect of environment on the fatigue of bonded composite joints. Part 1: testing and fractography

In this work, the effect that test environment and pre-conditioning had on the fatigue behaviour of CFRP/epoxy lap–strap joints was investigated. It was shown that the fatigue resistance of the lap–strap joints did not vary significantly until the glass transition temperature, T_g, was approached, at which point a considerable reduction in the fatigue threshold load was observed. It was also noted that absorbed moisture resulted in a significant reduction in the T_g of the adhesive. This must be taken into account when selecting an adhesive to operate at elevated temperatures. The locus of failure of the joints was seen to be highly temperature dependent, transferring from primarily in the composite adherend at low temperatures to primarily in the adhesive at elevated temperatures. It was also seen that as the crack propagated along the lap–strap joint, the resolution of the forces at the crack tip tended to drive it into the strap adherend, which could result in complex mixed mode fracture surfaces.     

Evaluating the strengths of thick aluminum-to-aluminum joints with different adhesive lengths and thicknesses

Composite joints are often the weakest elements in composite structures. In this paper, we propose a modified version of the damage zone theory based on the yield strain ratio. We use this framework to predict failure loads for various adhesive joints. Thick aluminum-to-aluminum joint specimens with eight different adhesive lengths and four adhesive thicknesses were manufactured and tested. The strengths of different adhesive lengths could be predicted to within 15.4% using the damage zone ratio method. In addition, the strengths of joints that feature different adhesive thicknesses were predicted to within 16.3% using the damage zone ratio method.     

Modeling of delamination using a discretized cohesive zone and damage formulation

Delamination initiation and growth are analyzed by using a discrete cohesive crack model. The delamination is constrained to grow along a tied interface. The model is derived by postulating the existence of a maximum load surface which limits the adhesive forces in the process zone of the crack. The size of this maximum load surface is made dependent on the amount of dissipated crack opening work, such that the maximum load surface shrinks to zero as a predefined amount of work is consumed. A damage formulation is used to reduce the adhesive forces. Mode I, II and III loading or any combined loading is possible. An analytical solution is obtained for a single mode opening and the implications of this result on the governing equations is discussed. The delamination model is implemented in the finite element code LS-DYNA and simulation results are shown to be in agreement with experimental results.     

基于循环载荷的单搭胶接接头残余强度分析

为研究循环载荷下单搭胶接接头的残余强度及失效机理,以5052铝合金单搭胶接接头为研究对象,先后对其进行静强度测试、疲劳强度测试和残余强度测试,引入威布尔分布对试验数据进行分析,检验其有效性,并采用超声扫描显微镜和扫描电子显微镜对失效胶层进行失效机理分析。结果表明,在疲劳循环载荷作用下,接头刚度基本稳定,而残余强度随着疲劳循环载荷周次的增加,呈现出先增大后减小的变化趋势;疲劳裂纹从接头搭接端部的界面端点处开始萌生,并快速向中间扩展,当疲劳循环达到一定次数时,胶层瞬间断裂,裂纹萌生阶段几乎占据了其全部疲劳寿命,失效后的胶层会出现"凹台"状微观结构。     

Mixed-mode quasi-static failure criteria for adhesively-bonded pultruded GFRP joints

The strain energy release rates of adhesively-bonded pultruded GFRP joints were determined experimentally. The crack propagated in the adherend along paths outside the symmetry plane accompanied by fiber bridging. A new method, designated the “extended global method”, was introduced to facilitate mode partitioning in the mixed-mode experiments. Non-linear finite element models were developed in order to quantify the effect of the observed fiber bridging on crack propagation. An exponential traction-separation cohesive law was used to model the fiber bridging zone and calculate the energy release rate due to the fiber bridging, while the virtual crack closure technique was used for calculation of the fracture components at the crack tip. Experimental, analytical and numerical analyses were used to establish quasi-static mixed-mode failure criteria for crack initiation and propagation. The derived mixed-mode failure criteria can be used for simulating progressive crack propagation in other joint configurations comprising the same adhesive and adherends.     

碳纤维/环氧树脂复合材料L型接头拉伸失效机制

设计了单L型(LS)及双L型(LD)两种重量相近的L型接头。采用试验与数值模拟相结合的方式对两种接头的拉伸失效机制进行了研究。通过自行设计的试验夹具在伺服液压试验机上将两种L型接头准静态加载至破坏,分析其破坏机制及应变分布。研究发现,两种L型接头存在不同的失效机制,在破坏阶段单L型接头表现出更好的延展性。单L型接头加载至峰值载荷时,在靠近加载侧的内侧螺栓孔附近首先出现破坏,随后损伤向外侧螺栓孔附近扩展,直至完全失效。双L型接头加载至峰值载荷的50%左右时,L型框体和L型片之间的胶膜首先发生破坏,随后载荷继续增加至峰值载荷时,L型框螺栓孔附近发生破坏,损伤向框体边缘扩展,载荷大幅下降。此外,两种接头的应变随载荷的增加存在不同的变化趋势。采用一种新型复合材料初始失效准则及刚度折减方法,编写用户自定义子程序(UMAT),结合内聚区模型建立复合材料L型接头的渐进损伤模型。基于ABAQUS软件进行计算,得到接头的预测失效载荷及破坏形式。结果表明：有限元分析所得复合材料L型接头的损伤位置及失效模式与试验吻合,预测载荷与试验值相差较小,证明了有限元模型的适用性。     

Determination of cohesive laws by the J integral approach

The determination of cohesive laws for describing large scale failure process zones is discussed. Firstly, a general approach for determination of cohesive laws, by the measurement of the J integral and end-opening of the cohesive zone of double cantilever beam specimens loaded with pure bending moments, is described. Next, two case stories are reviewed: failure of adhesive joints and splitting of a unidirectional carbon fibre/epoxy composite. For the adhesive joints, measured failure strengths of bonded panels having a central notch were found to in very good agreement with predictions from cohesive law parameters determined on test specimens. For the problem of splitting of unidirectional composites, micromechanisms were observed in situ during cracking. A cohesive law shape, predicted by a micromechanics model, was found to agree well with macroscopic cohesive law determined by the J integral approach. The cohesive law was used for predicting effect of specimen shape on strength; predictions were confirmed by experiments. Finally, some ideas regarding determination of mixed mode cohesive laws are discussed.