Functionally graded adhesive joints by graded mixing of nanoparticles

The main objective of the present study was to use a functionally modified adhesive in order to have an adhesive with properties that vary gradually along the overlap, allowing a uniform stress distribution along the overlap. This allows for a stronger and more efficient adhesive joint. It is possible to work with much smaller areas, reducing considerably the weight of the structure and obtaining more reliable joints. The adhesive stiffness would vary along the overlap, being maximum in the middle and minimum at the ends of the overlap. The processes tested in this work were dielectric heating using a domestic microwave oven and conventional oven heating. Different amounts of carbon black were used and functionally dispersed along the bondline length in order to obtain a functionally graded joint. The functionally graded joints were found to have a higher joint strength compared to the cases where the carbon black was dispersed uniformly along the overlap or where the adhesive was used without carbon black. An analytical model was used to assist with the prediction and the assessment of the possible effectiveness of a graded joint concept.     

Functionally graded adhesives for composite joints

Adhesives with functionally graded material properties are being considered for use in adhesively bonded joints to reduce the peel stress concentrations located near adherend discontinuities. Several practical concerns impede the actual use of such adhesives. These include increased manufacturing complications, alterations to the grading due to adhesive flow during manufacturing, and whether changing the loading conditions significantly impact the effectiveness of the grading. An analytical study is conducted to address these three concerns. An enhanced joint finite element, which uses an analytical formulation to obtain exact shape functions, is used to model the joint. Furthermore, proof-of-concept testing is conducted to show the potential advantages of functionally graded adhesives. In this study, grading is achieved by strategically placing glass beads within the adhesive layer at different densities along the joint.     

Analysis of tubular adhesive joints with a functionally modulus graded bondline subjected to axial loads

The strength and lifetime of adhesively bonded joints can be significantly improved by reducing the stress concentration at the ends of overlap and distributing the stresses uniformly over the entire bondline. The ideal way of achieving this is by employing a modulus graded bondline adhesive. This study presents a theoretical framework for the stress analysis of adhesively bonded tubular lap joint based on a variational principle which minimizes the complementary energy of the bonded system. The joint consists of similar or dissimilar adherends and a functionally modulus graded bondline (FMGB) adhesive. The varying modulus of the adhesive along the bondlength is expressed by suitable functions which are smooth and continuous. The axisymmetric elastic analysis reveals that the peel and shear stress peaks in the FMGB are much smaller and the stress distribution is more uniform along its length than those of mono-modulus bondline (MMB) adhesive joints under the same axial tensile load. A parametric evaluation has been conducted by varying the material and geometric properties of the joint in order to study their effect on stress distribution in the bondline. Furthermore, the results suggest that the peel and shear strengths can be optimized by spatially controlling the modulus of the adhesive.     

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.     

Free Vibration Analysis of an Adhesively Bonded Functionally Graded Tubular Single Lap Joint

In this study, the three-dimensional free vibration analysis of an adhesively bonded functionally graded tubular single lap joint was carried out using the finite element method. The functionally graded tubes of the adhesive joint are composed of ceramic (Al₂O₃) and metal (Ni) phases varying through the tube thickness. The adhesive material properties, such as modulus of elasticity, Poisson's ratio, and density were found to have negligible effect on the first ten natural frequencies and mode shapes of the adhesive joint. The optimal design parameters of the adhesive joint, such as overlap length, inner radius of the inner tube, outer and inner tube thicknesses, and the through-the-thickness material composition variation were searched using both the artificial neural networks (ANNs) and the genetic algorithms (GAs). For this purpose, the natural frequencies and modal strain energy values were calculated for an adhesive joint with random geometrical properties and material compositions through the tube thicknesses, and were used for training the proposed artificial neural network models. The outer tube thickness, the inner tube-inner radius, and the compositional gradient exponent had considerable effect on the natural frequencies, mode shapes, and modal strain energies of the functionally graded tubular single lap joint, whereas the overlap length and the inner tube thickness had a minor effect. The GAs integrated with ANNs was employed to determine optimal design parameters satisfying both maximum natural frequency and minimum modal strain energy conditions for each natural mode of the tubular adhesive joint.     

Analysis of mixed adhesive joints considering the compaction process

Incorporating a material properties variation along the bondlines has proved to be a useful method for improving adhesive joints performance. In this work, the potential of the technique is analysed for a single lap joint using the mixing adhesives approach. In order to include the compaction process effect in the structural analysis during the joint assembly, a computational fluid-dynamic model capable of integrating different resins along the bondline has been developed. Then, the results obtained from this model are mapped into a finite element model through an application developed for this purpose. Several parametric studies have been carried out comparing different configurations in terms of maximum load capacity of the joints. Finally, one of these joints configurations has been manufactured using a special device developed for assembling these mixed adhesive joints and tested. This banded configuration have shown both numerically and experimentally an ultimate load improvement of over 70%.     

Functionally graded adhesive joints by using thermally expandable particles

The main objective of this work was to use thermally expandable particles (TEPs) in order to create a graded adhesive along the overlap by local mixing of the particles. Different amounts of TEPs were used along the overlap with two different adhesives used in automotive industry. Tensile and four-point bend tests were performed on single lap joints with hard steel adherends in order to investigate the behaviour of TEPs-modified graded joints. It was found that the strength of the joints under tension decrease with increasing TEPs content even for small amount of particles (i.e. 1 and 5%). However, a slight increase in strength was found for the graded joints compared to homogeneous joints modified with the same %wt TEPs. In the four-point bending test, the graded joints presented slightly higher strength, if compared with the homogeneous joints modified with the same wt% TEPs. 5%wt TEPs-modified joints presented the highest strength when submitted to bending loading. The experimental results are compared with a finite element model and generally a reasonably good agreement was found.     

Three dimensional finite element analysis of bi-adhesively bonded double lap joint

Hybrid-adhesive joints are an alternative stress reduction technique for adhesively bonded joints. The joints have two types of adhesives in the overlap region. The stiff adhesive should be located in the middle and flexible adhesive at the ends. In this study, the effect of the hybrid-adhesive bondline on the shear and peeling stresses of a double lap joint were investigated using a three-dimensional finite element model. We developed a three dimensional model of the double lap joint based on solid and contact elements. Contact problem is considered to model the interface as two surfaces belonging to adherend and adhesive. Finite element analyses were performed for four different bond-length ratios (0.2,0.4,0.7 and 1.3). The results show that the stress components can be optimized using appropriate bond-length ratios. To validate the finite element analysis results, comparisons were made with available closed-form solutions. The numerical results were found in good agreement with the analytical solutions.     

Joint strength optimization by the mixed-adhesive technique

An ideal adhesive lap joint is one in which the adhesive flexibility and strength properties vary along the overlap length. Because of greater adhesive shear strains at the edges of the overlap, a ductile and flexible adhesive should be used at the overlap ends, while in the middle a stiff and less-ductile adhesive should be used. This technique has been investigated in the past but only a few studies have reported any experimental evidence. In the present study, single-lap adhesive joints were manufactured and tested maintaining the same brittle adhesive in the middle of the overlap and using three different ductile adhesives of increasing ductility at the ends of the overlap. A simple joint strength prediction is proposed for mixed-adhesive joints. The mixed-adhesive technique gives joint strength improvements in relation to a brittle adhesive alone in all cases. For a mixed adhesive joint to be stronger than the brittle adhesive and the ductile adhesive used individually, the load carried by the brittle adhesive must be higher than that carried by the ductile adhesive.     

The Differential Displacements and the Failure in Solvent-Welded Lap Joints

A recent analytical model for adhesive joints proposed by Yue and Cherry for analysing and predicting the strength of solvent-welded lap joints is examined. The experimental verification of an important assumed basis of the applicability of this model to solvent-welded joints is considered. The differential strain in the composite adhesive layer of the solvent-welded joint was shown to be approximately equal to the differential strain in its final adhesive layer. The differential strain and hence the stress concentration was largest near the edge of the overlap. Fractography suggested that failure of the joint initiated at the edge of the overlap.     

The Differential Displacements and the Failure in Solvent-Welded Lap Joints

A recent analytical model for adhesive joints proposed by Yue and Cherry for analysing and predicting the strength of solvent-welded lap joints is examined. The experimental verification of an important assumed basis of the applicability of this model to solvent-welded joints is considered. The differential strain in the composite adhesive layer of the solvent-welded joint was shown to be approximately equal to the differential strain in its final adhesive layer. The differential strain and hence the stress concentration was largest near the edge of the overlap. Fractography suggested that failure of the joint initiated at the edge of the overlap.     

Stress wave propagation in a functionally graded adhesive layer between two identical cylinders

This study investigates the stress wave propagation in circular aluminum cylinders bonded with a functionally graded adhesive layer subjected to an axial impulsive load. The adhesive joint consists of two identical (aluminum) cylinders and a functionally graded adhesive layer. The volume fractions of the two constituents: aluminum and epoxy in the adhesive layer were functionally tailored through the adhesive thickness by obeying a power-law. Therefore, the effective material properties at any point in the adhesive layer were predicted by the Mori-Tanaka homogenization scheme. The governing equations of the wave propagation in the joint were discretized by means of the finite difference method. The influence of the compositional gradient exponent on the displacement and stress distributions of the joint was examined. It was observed that changing the material composition of the adhesive layer had an evident effect on the displacement and stress levels, especially in the lower cylinder. On the contrary, the influence of the compositional gradient exponent was found to be minor on the displacement and stress distributions. The displacement and stress distributions were also investigated along the upper and lower cylinder-adhesive interfaces. Accordingly, with increasing the ductility of the adhesive layer the waves transmitted to the lower cylinder caused lower displacement levels. The normal stresses become peak at the bottom corners of the upper and lower cylinder-adhesive interfaces whereas the shear stresses concentrate in the middle region of the interfaces. In addition, the temporal variations of the displacement and stress components were evaluated at some critical points of the adhesive and lower cylinder. The compositional gradient exponent played an important role on the displacement and stress levels as well as the wave speeds in the adhesive and lower cylinder rather than in the upper cylinder. The stresses in the joints were observed to be alleviated by employing a functionally graded adhesive layer.     

Finite Element Analysis of Functionally Graded Bond-Lines for Metal/Composite Joints

Failure in adhesive joints is usually the result of the non-uniform distribution of stresses that generally appears along the bond-lines, with peak values near the ends of the overlaps and inner zones where the adhesive essentially does not work. For joints comprised of dissimilar materials, the stress fields are also affected by the absence of symmetry. The present work is focused on “functionally graded adhesive joints” to avoid this phenomenon and to improve the strength of aluminum/composite joints under shear loads. Looking for the most favorable grading of properties, a search/optimization procedure is implemented based on finite element calculations and considering continuous variations of the material responses within the adhesive layer. After this, a comparative analysis of the continuous distributions obtained against discrete/“banded” approximations is performed, as these configurations are more feasible for manufacturing and therefore more suitable for industrialization. In order to avoid singularities appearing in the “banded” solutions simulations, a numerical strategy is proposed to model the transitions between the different adhesive phases.     

Application of bi-adhesive in double-strap joints subjected to bending moment

Generally, all failures in adhesively-bonded joints begin at the overlap ends because of the stress concentration occurring at the ends. The approach which reduces stress concentration at the overlap ends increases the load capacity and delays the failure. The lower the stiffness of the adhesive used, the lower the stress concentration, and the lower stress concentration gives rise to higher joint strength. In this work, the results of the application of two adhesives, one stiff and one flexible, with very different mechanical behaviors along the overlap length in double strap joints subjected to bending moment, were analyzed. A stiff adhesive was applied in the middle portion of overlap, while a flexible adhesive was applied towards the edges. The results show that the bi-adhesively-bonded joints carry more loads and have higher strength when compared with single-adhesively-bonded joints.     

Strain energy release rate based damage analysis of functionally graded adhesively bonded tubular lap joint of laminated FRP composites

Strain energy release rate (SERR) based damage analyses of functionally graded adhesively bonded tubular lap joints of laminated fiber reinforced plastic (FRP) composites under varied loadings have been studied using three-dimensional geometrically non-linear finite element (FE) analyses. FE simulations have been carried out when a tubular joint is subjected to axial and pressure loadings. SERR is utilized as the characterizing and governing parameter for assessing damages emanating from the critical location. Individual and total SERR over the damage front have been computed using modified crack closure integral (MCCI) based on the concept of linear elastic fracture mechanics. Results reveal that damage initiation locations in tubular joints subjected to axial and pressure loadings are entirely different. Furthermore, modes responsible for propagation of such damages in tubular joints under axial and pressure loadings are also different. Based on the FE simulations, tubular joints under pressure loading are found to be more vulnerable for damage initiation and its propagation. Furthermore, the damage propagation behavior of tubular joints with pre-embedded damages at the critical location has been compared between conventional mono-modulus adhesives and functionally graded adhesives with appropriate material gradation profile. Results indicate that material gradient profile of the adhesive layer offers excellent reduction in SERR for shorter interfacial failure lengths in tubular joints under axial loading which is desired to delay the damage growth. Improved crack growth resistance in the joint enhances the structural integrity and service life of the tubular joint structure. However, considerable reduction in SERR has not been noticed in the said joint when subjected to pressure loading. Hence, the use of functionally graded adhesive along the bond layer is recommended for the designer/technologist while designing tubular joint under general loading condition.     

Design of functionally graded joints using a polyurethane-based adhesive with varying amounts of acrylate

Adhesives with graded properties along the bondline are being developed to increase the strength of adhesively bonded joints. Efforts to do this in the past have resulted in mixed results. Two adhesive parameters need to be considered: the geometry of the gradation and the material properties of the adhesive at different gradation levels. In order to consider both of these aspects, a computational model was created to aid in not only the design of adhesive gradations but also judge whether a specific adhesive gradation method will be able to result in strength increases. In this study, the model was introduced and compared with published results. A new adhesive gradation system was created by using a polyurethane-based adhesive with varying amounts of acrylate, and a numerical analysis was performed to determine the potential advantages of the adhesive gradation.     

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.     

Use of artificial neural networks for modelling rate dependent behaviour of adhesive materials

This research work highlights the use of artificial neural networks (ANN) for modelling the rate-dependent response of adhesive materials with the purpose of expanding the established method for modelling the response of adhesively bonded structures, and in particular single lap joints. The motivation for this work comes after a viscoplastic model developed in a previous research work failed to predict the response of single lap joints bonded with a rate dependent adhesive material. The viscoplastic model, however, was successful in replicating both bulk and shear properties of the used adhesive system. Predictions made using the rate-dependent von Mises material model proved to be successful in predicting the behaviour of single lap joints, but it could not model the shear data using the tensile data due to hydrostatic stress sensitivity in the adhesive itself. Accurate predictions of the rate-dependent behaviour using artificial neural networks are possible with the availability of stress and strain data sets from experiments. This is where the neural network constitutive model directly acquires the information on the material behaviour from experimental data sets. Material data defining both the tensile and shear response of the adhesive system was extracted from previous research work. An artificial neural network constitutive model was developed and then used to replicate experimental data and also to generate further data at other strain rates. The available model could be slightly modified and then used to investigate various geometrical parameters, such as overlap length, plate thickness and adhesive thickness on joint strength.     

A simple approach for characterizing the performance of metallic tubular adhesively-bonded joints under torsion loading

Adhesive bonding of joints is one of the most commonly and widely used joining methods in piping systems. This work is concerned with the investigation of the influence of the non-linear behavior of the adhesive used in such bonded joints on their performance. The parametric analysis module of ABAQUS was used to model the joint. The model facilitated the analysis of different geometric, loading and material characteristics of the system, in particular the adhesive nonlinearity, which is of prime interest in this work. By using the Ramberg–Osgood plasticity model, the failure threshold of the adhesive for various joint lengths (hereafter referred to overlap length) was characterized. The plasticity model used in this study was fine-tuned using only a limited number of known parameters, through comparison with the results of the finite element (FE) simulation. The results obtained from the FE analysis were verified by experimental results. The FE strategy is demonstrated to be an effective means for predicting the capacity of such joints, where conducting a pure shear test is either impossible or difficult to accomplish. Contrary to the findings based on the elastic finite element analysis, the plasticity analysis revealed that the overlap length affects the ultimate strength of the joint.     

The behaviour of single lap joints under bending loading

Four-point bend tests were performed on single lap joints with hard steel adherends and a structural epoxy adhesive. The effect of the overlap, the adherend thickness and the adhesive thickness was studied. It was found that the length of the overlap has no significant effect on the strength of the joints. This is because the load transfer is occurring in a very localised area around the edges of the overlap, being the failure governed by peel mechanisms. The thickness of the adherends strongly affects the strength of the joints. The thicker the adherend, the stronger is the joint. The experimental results are compared with a finite element model and reinforce the fact that the failure takes place due to local strains at the ends of the overlap in tension. An analytical model is also given to predict in a simple but effective way the joint strength and its dependence on the adherend thickness.