On the use of fracture mechanics in designing a single lap adhesive joint

The design of adhesively bonded joints is a quite difficult task, due to the stress singularity that arises at the edges of the adhesive adjacent to the loaded substrate. This stress singularity makes any design approach based on elastic stress analysis inconvenient. A more convenient design tool for an adhesive joint should be based on its mode of failure. Most of the adhesive joints fail at the adhesive/adherend interface or very close to it in the adhesive layer. Therefore, a fracture theory such as linear elastic fracture mechanics (LEFM) can be used to analyse the failure of an adhesive joint. In this paper, the design of a single lap joint using a fracture mechanics parameter, i.e. the strain energy release rate (SERR), is discussed. The SERR is extracted from a finite element model using Irwin's virtual crack closure integral. A design equation relating the lap length to the adherend thickness through some design parameters is derived.     

Shear behaviour of structural silicone adhesively bonded steel-glass orthogonal lap joints

This paper outlines an experimental study on the shear behaviour of structural silicone adhesively bonded steel-glass orthogonal lap joints. In the combination of steel plate and glass panel to form a hybrid structural glazing system, bonded joints with structural silicones can provide certain flexibility which relieves stress peaks at critical points of glass panel. The cohesive failure and its related fracture pattern of test joints with varied geometries of adhesives are examined experimentally. It is shown that the presence of two failure modes as discrete voids and macro cracks is closely related to the adhesive thickness. The effects of geometric parameters of adhesives on the joint shear strength are examined. It is demonstrated that the joint shear strengths are increased with increased individual overlap length, reduced adhesive thickness or increased adhesive width while the shear deformation corresponding to maximum shear force is mostly influenced by adhesive thickness. Mechanical contributions for those effects are analyzed accordingly. Finally, an analytical formula allowing for the equilibrium of strain and force on the adhesive and adherend is proposed for the analysis of shear strength. It is demonstrated that calculated normalized shear force ratios predicted by proposed formula agree well with those from experimental results.     

Taguchi analysis of bonded composite single-lap joints using a combined interface–adhesive damage model

The mechanical behaviour of bonded composite joints depends on several factors, such as the strength of the composite–adhesive interface, the strength of the adhesive and the strength of the composite itself. In this regard, a finite element model was developed using a combined interface–adhesive damage approach. A cohesive zone model is used to represent the composite–adhesive interface and a continuum damage model for the adhesive bondline. The influence of the composite–adhesive interfacial adhesion and the strength of the adhesive on the performance of a bonded composite single-lap joint was investigated numerically. A Taguchi analysis was conducted to rank the influence of material parameters on the static behaviour of the joint. It was found that the composite–adhesive interfacial fracture energy and the mechanical properties of the adhesive predominantly govern the static performance of the joints. A parametric study was performed by varying the most important material parameters, and a response surface equation is proposed to predict the joint strength. It is shown that the influence of experimental parameter variations, e.g. variation in adhesive curing and surface preparation conditions, can be numerically accommodated to investigate the static behaviour of bonded composite joints by combining finite element and statistical techniques. The methods presented could be used by practicing engineers to describe the failure envelope of adhesively bonded composite joints.     

Spatially-degraded adhesive anchors under material uncertainty

The classic problem of stress transfer in a cylinder through shear to a surrounding medium, is analyzed here in the context of pullout of an anchor under material uncertainty. Assuming a log-normal distribution for the random shear stiffness field of the adhesive, the stochastic differential equation (SDE) is formulated for spatially-tailored/degraded adhesive anchors. The stochastic shear stress distribution in the adhesive is presented for various embedment lengths and adhesive thicknesses clearly demarcating the regime over which failure would initiate. The stochastic variation of maximum shear stress of the adhesive as a function of embedment length and adhesive thickness is also presented. It is observed that the mean maximum shear stresses in the degraded adhesive for both fixed and free embedded-end cases converge and the influence of boundary condition at the embedded-end on shear stress field disappears as the embedment length is increased. For the parameters considered here, about 45% longer embedment length is required compared to an intact bondline for shear-dominated load transfer, suggesting that the design of adhesive anchors should adequately account for likely in-service damage that causes material uncertainty to avoid premature failure.     

Butt joint tensile strength: interface corner stress intensity factor prediction

The asymptotic form of the interface corner stress field in a butt joint is discussed, and a failure analysis based on the stress intensity factor defining the magnitude of this asymptotic stress field is validated. A stress singularity of type Kr^δ(δ < 0) exists at an interface corner in a butt joint (i.e. where an interface intersects a stress-free edge). A simple relation defines the stress intensity factor K for an idealized butt joint composed of a thin elastic adhesive layer bonded between rigid adherends and subjected to transverse tension and uniform adhesive shrinkage. This stress intensity factor, referred to here as the free-edge stress intensity factor K_f, is applicable to both plane strain and axisymmetric geometries. The way that uniform adhesive shrinkage (thermal contraction) during cure alters interface corner stress fields is also discussed. When adhesive shrinkage is present, both constant and singular terms must be included in the asymptotic solution to attain good agreement with full field finite element results over a reasonably large interface corner region. Experiments have been carried out to investigate the applicability of a K_f-based failure criterion to butt joints. Butt joints were fabricated by bonding two stainless steel rods together with an epoxy adhesive (Epon 828/T-403). The measured joint strength increased by a factor of 2 as the bond thickness was reduced from 2.0 to 0.25 mm. The observed bond thickness effect is accurately predicted when failure is presumed to occur at a critical K_f value. This fracture criterion suggests that the butt joint tensile strength varies roughly as the reciprocal of the cube root of bond thickness when the adhesive's Poisson's ratio is between 0.3 and 0.4, residual stress levels at the interface corner are negligible, the adherends are essentially rigid relative to the adhesive, and small-scale yielding conditions hold at the interface corner.     

An efficient analysis model for functionally graded adhesive single lap joints

Employing a functionally graded adhesive the efficiency of adhesively bonded lap joints can be improved significantly. However, up to now, analysis approaches for planar functionally graded adhesive joints are still not addressed well. With this work, an efficient model for the stress analysis of functionally graded adhesive single lap joints which considers peel as well as shear stresses in the adhesive is proposed. Two differential equations of the displacements are derived for the case of an axially loaded adhesive single lap joint. The differential equations are solved using a power series approach. The model incorporates the nonlinear geometric characteristics of a single lap joint under tensile loading and allows for the analysis of various adhesive Young׳s modulus variations. The obtained stress distributions are compared to results of detailed Finite Element analyses and show a good agreement for several single lap joint configurations. In addition, different adhesive Young׳s modulus distributions and their impact on the peel and shear stresses as well as the influence of the adhesive thickness are studied and discussed in detail.     

Experimental Analysis of the Bondline Stress Concentrations to Characterize the Influence of Adhesive Ductility on the Composite Single Lap Joint Strength

Adhesively bonded composite single lap joints were experimentally investigated to analyze the bondline stress concentrations and characterize the influence of adhesive ductility on the joint strength. Two epoxy paste adhesives—one with high tensile strength and low ductility, and the other with relatively low tensile strength and high ductility—were used to manufacture composite single lap joints. Quasi-static tensile tests were conducted on the single lap joints to failure at room temperature. High magnification two-dimensional digital image correlation was used to analyze strain distributions near the adhesive fillet regions. The failure mechanisms were examined using scanning electron microscopy to understand the effect of adhesive ductility on the joint strength. For a given surface treatment and laminate type, the results show that adhesive ductility significantly increases the joint strength by positively influencing stress distribution and failure mechanism near the overlap edges. Moreover, it is shown that high magnification two-dimensional digital image correlation can successfully be used to study the damage initiation phase in composite bonded joints.     

Fatigue life uncertainty of adhesively bonded composite scarf joints – an airworthiness perspective

Adhesively bonded repairs provide a highly structurally efficient and cost-effective means of restoring residual strength to aircraft components. However, gaining airworthiness approval for bonded repairs to primary structures is a significant problem. This is largely because of the failure of current non-destructive inspection techniques to detect weak or non-durable adhesively bonded joints. Due to the presence of undetectable defects and anomalies, recent airworthiness policy ignores the contribution of adhesively bonded joints to the fatigue durability of repaired load-carrying aircraft structures. The key requirement for airworthiness is to demonstrate an acceptable low probability of repair patch disbonding during the remaining life of the structure. In order to satisfy this requirement, it is necessary to identify and control all manufacturing defects and anomalies that influence the durability of the bonded joint. In this study, a methodology has been developed to control manufacturing defects including porosity, unbonded area, and adhesive thickness and flatness variation of bond area. To evaluate the effectiveness of the developed methodology, fatigue tests were conducted, and corresponding uncertainty was analysed. It was found that these defects and anomalies have a significant influence on the fatigue life and fatigue life uncertainty of bonded joints, with minimal effect on their static strength.     

Dynamic analysis of single-lap,adhesively bonded composite-titanium joints subjected to solid projectile impact

The transient stress in a single-lap, adhesively bonded composite-titanium joints subjected to solid projectile impact is analyzed using the three-dimensional finite element method. This method is constructed based on the progressive failure features of the composite adherend and the elastic-plastic property of the titanium adherend and adhesive. The effects of the thickness and overlap length of the adhesive layer, the solid projectile size and its velocity, and the strain-rate effect on the dynamic stress of the joints are examined. It is shown that the stress evolution with certain amplitude exists in the joint. During the impact process, compressive stress concentration is imparted at the point of the contact. Furthermore, experiments are carried out for measuring the strain responses of the adhesively bonded joints. A fairly good agreement is observed between the numerical and measured results.     

Non-linear failure criteria for a double lap bonded joint

This article introduces an analytical procedure based on the well-known Shear Lag theory of Volkersen [Die nietkraftverteilung in zugbeanspruchten mit konstanten laschenquerschritten, Luftfahrtforschung 1938;15:41–7], but allowing to take into account a multilinear mechanical behaviour of the adhesive in order to determine an average shear stress profile along the bonded joint. The aim is to provide for a civil engineering application a simple design tool of bonded anchorages. Using this method, more consistent results are obtained concerning the anchorage length and a failure criteria can be expressed in terms of a maximum yielded length along the bonded joint. The validity of this criteria is assessed via an experimental investigation which includes material characterization as well as double lap joints quasi-static loading. The studied materials are a two-component commercial epoxy adhesive and glass fibre pultruded adherends. Different parameters of the joint are varied (surface preparation, adherend and bond thickness, lap length, geometrical configuration) so that it is possible to check qualitative expectations, and define a quantitative failure prediction parameter. In the last part, the shear stress profiles obtained using the described analytical procedure are compared to finite element results and good agreement is found between both approaches.     

Analysis and design of adhesive-bonded tee joints

In this study, the stresses in adhesive-bonded tee joints, in which a right-angled plate is bonded to a rigid plate with an adhesive, have been analysed with a finite element method. It was assumed that the adhesive and adherends had linear elastic properties. The tee joint was analysed under three loading conditions, two linear and one bending moment. The stress distributions in the joint area are given by stress contours and XY plots under the three load conditions. It was found from the results that high stress concentrations occur in the inside corner of the angle plate for loading in the x-direction (P_x) and under bending moment (M), this suggesting that failure would not occur in the bonded joint. However, for loading in the y-direction (P_y), the maximum normal stresses are concentrated at the left free end of the adhesive layer in the joint, and the first failure may be expected at this edge. Since the geometry of the joints affects the analysis and design of such joints, the influences on the stress distributions of the overlap length, adhesive thickness and adherend thickness were investigated. Practical experiments were carried out and it was found that experimental results were in good agreement with those of the finite element analysis.     

Multivariate analysis of high through-put adhesively bonded single lap joints

The goal of this research was to experimentally demonstrate the correlations between processing variables (adhesive type, bondline thickness, adherend thickness, surface pretreatment, overflow fillet) and effective strength in adhesively bonded single lap joints. While generalizations between effective strength and individual joint design parameters have been assumed for decades, the multifaceted interplay between parameters is complex and remains difficult to understand. Traditionally reported studies of the adhesive bond strength of single lap joints are often limited in the sample size populations needed to statistically probe concurrent design variables. To overcome sample size limitations a test matrix of 1200 single lap joints, partitioned by 96 unique fabrication conditions, was processed and tested using a workflow protocol orchestrated through a relational database. The enhanced pedigree and integrity enabled by using a relational database centered workflow allowed for multivariate principal component analysis of the joint design parameters, with all experimental data input available for peer audit. The results of this study revealed that the adhesive type biases the remaining joint configuration variables towards more influence with respect to either mechanical load or displacement to failure.     

Piezoelectric monitoring of the reliability of adhesive joints

Since the reliability of adhesively bonded joints for composite structures is dependent on many parameters such as the shape and dimensions of joints, type of applied load, and environment, so an accurate estimation of the fatigue life of adhesively bonded joints is seldom possible, which necessitates an in-situ reliability monitoring of the joints during the operation of structures. In this study, a self-sensor method for adhesively bonded joints was devised, in which the adhesive used works as a piezoelectric material to send changing signals depending on the integrity of the joint. In order to validate the method, the piezoelectric properties of the adhesive were measured during the fatigue test. Electrically conducting adherends were used as electrodes without embedded sensors, and the adhesively bonded joint was modeled as the equivalent parallel circuit composed of electric charge and capacitance. From the investigation, it was found that the electric charge increased gradually as cracks initiated and propagated in the adhesive layer, and had its maximum value when the adhesively bonded joint failed. So it is feasible to monitor the integrity of the joint during its lifetime. Finally, a relationship between the piezoelectric property of the adhesive and crack propagation was obtained from the experimental results.     

Static and fatigue behavior of adhesive joints in SMC-SMC composites

This paper discusses the static and fatigue behavior of adhesively bonded single lap joints in SMC-SMC composites. Effects of lap length and adhesive thickness on the static and fatigue strength of SMC-SMC adhesive joints are studied. Effects of SMC surface preparation and test speed on the joint performance are evaluated. Finally, the effect of water exposure on the joint durability is also investigated. Results show that the static behavior of adhesive joints in SMC-SMC composites is significantly influenced by the lap length and adhesive thickness. With an increase in lap length from 12.7 mm to 38.1 mm, the joint failure load increases by 37%. The joint failure load also increases with the adhesive thickness, but it reaches a maximum at an adhesive thickness of 0.33 mm and then decreases. However, lap length and adhesive thickness have negligible effect on the ratio of fatigue strength to static strength. The fatigue strength at 10⁶ cycles is approximately 50% to 54% of the static strength for various adhesive thicknesses and lap lengths investigated in this study. Adhesive failure, fiber tear or combination of these two failure modes are observed during both static and fatigue tests.     

Progressive failure and experimental study of adhesively bonded composite single-lap joints subjected to axial tensile loads

Experimental tests and finite element method (FEM) simulation were implemented to investigate T700/TDE86 composite laminate single-lap joints with different adhesive overlap areas and adherend laminate thickness. Three-dimensional finite element models of the joints having various overlap experimental parameters have been established. The damage initiation and progressive evolution of the laminates were predicted based on Hashin criterion and continuum damage mechanics. The delamination of the laminates and the failure of the adhesive were simulated by cohesive zone model. The simulation results agree well with the experimental results, proving the applicability of FEM. Damage contours and stress distribution analysis of the joints show that the failure modes of single-lap joints are related to various adhesive areas and adherend thickness. The minimum strength of the lap with defective adhesive layer was obtained, but the influence of the adhesive with defect zone on lap strength was not decisive. Moreover, the adhesive with spew-fillets can enhance the lap strength of joint. The shear and normal stress concentrations are severe at the ends of single-lap joints, and are the initiation of the failure. Analysis of the stress distribution of SL-2-0.2-P/D/S joints indicates that the maximum normal and shear stresses of the adhesive layer emerge on the overlap ends along the adhesive length. However, for the SL-2-0.2-D joint, the maximum normal stress emerges at the adjacent middle position of the defect zone along the adhesive width; for the SL-2-0.2-S joint, the maximum normal stress and shear stress emerge on both edges along the adhesive width.     

Characterization of fracture in adhesively bonded double-lap joints

A broad finite element study was carried out to understand the stress fields and stress intensity factors behavior of cracks in adhesively bonded double-lap joints, which are representative of loading in real aerospace structures. The interaction integral method and fundamental relationships in fracture mechanics were used to determine the mixed-mode stress intensity factors and associated strain energy release rates for various cases of interest. The numerical analyses of bonded joints were also studied for various kinds of adhesives and adherends materials, joint configurations, and thickness of adhesive and different crack lengths. The finite element results obtained show that the patch materials of low stiffness, low adhesive moduli and low tapering angles are desirable for a strong double-lap joint. In the double-lap joint, the shearing-mode stress intensity factor is always larger than that of the opening-mode and both shearing and opening mode stress intensity factors increase as the crack length increases, but their amplitudes are not sensitive to adhesive thickness. Results are discussed in terms of their relationship to adhesively bonded joints design and can be used in the development of approaches aimed at using adhesive bonding and extending the lives of adhesively bonded repairs for aerospace structures.     

钛合金‑芳纶纤维复合材料单搭接胶接接头渐进破坏分析

采用芳纶纤维复合材料与钛合金制备单搭接胶接连接实验件。利用万能实验机、DIC、应变采集系统等手段,对胶接接头的极限载荷、应变场、应变分布和破坏模式进行表征,分析了拉伸载荷下胶接接头的应变分布规律和复合材料层合板刚度折减规律,探究了异质材料单搭接胶接接头的破坏过程。结果表明,胶接接头破坏模式为搭接接头两端胶层界面破坏,中间部位复合材料层间破坏。接头破坏过程为渐进破坏,受载时复合材料端头产生较大的剪切应变,裂纹在此处萌生,并不断向钛合金端头扩展,扩展部位复合材料层合板刚度不断折减,直到搭接面积过小胶层突然发生界面破坏。     

Fracture of adhesive joints

This paper presents some of the important results obtained from a series of studies on cohesive fracture in adhesively bonded joints. Due to the complex nature of the adhesive joint fracture, an accurate and efficient numerical method particularly suitable for the present problem has been developed, based on a hybrid-stress finite element formulation. Fracture characteristics in adhesively bonded joints are described in terms of local crack-tip deformation and stress fields in the polymeric adhesive layer. Effects of material properties, joint geometry, and bond-line thickness on the crack behavior are studied for classical lap-shear and currently used double-cantilever-beam joints. Of particular interest are the crack-tip stress intensities in the adhesive layer; their values are obtained for several cases of practical importance.     

Analysis and design of adhesively bonded tee joints with a single support plus angled reinforcement

In this study, stress and stiffness analyses of adhesively bonded tee joints with a single support plus angled reinforcement were carried out using the finite element method. It was assumed that the adhesive had linear elastic properties. In actual bonded joints, some amount of adhesive, called the spew fillet, accumulated at the free ends of the adhesive layer; therefore, the presence of the adhesive fillet at the adhesive free ends was taken into account. The tee joints were analysed for two boundary conditions: a rigid base and a flexible base. In addition, each boundary condition was analysed for four loading conditions: tensile, compressive, and two side loadings. The stress analysis showed that both side loading conditions resulted in higher stress levels in the joint region in which the vertical plate and supports are bonded to each other, as well as in the adhesive layer in this region for both rigid and flexible base boundary conditions. In adhesively bonded joints, the joint failure is expected to initiate in the adhesive regions subjected to high stress concentrations; therefore, the peak adhesive stresses were evaluated in these critical regions. In the case of the rigid base, the peak adhesive stresses occurred at the corner of the vertical plate, which was bent at right angles, for the tensile and compressive loading conditions, and in the adhesive fillet at the upper free end of the vertical adhesive layer-vertical support interface for both the left and the right side loading conditions. However, in case of the flexible base, the peak adhesive stresses occurred in the adhesive fillet at the right free end of the horizontal adhesive layer-horizontal support interface for the tensile, compressive, and the right side loading conditions, and in the vertical adhesive fillet at the upper free end of the vertical adhesive layer-vertical support interface for the left side loading condition. Furthermore, the adhesive stresses showed a nonlinear variation in the direction of the adhesive thickness for all boundary and loading conditions. The left side loading condition, among the present loading conditions, which results in the highest adhesive stresses is the most critical loading condition for both boundary conditions. The effects of horizontal and vertical support lengths on the peak adhesive stresses and on the joint stiffness were also investigated and the appropriate support dimensions relative to the plate thickness were determined based on the stress and stiffness analyses.     

Experimental and Numerical Study of Adhesively Bonded CFRP Scarf-Lap Joints Subjected to Tensile Loads

The tensile performance of adhesively bonded CFRP scarf-lap joints was investigated experimentally and numerically. In this study, scarf angle and adherend thickness were chosen as design parameters. The lap shear strength is not directly proportional to scarf angle and adherend thickness for the brittle adhesive studied in the paper. The major failure mode includes cohesive shear failure and adherend delamination failure. The results present a stepped failure morphology along the bondline in the adhesive layer. A finite element model based on cohesive zone model was established to further investigate the stress distribution of scarf-lap joints with different lap parameters. The numerical results were compared with the experiment results, showing a good agreement, thus verifying the validity of the established numerical model.