Development of a Fatigue Failure Model for the Adhesively Bonded Tubular Single Lap Joint under Dynamic Torsional Loading

The adhesively bonded tubular single lap joint shows nonlinear torque transmission capability and deformation characteristics under static torsional loading because of nonlinear properties of the adhesive. However, the dynamic or fatigue torque transmission capability can be calculated with linear, analysis because the stress-strain relation under torsional fatigue loading is linear, due to the small dynamic transmission capability compared with the static torque transmission capability.

In this paper, a failure model for the adhesively bonded tubular single lap joint under torsional fatigue loading was developed with respect to the adhesive thickness, which is the critical factor for the static torque transmission capability. Also, a design method for the adhesively bonded tubular single lap joint under torsional fatigue loading was proposed.     

Development of a Fatigue Failure Model for the Adhesively Bonded Tubular Single Lap Joint under Dynamic Torsional Loading

The adhesively bonded tubular single lap joint shows nonlinear torque transmission capability and deformation characteristics under static torsional loading because of nonlinear properties of the adhesive. However, the dynamic or fatigue torque transmission capability can be calculated with linear, analysis because the stress-strain relation under torsional fatigue loading is linear, due to the small dynamic transmission capability compared with the static torque transmission capability.

In this paper, a failure model for the adhesively bonded tubular single lap joint under torsional fatigue loading was developed with respect to the adhesive thickness, which is the critical factor for the static torque transmission capability. Also, a design method for the adhesively bonded tubular single lap joint under torsional fatigue loading was proposed.     

Effects of adhesive fillers on the strength of tubular single lap adhesive joints

When an adhesively bonded joint is exposed to a high environmental temperature, the tensile load capability of the adhesively bonded joint decreases because the elastic modulus and failure strength of the adhesive decrease. In this paper, the elastic modulus and failure strength of the adhesive as well as the tensile load capability of the tubular single lap adhesively bonded joint were experimentally and theoretically investigated with respect to the volume fraction of filler and the environmental temperature. Two types of fillers - Al₂O₃ (alumina) and chopped fiber E glass - were used. From the experiment, it was found that the elastic modulus and failure strength of the adhesive increased in accordance with the increase of volume fraction of the filler and decreased with the environmental temperature rise. It was also found that the tensile load capability of the tubular single lap adhesively bonded joint decreased as the environmental temperature increased; however, it had no correlation with the volume fraction of filler because of the effect of the fabrication thermal residual stresses generated by the CTE difference between the adherend and adhesive.     

Optimization of smart adhesively bonded single-strap composite joint

In order to reduce the stress concentration and improve the failure strength of adhesively bonded joint structures, a smart adhesively bonded joint structure has been developed by integrating piezoelectric layers into the adherends. For better design guide, a combined theoretical model and multi-objective optimization approach is employed to optimize the smart joint in this study. Firstly, the first-order shear deformation theory is utilized to model and analyze the detailed peel and shear stresses distribution in the adhesive layer. Further, considering the characteristics of the stress distribution, the interface debonding failure criterion is used to set up the objective; optimization variables are considered as the stacking sequence, geometries and applied electric fields of the integrated piezoelectric layer. Thus, with the aid of the Mathematica software, the optimal smart adhesively bonded joint system can be determined. Finally, some detailed examples are analytically solved to show the considerable difference between the preoptimized and optimized smart joint systems, which validate that the developed theoretical model and multi-objective optimization approach can be used to enhance adhesively bonded joint failure strength.     

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.     

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 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.     

Effects of Different Curvature Patches on the Strength of Double-Strap Adhesive Joints

In general, the damage in adhesively bonded joints initiates from and propagates through the ends of the overlap area due to high stress concentration in that area. The reduction of these stress concentrations results in an increase in the strength of the joints. For this reason, the rounding of the overlap region before bonding and then applying compression during the bonding process will exert compressive residual stresses on the adhesive layer in the overlap end regions. It is known that the residual stresses formed in this process increase the failure strength of the joint and hence delay the initiation of the damage.

In this study, the effects of overlap length (L = 50,75, and 100 mm), patch thickness (h = 1.6, 3.2, and 5 mm) and patch materials (AA2024 aluminum alloy, AISI 304 steel, AISI 1040 steel) on bond strength were experimentally investigated for adhesively bonded double-strap joint (DSJ) and curvature double-strap joint (CDSJ) subjected totensile loading. The experimental study showed that the overlap length, patch thickness and patch materials have considerable influence on the failure strength and displacement capacity of the joints.     

Solvent stress cracking and failure mechanisms in polyetherimide composites

Solvent stress cracking studies have been carried out in o-xylene and other solvents on polyetherimide (PEI) based materials including neat resin, woven fabric composites, and adhesively bonded systems. The results show crack growth in solvents at very low G_I levels as compared with tests in air. The composite and adhesively bonded systems have sufficiently high residual thermal stresses to drive an array of intersecting matrix/adhesive cracks even without mechanical loading. The matrix/adhesive residual stress driven crack patterns in these systems are shown to retard main delamination crack growth relative to that in the neat resin, and to raise the applied threshold G₁ level for main crack growth by about a factor of ten, as predicted by an approximate model.     

Stress analyses of composite tee joints at elevated temperature

Thermal–structural coupling nonlinear finite element analyses are conducted in this paper to determine three-dimensional stresses of a composite tee joint, which is formed when a right angled plate is adhesively bonded to a base plate at elevated temperature. The von-Mises stresses of the adhesive layer of the tee joint with three different laminate stacking sequences viz. unidirectional [0]₈, cross-ply [(0/90)_s]₂, and angle-ply [(+45/?45)_s]₂ laminates have been evaluated when the tee joint is subjected to an out-of-plane loading through the right angled plate in addition to an elevated temperature applied at the undersurface of the base plate. The effects of laminate stacking sequence and temperature on von-Mises stresses have been investigated in this paper. The effects of the coefficient of thermal expansion and thermal conduction of the adhesive layer on von-Mises stresses have also been studied. Conclusions about the stresses of the composite tee joint with different stacking sequence, different coefficient of thermal expansion, and different thermal conduction of the adhesive layer are drawn.     

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.     

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.     

Observations in the structural response of adhesive bondline defects

In terms of adhesively bonded repairs there are two main concerns with regard to structural integrity. These are the effect of debonds and weak bondlines on the load transfer and durability of the joint. The influence of load transfer depends on the stiffness of the bondline. When this is degraded the out-of-plane deformation of the joint will be modified locally. Observation of the out-of-plane deformation is a key in the identification of weakened bondline and represents an indication that either poor surface preparation or aging effects have occurred. Holographic interferometry has been used to better understand the structural response of bondline defects, both debonds and weak bonds. The interferogram fringe patterns show the structural response and indicate whether the bondline has been broken or is weakly bonded. The significance of this observation is that weak bonds do affect the structural load response of the bondline in a number of ways. This effect is due to the reduction in bondline stiffness.     

Development of a Failure Model for the Adhesively Bonded Tubular Single Lap Joint

The accurate calculation of the stresses and torque capacities of adhesively bonded joints is not possible without understanding the failure phenomena of the adhesive joints and the nonlinear behavior of the adhesive.

In this paper, an adhesive failure model of the adhesively bonded tubular single lap joint with steel-steel adherends was proposed to predict the torque capacity accurately.

The model incorporated the nonlinear behavior of the adhesive and the different failure modes in which the adhesive failure mode changed from bulk shear failure, via transient failure, to interfacial failure between the adhesive and the adherend, according to the magnitudes of the residual thermally-induced stresses from fabrication.     

Finite Element Based Design and Adhesion Failure Analysis of Bonded Tubular Socket Joints Made with Laminated FRP Composites

This paper deals with Finite Element Analysis of bonded Tubular Socket Joints (TSJs) made with laminated Fibre Reinforced Plastic (FRP) composite structures. The effective coupling length for suitable performance of the joint is determined based on the Tsai–Wu failure criterion. The analysis revealed the three-dimensional nature of the stresses and are found to be concentrated in the close vicinity of the free edges and junction of the adherends in the coupling region of the bonded TSJ. Shear stress ( τ_r ), though comparatively small in magnitude, is found to be extremely sensitive to three-dimensional effects as compared to stresses τ_zr and σ_r . Failure indices at different critical interfaces are determined using Quadratic Failure Criterion (QFC) within the adhesive and Tsai–Wu coupled stress criterion for the adherend–adhesive and socket–adhesive interfaces. Based on the latter criterion, locations prone to adhesion failure initiation are identified to be existing near the free edges of the adherend–adhesive interfaces in the coupling region of the bonded TSJ. Strain Energy Release Rate (SERR) calculated using Modified Crack Closure Integral (MCCI) vis-à-vis Virtual Crack Closure Technique (VCCT) has been used as the characterizing parameter for assessing the growth of adhesion failures. The adhesion failure damages have been observed to propagate at the same rate in a self-similar manner mainly in the in-plane shearing mode. Quasi-isotropic and angle-ply orientations of the FRP composite laminates are more resistant to opening mode growth of failure, whereas cross-ply and unidirectional oriented socket/adherends offer better resistance to in-plane shearing mode of adhesion failure damage growth. Plies oriented in the direction of the applied load, especially Graphite/Epoxy (Gr/E) [90]₁₆, are found to offer the best resistance to all types of adhesion failure growth modes and hence are the most preferred fibre orientations for the bonded TSJ under tension. Increasing the degree of anisotropy of the composite socket/adherends improves the adhesion failure damage growth resistance of the bonded TSJ. Boron/Epoxy (B/E) FRP composites are found to be the best in slowing down the growth rate of the adhesion failures among the various FRP composite socket/adherends considered in the present study.     

Experimental study of adhesively bonded CFRP joints subjected to tensile loads

The tensile performance of adhesively bonded CFRP joints has been investigated experimentally. In this study, overlap length, adherend thickness, adherend width and scarf angle were chosen as design parameters. All load–displacement curves are linear, except that the thicker single-lap joints behave slightly nonlinearity due to the bending effect caused by eccentric loading. The lap shear strength is not directly proportional to overlap length, adherend thickness, adherend width and scarf angle for the brittle adhesive studied in the paper. The major failure mode includes adhesive shear failure and adherend delamination failure, sometimes accompanying with some fiber pull-out. Finally, the lap shear strength of three different lap types with similar bonding area (W=25 mm, L=10 mm, θ=5.71°) and adherend thickness (0.96 mm) was analyzed. It is found that the double-lap joint has the highest ultimate failure load. However, when considering the lap region weight, the scarf-lap joint is the most efficient.     

A Study of the Pull‐Out Performance of PPTA Fibres in Composites of Ethylene‐Type Ionomer Matrices/PPTA Fibres

The mean frictional shear stresses of six ionomer resins and sized Kevlar fibre were determined from fibre pull‐out tests. A study of the failure mechanisms occurring during pull‐out revealed that fibre delamination and fibre resin adhesion were factors which increased the measured frictional shear stresses and that there was a definite grouping of high and low frictional shear stress values. The low frictional shear stress values were used to calculate the mean frictional shear stress values, τ_B, because these were uncomplicated by fibre delamination and fibre resin adhesion, since these factors (delamination and adhesion) are certainly not unexpected in an ionomer/Kevlar composite. From these shear stress values, it was determined that critical fibre lengths should be between 35 and 72 mm for the high tensile strength Kevlar fibres within an ionomer matrix, for the composite to be used effectively. The ratio of the debonding force (F_B) to the frictional shear force (F_F), θ, did not vary significantly with the lengths of the embedded reinforcing fibres. Both debonding and frictional forces indicate increasing trends with the interfacial contact areas. The ratio of the interfacial bonding strength (τ_B) to the frictional shear stress (τ_F), ϕ, for the resin PEA‐6 compared to the surface modified poly(p‐phenylene terephthalamide) (PPTA) fibre ranged from 2 to 24. These ratios were grouped into two, viz: those where ϕ > 11 and those with ϕ < 7. Using only the τ_F where ϕ > 11 provided a mean frictional shear stress of 0.94 MPa and a standard deviation, s, of 0.23 MPa (the number of test samples, n, was 9). This value is little different from the frictional shear stresses measured for sized PPTA (0.84 MPa). The decrease in the values of ϕ is attributed to the decrease in τ_B, due to the surface modification reaction, without necessarily affecting the frictional shear stress, τ_F.     

An analytical model for interfacial stresses in double-lap bonded joints

Due to their many advantages, adhesively bonded joints are widely used to join components in composite structures. However, premature failure due to debonding and peeling of the joint is the major concern for this technique. Existing analytical models suffer from two major drawbacks: 1) not satisfying zero-shear stress boundary conditions at the adhesive layer’s free edges^[1] and 2) failure to distinguish the peel stress along two adherend/adhesive interfaces^[2]. In this study, we develop a novel three parameter elastic foundation (3PEF) model to analyze a representative adhesively bonded joint, the symmetric double-lap joint, which is believed to have relatively low peel stresses. Explicit closed-form expressions of shear and peel stresses along two adhesive/adherend interfaces are yielded. This new model overcomes the existing model’s major drawbacks by satisfying all boundary conditions and predicting various peeling stresses along two adherend/adhesive interfaces. It not only reaches excellent agreement with existing solutions and numerical results based on finite element analysis but also correctly predicts the failure mode of an experimentally tested double-lap joint. This new model therefore reveals the peel stresses’ significant role in the failure of the double-lap joint, but the classical 2PEF model cannot create it.     

Ageing of adhesively bonded joints—fracture and failure analysis using video imaging techniques

An investigation into the durability of adhesively bonded joints has been undertaken to help improve the prediction of joint lifetimes. Polymethylmethacrylate (PMMA) substrates have been bonded with a two-part acrylic adhesive to make single lap-shear joints. Joints have been aged in a hot/wet environment (40°C and 95% humidity) with no applied stress for up to 4000 h and were tested in tension. The novel aspect of the research has been the development of a video imaging analysis technique which allows damage initiation and propagation within the joint to be detected as load is applied to the joint. Images of fracture initiation and damage propagation have been correlated with stress/displacement data for joints under tensile loading. The data from aged samples is compared with data from un-aged samples. Both the stresses at which damage is seen to initiate and the final failure stress of the joints decrease as the ageing time increases. The failure mode changes from cohesive failure within the PMMA substrate to failure within the adhesive, near the PMMA/acrylic adhesive interface.     

Experimental and numerical investigations of adhesively bonded CFRP single-lap joints subjected to tensile loads

In this study, both experimental tests and numerical simulation are implemented to investigate the tensile performance of adhesively bonded CFRP single-lap joints (SLJs). The study considers 7 different overlap lengths, 5 adherend widths and 3 stacking sequences of the joints. Three-dimensional (3D) finite element (FE) models are established to simulate the tensile behavior of SLJs. The failure loads and failure modes of SLJs are investigated systematically by means of FE models and they are in good agreement with those of experiments, proving the accuracy of finite element method (FEM). It is found that increasing the adherend width can improve the load-carrying capacity of the joint better than increasing the overlap length does. Moreover, choosing 0° ply as the first ply is also beneficial for upgrading joint's strength. With respect to failure modes, cohesive failure in adhesive and delamination in adherend take dominant, while matrix cracking and fiber fracture only play a small part. With overlap length increasing or adherend width decreasing, cohesive failure takes up a smaller and smaller proportion of whole failure area, but the opposite is true for delamination. SLJs bonded with [0/45/-45/90]_3S adherends are prone to cohesive failure, and [90/-45/45/0]_3S adherends are easy to appear delamination. Both shear and peel stress along the bondline indicate symmetrical and non-uniform distributions with great stress gradient near the overlap ends. As the load increases, the high stress zone shifts from the end to the middle of the bondline, corresponding to the damage initiation and propagation in the adhesive layer.