Modelling Environmental Degradation in EA9321-Bonded Joints using a Progressive Damage Failure Model

A progressive cohesive failure model has been proposed to predict the residual strength of adhesively bonded joints using a moisture-dependent critical equivalent plastic strain for the adhesive. Joints bonded with a ductile adhesive (EA9321) were studied for a range of environmental degradations. A single, moisture-dependent failure parameter, the critical strain, was calibrated using an aged, mixed-mode flexure (MMF) test. The mesh dependence of this parameter was also investigated. The parameter was then used without further modification to model failure in aluminum and composite single-lap joints (SLJ) bonded with the same adhesive. The FEA package ABAQUS was used to implement the coupled mechanical-diffusion analyses required. The elastic–plastic response of the adhesive and the substrates, both obtained from the bulk tensile tests, were incorporated. Both two-dimensional and three-dimensional modelling was undertaken and the results compared. The predicted joint residual strengths agreed well with the corresponding experimental data, and the damage propagation pattern in the adhesive was also predicted correctly. This cohesive failure model provides a simple but reliable method to model environmental degradation in ductile adhesive bonded joints, where failure is predominantly within the adhesive layer.     

Interfacial failure analysis of functionally graded adhesively bonded double supported tee joint of laminated FRP composite plates

This paper deals with three-dimensional non-linear finite element analyses to assess the structural behavior of adhesively-bonded double supported tee joint of laminated FRP composites having embedded interfacial failures. The onset of interfacial failures is predicted by using Tsai–Wu coupled stress failure criterion with pre-determined stress values. The concept of fracture mechanics principle is utilized to study the sustainability of the tee joint having interfacial failures pre-existed at the critical locations. Individual modes of the strain energy release rates (SERR) G_I, G_II and G_III, are considered as the damage growth parameters and, are evaluated using the Modified crack closure integral (MCCI) technique based on the concept of linear elastic fracture mechanics (LEFM). Based on the stress analyses, it has been observed that the interfacial failures in tee joint structure trigger at the interface of base plate and adhesive layer from both ends of base plate. Depending on the SERR magnitudes, it has been noticed that the interfacial failure propagates under mixed mode condition. Therefore total SERR (G_T) is considered as the governing parameter for damage propagation. Furthermore, efforts have been made to retard damage propagation rate by employing functionally graded adhesive (FGA) instead of monolithic adhesive material. Series of numerical simulations have been performed for varied interfacial failure length in functionally graded adhesively bonded double supported tee joint structure in order to achieve the significant effect of FGA with various modulus ratios on SERR. Material gradation of adhesive indicates significant SERR reduction at the incipient stage of failure which necessitates the use of functionally graded adhesive for the tee joint and prolong the service life of the structure.     

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.     

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。     

Modelling Environmental Degradation in EA9321-Bonded Joints using a Progressive Damage Failure Model

A progressive cohesive failure model has been proposed to predict the residual strength of adhesively bonded joints using a moisture-dependent critical equivalent plastic strain for the adhesive. Joints bonded with a ductile adhesive (EA9321) were studied for a range of environmental degradations. A single, moisture-dependent failure parameter, the critical strain, was calibrated using an aged, mixed-mode flexure (MMF) test. The mesh dependence of this parameter was also investigated. The parameter was then used without further modification to model failure in aluminum and composite single-lap joints (SLJ) bonded with the same adhesive. The FEA package ABAQUS was used to implement the coupled mechanical-diffusion analyses required. The elastic-plastic response of the adhesive and the substrates, both obtained from the bulk tensile tests, were incorporated. Both two-dimensional and three-dimensional modelling was undertaken and the results compared. The predicted joint residual strengths agreed well with the corresponding experimental data, and the damage propagation pattern in the adhesive was also predicted correctly. This cohesive failure model provides a simple but reliable method to model environmental degradation in ductile adhesive bonded joints, where failure is predominantly within the adhesive layer.     

Modeling of cohesive failure processes in structural adhesive bonded joints

This paper presents an approach to predicting the strength of joints bonded by structural adhesives using a finite element method. The material properties of a commercial structural adhesive and the strength of single-lap joints and scarf joints of aluminum bonded by this adhesive were experimentally measured to provide input for and comparison with the finite element model. Criteria based on maximum strain and stress were used to characterize the cohesive failure within the adhesive and adherend failure observed in this study. In addition to its simplicity, the approach described in this paper is capable of analyzing the entire deformation and failure process of adhesive joints in which different fracture modes may dominate and both adhesive and adherends may undergo inelastic deformation. It was shown that the finite element predictions of the joint strength generally agreed well with the experimental measurements.     

Transverse cracking of a simple lap joint under axial load

The failure mode of axially loaded simple, single lap joints formed between thin adherends which are flexible in bending is conventionally described as one of axial peeling. We have observed – using high-speed photography – that it is also possible for failure to be preceded by the separation front, or crack, moving in a transverse direction, i.e. perpendicular to the direction of the axial load. A simple energy balance analysis suggests that the critical load for transverse failure is the same as that for axial separation for both flexible lap joints, where the bulk of the stored elastic energy lies in the adhesive, and structural lap joints in which the energy stored in the adherends dominates. The initiation of the failure is dependent on a local increases in either stress or strain energy to some critical values. In the case of a flexible joint, this will occur within the adhesive layer and the critical site will be close to one of the corners of the joint overlap from which the separation front can proceed either axially or transversely. These conclusions are supported by a finite element analysis of a joint formed between adherends of finite width by a low modulus adhesive.     

Geometrically non-linear analysis of adhesively bonded double containment cantilever j oints

Under an increasing load, the adhesively bonded joints may undergo large rotations and displacements while strains are still small and even all joint members are elastic. In this case, the linear elasticity theory cannot predict correctly the nature of stress and deformation in the adhesive joints. In this study, an attempt was made to develop an analysis method considering the large displacements and rotations in the adhesive joints, assuming all joint members to be still elastic. An incremental finite element method was used in the application of the small strain-large displacement theory to the adhesively bonded joints. An adhesively bonded double containment cantilever (DCC) joint was analysed using this incremental finite element method under two different loadings: a tensile loading at the horizontal plate free end, P_x. and one normal to the horizontal plate plane, P_y. The adhesive and plates were assumed to have elastic properties, and some amount of adhesive, called spew fillet, that accumulated at the adhesive free ends was also taken into account. The analysis showed that the geometrical non-linear behaviour of adhesively bonded joints was strictly dependent on the loading and boundary conditions. Thus, a DCC joint exhibits a high non-linearity in the displacements, stresses, and strains in the critical sections of the adhesive and horizontal plate under a tensile loading at the free end of the horizontal plate, P_x, while a similar behaviour in these regions was not observed for a loading normal to the horizontal plate plane, P_y. However, an increasing non-linear variation in the stresses and deformations of the horizontal plate appeared from the free ends of the adhesive-horizontal plate interfaces to the free end of the horizontal plate for both loading conditions. Consequently, joint regions with a low stiffness always undergo high rotations and displacements, and if these regions include any adhesive layer, the non-linear effects will play an important role in predicting correctly the stresses and deformations in the joint members, especially at the adhesive free ends at which high stress concentrations occurred. In addition, the DCC joint exhibited a higher stiffness and lower stress and strain levels in the joint region in which the support and horizontal plate are bonded than those in the horizontal plate.     

Strength prediction of bonded single lap joints by non-linear finite element methods

A non-linear finite element technique has been used to predict the mode of failure and failure load of single lap joints made from three aluminium alloys and four epoxy adhesives, and the results compared with those obtained from experiment and closed-form analyses. The finite element program used was able to account for the large displacement rotations that occur in a single lap joint under load, and allowed the effects of elasto-plasticity in both the adhesive and adherends to be modelled. A failure criterion based on the uniaxial tensile properties of the adhesive was used: for two untoughened adhesives a maximum stress criterion was found to be appropriate while for two toughened adhesives a maximum strain criterion was employed.     

Interfacial failure in adhesive joints: Experiments and predictions

The aim of this paper is the development of a method to predict interfacial failure in adhesive joints. The main originality of the paper resides on the application of a twofold criterion involving stress and energy conditions simultaneously to predict adhesive failure onset in different geometries of adhesive joints subjected to diverse loadings. Butt joints and double lap joints made of linear elastic materials are tested in torsion and tension. The failure onset predictions are based on finite element calculations and a twofold criterion which considers a novel stress condition. These predictions are accurate and prove the validity of the method to predict adhesive failure for different adhesive joint configurations and loadings.     

Residual static strength and the fracture initiation path in adhesively bonded joints weakened with interfacial edge pre-crack

This paper deals with the application of fracture mechanics approaches for predicting the residual static strength and the crack kinking angle of adhesively bonded joints containing interfacial edge pre-cracks. The interfacial cracks are created due to different factors such as inappropriate surface preparation which cause a significant reduction of the joint strength. To investigate the residual strength of interfacial cracked adhesive joints and predict the crack kinking angle, three different approaches including the maximum tangential stress (MTS), the minimum strain energy density (SED) and the maximum tangential strain energy density (MTSED) were assessed. To this end, single lap joints (SLJs) containing a brittle adhesive material and with different pre-crack sizes and various substrate thicknesses were manufactured and tested. The results were also verified by applying fracture mechanics approaches on previously published experimental data. According to the results, it was concluded that in mode II dominant cases, the predictions of kinking angle using the MTS method was in good agreement with the experimental observations, while in mode I dominant cases the mentioned approach provided poor predictions. It was also found that the SED criterion could be a precise model for predicting the crack extension angle in mode I dominant conditions. The results also showed that the MTS criterion predicts the residual static strength of interfacial cracked adhesive joints very well.     

Behaviour of Bi-adhesive Joints

The use of relatively low modulus adhesive at the ends of overlap in a bi-adhesive bondline of a bonded joint can reduce the stress concentration significantly and, therefore, potentially lead to higher strength of the joint. This study presents the two-dimensional and three-dimensional nonlinear (geometric and material) finite element analyses of adhesively bonded single lap joints having modulus-graded bondline under monotonic loading conditions. The adhesives were modelled as an elasto-plastic multi-linear material, while the substrates were regarded as both linear elastic and bi-linear elasto-plastic material. The computational simulations have been performed to investigate the bondline behaviour by studying the stress and strain distributions both at the mid-plane as well as at the interface of the bondline. It has been observed that the static strength is higher for joints with bi-adhesive bondlines compared to those with single adhesives in bondline. Higher joint strength has also been observed for optimum bi-adhesive bondline ratio through parametric studies. Effects of load level, and bondline thickness on stress distribution in the bi-adhesive bondline have also been studied. 3D analysis results reveal the existence of complex multi-axial stress/strain state at the ends of the overlap in the bondline which cannot be observed in 2D plane strain analysis. About 1/3rd of the width of the joint from the free edge in the width direction has 3D stress state, especially in the compliant adhesive of the bondline. Magnitudes of longitudinal and lateral stress/strain components are comparable to peel stress/strain components. It has also been analytically shown that the in-plane global stiffness of the joint remains unaffected by modulus gradation of the bondline adhesive.     

Geometrically non-linear analysis of adhesively bonded modified double containment corner j oints - II

In this study, the geometrical non-linear analysis of an adhesively bonded modified double containment comer joint, which is presented as an alternative to previous comer joints, was carried out using the incremental finite element method based on the small strain-large displacement (SSLD) theory. The analysis method assumes the joint members such as the support, plates, and adhesive layers to have linear elastic properties. Since the adhesive accumulations (spew fillets) around the adhesive free ends have an important effect on the peak adhesive stresses, their presence was taken into account by idealizing them as triangular in shape. The joint was analysed for two different loading conditions: one load normal to the horizontal plate plane, P_y, and one load horizontal at the horizontal plate free edge, P_x. Finally, small strain-small displacement (SSSD) analysis of the joint was carried out and the results of both analyses were compared in order to determine the capability of the two theories in predicting the effects of large displacements on the stress and deformation states in the joint members. Both analyses showed that the peak stress values appeared at the slot comers inside the adhesive fillets and at the upper and lower longitudinal fibres (top and bottom longitudinal surfaces) of the horizontal and vertical plates corresponding to the horizontal and vertical slot free ends. In the case of the load P_y, the right vertical adhesive fillet and both plates were the most critical joint regions, whereas the lower horizontal fillet and both plates were determined to be the most critical regions for the load P_x. The SSLD theory predicted a non-linear effect on the variations of the displacement and stress components at these critical adhesive and plate locations for the load P_x, whereas the stress components at the critical adhesive locations presented variations very close to those determined by the SSSD theory for the load P_y, but this non-linear effect appeared on the displacement and stress variations at the critical locations of both plates. In addition, the SSSD theory predicted that the displacement and stress components would have lower variations proportional to the increasing load for both loading conditions. The stress and deformation states of all joint members are strictly dependent on the boundary and loading conditions. In addition, whereas the SSSD theory may be misleading for some loading conditions, the SSLD theory gives more realistic results, since it takes into account the non-linear effect of large displacements and rotations.     

Design and analysis of functionally graded adhesively bonded double supported tee joint of laminated FRP composite plates under varied loading

The present research deals with three-dimensional nonlinear finite element analyses for a functionally graded adhesively bonded tee joint made of laminated fiber reinforced polymeric composites when the tee joint is subjected to different types of loadings. The out-of-plane stress components have been evaluated along the interfacial surfaces of bond line of the tee joint. Using the stress values, the failure indices are computed by using Tsai–Wu coupled stress failure criterion in order to predict the location of onset of failures within the interfacial surfaces. Accordingly, critical location is identified based on the magnitude of failure indices for varied load conditions. It has been observed that tee joint under bending load is vulnerable for early failure compared with that when the joint is subjected to tensile and compressive loading. The location of failure is found to be different in tee joint under bending load compared with tensile and compressive loadings. Further, efforts have been made to reduce out-of-plane stress concentration by implementing functionally graded adhesive (FGA) with appropriate smooth and continuous gradation function profile. Further, effects of material gradation function profile with varied modulus ratios on out-of-plane stresses and failure indices are observed along the different interfacial surfaces. Series of numerical simulation result significant reduction in peak values failure index. Based on the present research findings, the FGA is recommended for higher and efficient joint strength. Results also exhibit delayed failure onset and improved structural integrity in the tee joint structure with the use of FGA material.     

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.     

Strength model of adhesive-bonded double-lap joints under cantilevered bending

The objective of this study was to develop mathematical relations for predicting the strength of adhesive-bonded double-lap joints under cantilevered bending. Based on the strength of composite materials theory, two models were proposed to predict the stress-strain distribution and vertical deflection of the laminates and the adhesive under this loading condition. The first model was based on the basic beam theory with the assumption that every cross section in a plane before bending remains plane after the bending load is applied. In the other model, a strain gap between each bonded surface is assumed. Based on the second model and the predicted peel failure mode, the effects of shear modulus of the adhesive, joint length, and adhesive thickness on the joint strength were evaluated. Scotchply composite laminates were used as the adherends of the double-lap joints in the experimental investigation. An Instron machine fitted with a special apparatus was used for conducting the experiments. By the attachment of strain gages to the adherends and through the use of a dial indicator, the theoretical models were verified experimentally.     

Progressive Failure Analysis in Adhesively,Riveted, and Hybrid Bonded Double-Lap Joints

One of the important processes in structural design is the joining technique. Failure of composite joints involves different failure mechanisms depending upon the joining technique. In this study, a progressive failure analysis was performed on adhesively, riveted, and hybrid bonded double-lap joints. In the joints, a woven-type fiberglass-reinforced composite material was used as the main material; AV 2015 was used as the adhesive, and steel as the rivet material. The analyses were performed using ANSYS 12.1 finite element package software via software written using parametric design language (APDL) codes. At the end of the progressive failure analysis, failure loads and failure modes were determined for 30-, 45-, and 60-mm overlap lengths in accordance with the Maximum Shear Stress Theory and Hashin Criteria. For 45-mm overlap lengths, the joint strength of hybrid joints proved to be 2.72 and 1.145 times higher, respectively, than adhesive and fastening joints. Results showed that the failure load of the joint increased when the overlap length increased. In riveted joints, the failure occurring in the composite plates began around the rivet hole and the catastrophic failure of these types of joints resulted from fiber tensile failure.     

Nonlinear Stress Analysis of an Adhesive Tubular Lap Joint

The analysis of adhesive bonded joints have been based, generally, on the assumption that the adhesive behaves as a linearly elastic material. Many adhesives, however, exhibit nonlinear stress-strain behaviour, particularly near failure. This article reports an attempt on the analysis of an adhesive tubular lap joint with the adhesive obeying a nonlinear stress-strain law. The Finite Element method has been employed for the solution.     

Geometric Factors Impacting Adhesive Lap Joint Strength and Design

Too often adhesive thickness, adherend thickness and other geometric factors are not explicitly considered in adhesive joint design. This study includes experimental and computational research exploring the means of enhancing the engineering design process for adhesive lap joints to include such effects. It clearly demon-strated that both the cleavage stresses and the shear stresses, near the bond termini, play important roles in lap 'shear' joint failure. Finite Element and Fracture Mechanics analyses were used to examine the energy release rate applied to growth of cracks in adhesive lap joints. Lap joints with similar geometries to those analyzed were designed, fabricated and tested. In a separate set of experiments the bond termini were constrained in the direction normal to the uniaxial loading. If the strength of lap shear joints is dominated by the adhesive shear strength, then constraining the lateral motion of the bond termini should have little or no effect on the overall shear strength of the adhesive joint. This work clearly demonstrates that this is not the case. If cleavage stresses are important in lap joints then constraining the bond termini, in a direction normal to the bond area, should have a commensurate effect on the overall strength of the lap joint. None of the ASTM standardized 'lap shear tests' provide any insight into this premise. This paper also presents analyses and experimental results for lap joints to which several methods of lateral constraint were applied near the bond termini. The analytical and numerical methods described and used for explaining and predicting such effects might be a useful adhesive joint design tool.     

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.