Predicting the strength of adhesively bonded joints of variable thickness using a cohesive element approach

One major characteristic of bonded structures is the highly localised nature of deformation near sharp corners, ply-terminations, and ends of joints where load transfer occurs. This paper presents an investigation of the use of a cohesive zone model in predicting the strong effects of stress concentration due to varying adherend thickness on the pull-off strength measured by the Pneumatic Adhesion Tensile Testing Instrument. A comparison is made with the point-strain-at-a-distance criterion, where the plastic deformation of the adhesive is analysed using a modified Drücker–Prager/cap plasticity material model. The fracture properties of the cohesive zone model were determined using double-cantilever and end-notch flexural specimens, and the cohesive strengths were measured using tensile and lap shear tests. Comparisons with experimental results reveal that the cohesive zone model with perfectly plastic (or non-strain-softening) cohesive law provides accurate predictions of joint strengths.     

A review of finite element analysis of adhesively bonded joints

The need to design lightweight structures and the increased use of lightweight materials in industrial fields, have led to wide use of adhesive bonding. Recent work relating to finite element analysis of adhesively bonded joints is reviewed in this paper, in terms of static loading analysis, environmental behaviors, fatigue loading analysis and dynamic characteristics of the adhesively bonded joints. It is concluded that the finite element analysis of adhesively bonded joints will help future applications of adhesive bonding by allowing system parameters to be selected to give as large a process window as possible for successful joint manufacture. This will allow many different designs to be simulated in order to perform a selection of different designs before testing, which would currently take too long to perform or be prohibitively expensive in practice.     

A damage zone model for the failure analysis of adhesively bonded joints

The design of structural adhesively bonded joints is complicated by the presence of singularities at the ends of the joint and the lack of suitable failure criteria. Literature reviews indicate that bonded joint failure typically occurs after a damage zone at the end of the joint reaches a critical size. In this paper, a damage zone model based on a critical damage zone size and strain-based failure criteria is proposed to predict the failure load of adhesively bonded joints. The proposed damage zone model correctly predicts the joint failure locus and appears to be relatively insensitive to finite element mesh refinement. Results from experimental testing of various composite and aluminium lap joints have been obtained and compared with numerical analysis. Initial numerical predictions indicate that by using the proposed damage zone model, good correlation with experimental results can be achieved. A modified version of the damage zone model is also proposed which allows the model to be implemented in a practical engineering analysis environment. It is concluded that the damage zone model can be successfully applied across a broad range of joint configurations and loading conditions.     

Mechanism of ultrasonic vibration effects on adhesively bonded ceramic matrix composites joints

Ultrasonic vibration treatment is being utilized to improve adhesive bonding performance, but the mechanisms remain unclear. Moreover, few studies have been carried out on improvement of adhesive bonding of ceramic matrix composites (CMCs) by ultrasonic vibration. In this work, a mathematical model based on fluid mechanics and capillary rise theory is developed to determine the adhesive penetration ability. The effect of ultrasonic vibration on adhesive bonding performance of CMCs is studied. Based on the experimental results, a good agreement is found with respect to measurements of hydraulic force and pressure. Ultrasonic vibration-assisted processing can improve interfacial adhesion strength due to adhesive has high wettability and penetration ability. Furthermore, it is found that delamination and ply-delamination are the main failure modes for all conditions, but porous areas are reduced by ultrasonic treatment.     

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.     

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.     

Damage tolerance analysis of adhesively bonded composite single lap joints containing a debond flaw

Adhesive bonding technology is being increasingly used in the assembly and repair processes of composite structures. The existence of debond flaws weakens the performance of adhesively bonded structures. This article presents the results from an investigation into the effects of debond flaws on the mechanical performance of adhesively bonded single lap joints. The experimental results show that both the load-carrying capability and the failure mode of the single lap joints vary with the location of the debond flaws. Three-dimensional progressive damage finite-element models were developed in ABAQUS to simulate the tensile behaviour of single lap joints. The simulation results agree with the experimental data. The flaws located at 1/4 lap length result in a more pronounced reduction in the load-carrying capability than those located at the edge and the middle portion of the bond region. Compared with the other two locations, the residual strength of the single lap joint with a flaw at 1/2 lap length possesses a higher value. Moreover, the effects of flaws on strength reduction are more prominent for damage propagation than damage initiation.     

Finite element analysis of torsional free vibration of adhesively bonded single-lap joints

Adhesively bonding is a high-speed fastening technique which is suitable for joining advanced lightweight sheet materials that are dissimilar, coated and hard to weld. In this paper, the free torsional vibration characteristics of adhesively bonded single-lap joints are investigated in detail using finite element method. The effectiveness of finite element analysis technique used in the study is validated by experimental tests. The focus of the analysis is to reveal the influence on the torsional natural frequencies and mode shapes of these joints caused by variations in the material properties of adhesives. It is shown that the torsional natural frequencies and the torsional natural frequency ratios of the adhesively bonded single-lap joints increases significantly as the Young′s modulus of the adhesives increase, but only slight changes are encountered for variations of Poisson's ratio. The mode shapes analysis show that the adhesive stiffness has a significant effect on the torsional mode shapes. When the adhesive is relatively soft, the torsional mode shapes at the lap joint are slightly distorted. But when the adhesive is relatively very stiff, the torsional mode shapes at the lap joint are fairly smooth and there is a relatively higher local stiffening effect. The consequence of this is that higher stresses will be developed in the stiffer adhesive than in the softer adhesive.     

A numerical study of adhesively bonded lap joints

The two types of joint discussed in this paper are a thick adherend symmetrical lap joint, and a symmetrical double lap joint. The effect of varying adherend and adhesive thicknesses on the stress distribution in the thin adhesive layer is discussed. These analyses were used in the design on a lap shear test to characterize certain aerospace adhesives used in bonded repair of structural components. An alternative analytical approach for the estimation of the load-carrying capacity of the double lap joint is also presented.     

Failure prediction of adhesively bonded CFRP-Aluminum alloy joints using cohesive zone model with consideration of temperature effect

To predict the failure of adhesively bonded CFRP (Carbon Fiber Reinforced Plastics)-aluminum alloy joints applied to High Speed EMU (Electric Multiple Units) more accurately with consideration of temperature influence, a combined experimental-numerical approach is developed in this study. Bulk specimens and adhesive joints, including thick-adherend shear joints(TSJ), scarf joints(SJ) with scarf angle 30°(SJ30°), 45°(SJ45°), and 60°(SJ60°), as well as butt joints(BJ), were manufactured and tested at 23°C (room temperature, RT), 80°C (high temperature, HT) and ?40°C (low temperature, LT). Quadratic stress criteria built at different temperatures were introduced in the cohesive zone mode (CZM) to conduct a simulation analysis. Test results suggest that the effects of HT on mechanical properties of adhesive are more obvious than the effects of LT. It is also found that TSJ show the greatest improvements in failure strengths at LT due to the occurrence of cohesive failure, while SJ and BJ tend to develop fiber tears due to the presence of normal stress. Stress distributions of adhesive layer are found to be symmetrical except for the normal stress of SJ. This simulation analysis shows that the prediction accuracy is related to quadratic stress criteria applied, and that the relative errors of prediction results are less than 7.5% for engineering applications.     

Strength prediction of epoxy adhesively bonded scarf joints of dissimilar adherends

In this study, strength of epoxy adhesively bonded scarf joints of dissimilar adherends, namely SUS304 stainless steel and YH75 aluminum alloy is examined on several scarf angles and various bond thicknesses under uniaxial tensile loading. Scarf angle, θ=45°, 60° and 75° are employed. The bond thickness, t between the dissimilar adherends is controlled to be ranged between 0.1 and 1.2 mm. Finite element (FE) analysis is also executed to investigate the stress distributions in the adhesive layer of scarf joints by ANSYS 11 code. As a result, the apparent Young's modulus of adhesive layer in scarf joints is found to be 1.5-5 times higher than those of bulk epoxy adhesive, which has been obtained from tensile tests. For scarf joint strength prediction, the existing failure criteria (i.e. maximum principal stress and Mises equivalent stress) cannot satisfactorily estimate the present experimental results. Though the measured stress multiaxiality of scarf joints proportionally increases as the scarf angle increases, the experimental results do not agree with the theoretical values. From analytical solutions, stress singularity exists most pronouncedly at the steel/adhesive interface corner of joint having 45-75° scarf angle. The failure surface observations confirm that the failure has always initiated at this apex. This is also in agreement with stress-y distribution obtained within FE analysis. Finally, the strength of scarf joints bonded with brittle adhesive can be best predicted by interface corner toughness, Hc parameter.     

Strength prediction of adhesively bonded carbon/epoxy joints

A finite element approach has been used to obtain the stress distribution in some adhesive joints. In the past, a strength prediction method has not been established. Therefore in this study, a strength prediction method for adhesive joints has been examined. First, the critical stress distribution of single-lap adhesive joints, with six different adherend thicknesses, was examined to obtain the failure criteria. It was thought that the point stress criterion, which has been previously used for an FRP tensile specimen with a hole, was effective. The proposed method using the point stress criterion was applied to adhesive joints, such as single-lap joints with short non-lap lengths and bending specimens of single-lap joints. Good agreement was obtained between the predicted and experimental joint strengths.     

Modeling the constant amplitude fatigue behavior of adhesively bonded pultruded GFRP joints

The constant amplitude fatigue behavior of adhesively bonded pultruded glass fiber reinforced polymer double-lap joints were modeled by a number of conceptually different phenomenological S–N (cyclic stress vs. number of cycle) formulations. An extended database containing constant amplitude fatigue data under tension (R?=?0.1), compression (R?=?10), and reversed loading (R?=??1) were analyzed in order to investigate whether or not there exists an appropriate fatigue formulation for accurate modeling of the behavior of the examined joints throughout their lifetime, from the very low-cycle fatigue to the high-cycle fatigue regions. Based on an extensive review, appropriate fatigue formulations that take into account the probabilistic nature of lifetime measurements were selected and their fundamental assumptions were examined. The validity of the statistical assumptions of these models was found to be influenced by the applied loading conditions. The modeling results were similar for all selected fatigue formulations with the derived S–N curves exhibiting differences mainly in the low- and high-cycle fatigue regimes. The formulations insensitive to the scatter in the experimental data were found to be the most appropriate models.     

Geometrically non-linear analysis of adhesively bonded corner joints

When adhesively bonded joints are subjected to large displacements, the small strain-small displacement (linear elasticity) theory may not predict the adhesive or adherend stresses and deformations accurately. In this study, a geometricaly non-linear analysis of three adhesively bonded corner joints was carried out using the incremental finite element method based on the small strain-large displacement (SSLD) theory. The first one, a corner joint with a single support, consisted of a vertical plate and a horizontal plate whose left end was bent at right angles and bonded to the vertical plate. The second corner joint, with a double support, had two plates whose ends were bent at right angles and bonded to each other. The final corner joint, with a single support plus angled reinforcement, was a modification of the first corner joint. The analysis method assumes that the joint members, such as the support, plates, and adhesive layers, have linear elastic properties. Since the adhesive accumulations (spew fillets) around the adhesive free ends have a considerable effect on the peak adhesive stresses, they were taken into account. The joints were analyzed for two different loading conditions: one loading normal to the horizontal plate plane P_y and the other horizontal loading at the horizontal plate free edge P_x. In addition, three corner joints were analyzed using the finite clement method based on the small strain-small displacement (SSSD) theory. In predicting the effect of the large displacements on the stress and deformation states of the joint members, the capabilities of both analyses were compared. Both analyses showed that the adhesive free ends and the outer fibres of the horizontal and vertical plates were subjected to stress concentrations. The peak stresses appeared at the slot corners inside the adhesive fillets and at the horizontal and vertical plate outer fibres corresponding to the locations where the horizontal and vertical adhesive fillets finished. The SSLD analysis predicted that the displacement components and the peak adhesive and plate stress components would show a non-linear variation for the loading condition P_x, whereas the SSSD analysis showed smaller stress variations proportional to the applied load. However, both the SSLD and the SSSD analyses predicted similar displacement and stress variations for the loading condition P_y. Therefore, the stress and deformation states of the joint members are dependent on the loading conditions, and in the case of large displacements, the SSSD analysis can be misleading in predicting the stresses and deformations. The SSLD analysis also showed that the vertical and horizontal support lengths and the angled reinforcement length played an important role in reducing the peak adhesive and plate stresses.     

Stress analysis of adhesively bonded double strap joints with or without intermediate part subjected to tensile loading

Accidents in the industry, especially in the field of aerospace, are quite common. Damages like tears cracks and holes occur especially when small sand particles present in the airfield collide with the body and wings of an airplane during takeoff and landing. This torn, cracked, or pierced region should be repaired gently. Damaged parts are frequently small regions for which repair is more suitable than complete replacement as workmanship; cost and time are an important concept in today’s world.

A gap occurs between the patches if double-bonded patches are used in the repair of the damaged parts. In this study, the region between patches in a joint with and without intermediate parts was modeled and its effect on strength was examined numerically and experimentally. The effects of patch thickness, overlap length, adherent thickness, and gap length on the strength of the joints with and without intermediate part was compared. The results show that the intermediate part does not have any influence on the strength of the lap joint such that double strap joints without intermediate part have higher failure load. Additionally, it is seen that the failure load decreased with increasing patch thickness and increased with the thickness of the adherent.     

Experimental investigation on transverse low-speed impact behavior of adhesively bonded similar and dissimilar clamped plates

This experimental study investigates the low-speed impact behavior of adhesively bonded similar (Al–Al, St–St) and dissimilar (Al–St, St–Al) plates. The after-impact geometries of the front and back faces of the bonded plates, which were visualized by measuring the displacements, were in good agreement with the simulated surface geometries obtained by using explicit finite element method. The plate stiffness was affective on the deflections of the bonded plates; thus, the bonded Al–Al plates exhibited maximum deflections, contact durations, and minimal contact force levels, whereas the bonded St–St plates had minimum deflections, contact durations, and maximum contact force levels. As the impact energy is increased, the impact forces, durations, and deflections increased naturally; however, the impact force-time histories were not affected evidently. The bonded Al–Al plates can dissipate the impact energy more effectively than the bonded St–St plates. The experimental and simulated contact force-time histories were generally in good agreement. Based on the cross-section photographs of the damaged impact regions the bonded Al–Al plates with low stiffness can deform plastically and dissipate most of the impact energy, and the adhesive layer remains compatible with the deformation of the plates. The interfacial fractures appear along the back plate–adhesive interface for the low impact energy but along both front and back plate–adhesive interfaces and cracks propagated to the back interface to lower interface through the adhesive thickness near the boundaries of the impactor trace. The bonded St–St plates behave more rigid, transmit the impact energy directly to the adhesive layer and the high impact force distributions result severe fractures not only interfacially but also through the adhesive thickness. The color transformations, which are indications of fracture formation and propagation speed in some way, were observed around the adhesive fractures. Although the bonded St–Al and Al–St plates had a fracture mechanism similar to those of the bonded Al–Al plates but the color transformation near the fractures and the crack opening displacement levels were more evident. The existence of a stiffer plate affects considerably the damage formation in the adhesive layer and in the plates, whereas the less stiff plates can dissipate the impact energy by deforming plastically and the adhesive layer experiences less local damages.     

Prediction of mechanical behaviour of adhesively bonded CFRP scarf jointed specimen under tensile loading using localised DIC and CZM

The present study focuses on the mechanical behaviour of both single and double tapered scarf adhesively bonded joint of Carbon fibre reinforced polymer (CFRP) laminate as adherend subjected to tensile loading. The layup sequence of the CFRP adherend having unidirectional (UD) [0⁰]₁₆ and quasi [+45/−45/0/90]_2S are studied. The adhesive used here is Araldite 2015 supplied by Huntsman which is a two part epoxy system of intermediate toughness grade. Here, 2D digital image correlation (DIC) technique is used for capturing the whole field longitudinal, peel and shear strain distribution over the adhesive bond line of the CFRP specimen. Further, a localised DIC measurement is also carried out using microscopic tube lens for precisely capturing strain field over concentrated zones where damage initiation occurs. The evolution of whole field strain distribution with increasing load is captured to predict the mechanical behaviour and failure mechanism of a tapered scarf joint specimen. In addition, 2-D finite element analysis (FEA) of scarf joint model is carried out for validating the DIC results. In the finite element model cohesive zone elements are used for the modelling of both adhesive layer and inter/intra laminar interface of the composite laminate. Initially, to verify the proposed numerical model, joint's initial stiffness, failure load and corresponding displacement obtained from FEA are compared against the experimental load – displacement results. Later, qualitative and quantitative comparison of longitudinal, peel and shear strain values obtained over the adhesive layer by DIC and FEA is carried out to confirm the accuracy of the DIC results. A decent correlation is found to exist between the DIC predictions and numerical results thereby confirming the accuracy of the DIC technique. Analytical solutions are also derived for the same problem based on mechanics of material and further it is compared with both FEA and DIC predictions for completeness.     

Numerical design and multi-objective optimisation of novel adhesively bonded joints employing interlocking surface morphology

A novel concept for joining materials is presented which employs adhesive joints with interlocking bond-surface morphology formed on the surfaces of male and female adherends that mechanically interlock in shear when brought together. In the present work, miniature, single-lap joint specimens with a single truncated square pyramid interlocking profile, centred in the bond area, are investigated. The performance of the concept is assessed through finite element analysis (FEA) by incorporating yield criteria representing plasticity in the adherends and a cohesive zone model to represent damage in the adhesive layer. This allows for effective simulation of the joint response until ultimate failure and thus, full assessment of the concept's performance. Various interlocking geometries are explored and refined through an adaptive surrogate modelling design optimisation procedure coupled with FEA. The results indicated that significant improvements in work to failure, of up to 86.5%, can be achieved through the more progressive failure behaviour observed compared to that of a traditional adhesively bonded joint. Improvements in the joint's ultimate failure load can also be achieved with a relatively ductile adhesive system.     

Improving the strength of adhesively bonded joints through the introduction of various surface treatments

The aim of this paper is to model an interface adhesion and failure mechanism of single lap joints, subjected to tensile loading, focusing on the effects of various surface treatments, including surface characterization parameters, such as surface roughness and contact angle of adherend surfaces. The applied surface treatments are sandblasting, etching, anodic oxidation and hybrid processes. The influence of surface treatment techniques and conditions on single lap joint strength and interfacial properties is investigated by performing a static tensile test. A numerical approach, which is a cohesive zone model, is implemented using ABAQUS? and introduced to create a correlation between maximum interface traction and surface processing parameters, such as surface roughness and work of adhesion. As a result of experiments, an etching plus sanding process was found to provide the best single lap joint performance (8726 N), having surface roughness of Ra = 2.93 μm and work of adhesion, W_a = 119.4 mJ/m². Based on numerical solutions, a correlation between maximum interface traction and type of surface treatment process has been established, taking certain assumptions into consideration.