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.     

Adhesion failure propagation in adhesively-bonded single-lap laminated FRP composite joints

This paper deals with three-dimensional non-linear finite element analyses to study the behaviour of embedded adhesion failure propagation in adhesively-bonded single-lap laminated FRP composite joints clamped at one end and subjected to uniform extension at the other end. Because of loading eccentricity and joint material heterogeneity, the embedded adhesion failure is likely to initiate from the stress singularity points and will propagate from either end of the adhesive layer along the adherend–adhesive interfaces. The effects of interaction of such failures and their propagations along the interfaces of the adherends and adhesive are the main concerns of this paper. The peel and shear stresses have been computed along the mid-surface of the adhesive layer for varying adhesion failure lengths to find out the influence of adhesion failure length on the strength of the joint being analyzed. The concept of fracture mechanics has been used to calculate the strain energy release rate (SERR) as the adhesion failure propagates using the virtual crack closure technique (VCCT). It is seen that mode-II SERR is predominant in the propagation of such adhesion failures. The SERR values computed with respect to the adhesion failure lengths being propagated from the two ends of the adhesive layer are seen to be different.     

FEM stress analysis and strength of adhesive butt joints of similar hollow cylinders under static and impact tensile loadings

The stress wave propagations in butt adhesive joints of similar hollow cylinders subjected to static and impact tensile loadings are analyzed in elastic and elasto-plastic deformation ranges using the finite-element method (FEM). The impact loading is applied to the joint by dropping a weight. The upper end of the upper adherend is fixed and the lower adherend of which the lower end is connected to a guide bar is subjected to the impact loading. The FEM code employed is DYNA3D. The effects of the adhesive thickness and Young's modulus of the adhesive on the stress wave propagation at the interfaces are examined. In addition, the characteristics of the joints subjected to impact loadings are compared with those of the joints under static loadings and the joint strengths are estimated by using the interface stress distributions. It is found that the maximum value of the maximum principal stress, σ₁ occurs at the outside edge of the interface of the lower adherend to which the impact loading is applied. The maximum value of the maximum principal stress, σ₁ increases as Young's modulus of the adhesive increases when the joints are subjected to impact loadings. It is found that the characteristics of the joints subjected to impact loadings are opposite to those subjected to static loadings. In addition, experiments were carried out to measure the strain response of the butt adhesive joints subjected to impact and static tensile loadings using strain gauges and the joint strengths were also measured. Fairy good agreements are observed between the numerical and the measured results.     

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.     

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.     

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.     

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.     

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.     

Numerical analysis of the strength and interfacial properties of adhesive joints with graded adherends

The strength and interfacial behavior of single lap joints with graded adherends subjected to uniaxial tensile loading are investigated in the present paper. A bilinear cohesive zone model coupled with the finite element method is adopted to describe the damage and failure process of the adhesive layer. The peak loading, the rotation angle between the overlap of the joint and the horizontal direction, as well as the failure energy are investigated comprehensively. It is interesting to find that adopting different variation law in the graded adherends may result in varying strength of adhesive joints. By means of choosing proper material and geometry parameters of adhesive joints, the peak loading, the rotation angle and the failure energy of joints can be greatly improved. What is more, the strength of the SLJ is found to depend much more on the property of the soft part near the adhesive layer. The results should be helpful to guide the design of novel structures of adhesive joints in present and potential applications.     

Prediction of crack length and crack growth rate of adhesive joints by a piezoelectric method

As adhesive joints have been widely used for fastening thin adherends, the damage tolerance design of adhesive joints has become important, and the estimation of initiation and propagation of a fatigue crack in the adhesive has become necessary. However, the measurement of crack length of tubular joints has been difficult because the observation of crack initiation and growth in the adhesive layer by conventional methods is not easy. In this work, a prediction method for the fatigue crack length in the adhesive layer of tubular single-lap adhesive joints was developed by the piezoelectric method. In order to obtain the relationship between the fatigue crack length and the piezoelectric signal, finite element analysis was conducted and verified by experiments. The damage of the adhesive joints was monitored by the piezoelectric method during torsional fatigue tests on tubular single-lap adhesive joints. Using the damage monitoring signals and the relationship between the fatigue crack length and the piezoelectric signal, a method for predicting fatigue crack growth in the adhesive layer of tubular single-lap adhesive joints was developed.     

Fracture analysis in adhesive composite material/aluminum joints under mode-I loading; experimental and numerical approaches

Assessment and evaluation of fracture characteristics are very important in adhesive joint for achieving a safety mode. In this paper, fracture was investigated in mode-I in adhesive composite material/aluminum alloy joints. To achieve this aim, Double Cantilever Beam (DCB) was used to evaluate fracture in mode-I loading (opening). Bonding was realized by epoxy adhesive as one of the most important and widely used adhesives in aerospace and automotive industries. Modified Beam Theory (MBT) and Compliance Calibration Method (CCM) were formulated to calculate Strain Energy Release Rate (SERR). The obtained experimental results were verified by comparison with Finite Element (FE) analysis. FE results were derived from using Virtual Crack Closure Technique (VCCT) and J-integral approaches in two and three dimension (2-D & 3-D) simulation. Experiment tests and numerical analyses showed good agreement and demonstrated the effectiveness of the proposed experiment and numerical methods.     

Comparison of fracture behavior between acrylic and epoxy adhesives

An experimental study was conducted on the strength of adhesively bonded steel joints, prepared epoxy and acrylic adhesives. At first, to obtain strength characteristics of these adhesives under uniform stress distributions in the adhesive layer, tensile tests for butt, scarf and torsional test for butt joints with thin-wall tube were conducted. Based on the above strength data, the fracture envelope in the normal stress-shear stress plane for the acrylic adhesive was compared with that for the epoxy adhesive. Furthermore, for the epoxy and acrylic adhesives, the effect of stress triaxiality parameter on the failure stress was also investigated. From those comparison, it was found that the effect of stress tri-axiality in the adhesive layer on the joint strength with the epoxy adhesive differed from that with the acrylic adhesive. Fracture toughness tests were then conducted under mode l loading using double cantilever beam (DCB) specimens with the epoxy and acrylic adhesives. The results of the fracture toughness tests revealed continuous crack propagation for the acrylic adhesive, whereas stick-slip type propagation for the epoxy one. Finally, lap shear tests were conducted using lap joints bonded by the epoxy and acrylic adhesives with several lap lengths. The results of the lap shear tests indicated that the shear strength with the epoxy adhesive rapidly decreases with increasing lap length, whereas the shear strength with the acrylic adhesive decreases gently with increasing the lap length.     

Effects of applied pressure and temperature during curing operation on the strength of tubular single-lap adhesive joints

Adhesive joints have been widely used for fastening thin adherends because they can distribute the load over a larger area than the mechanical joint, require no holes, add very little weight to the structure and have superior fatigue resistance. However, the load capabilities of adhesive joints are affected by both applied pressure and temperature during cure, as well as by service environments because the adhesion characteristics of adhesives are very sensitive to manufacturing and environmental conditions. In this study, the tensile load capabilities of tubular single-lap adhesive joints with an epoxy adhesive were experimentally investigated with respect to service temperature and the applied pressure and temperature during curing operation. The effects of the applied pressure on the tensile load capabilities of tubular single-lap adhesive joints were studied by measuring the actual cure finish temperature using thermocouples and dielectrometry. From the experiments, it was found that the actual cure finish temperature of tubular single-lap adhesive joints increased as applied pressure increased, which increased residual thermal stress in the adhesive layer to decrease the load capabilities of adhesive joints. From finite element analysis and experimental results of tubular singlelap adhesive joints, the optimal geometry condition for adhesive joints was also investigated.     

Numerical Study of Adhesive Single-Lap Joints with Composite Adherends Subjected to Combined Tension–Torsion Loads

The present investigation focuses on modifying the strength of single-lap adhesively bonded joints under tension–torsion loading with the use of three-dimensional finite element (FE) modeling. A single-lap adhesively bonded joint is reinforced by fibers and analyzed by means of ABAQUS-6.9.1 FE code. The adherends are considered to be made of orthotropic materials, while the adhesive is neat resin or reinforced by various types of fibers. The carbon and glass unidirectional fibers are used for adhesive reinforcement. In the FE modeling, the behavior of all the members is assumed to be linear elastic. The ultimate bond strength is increased as the fiber volume fraction in the adhesive is increased. By changing the properties and the behavior of the adhesive from neat resin (isotropic) to fiber composite adhesive (orthotropic) and with various fiber volume fractions and by changing the orientation of the fibers in the adhesive region with respect to the global axes, the bond strength in tension–torsion loadings are changed. Also, the excessive adhesive layer is modeled and its effect on the joint strength is investigated.     

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.     

Dynamic compressive creep behaviour of structural silicone-to-aluminum and silicone-based sealant-to-aluminum joints

This paper outlines an experimental study on the static and dynamic compressive creep behaviour of structural silicone adhesively bonded joints. The silicone adhesives are subjected to dynamic compressive loading, which is a common case for structural façade and hybrid glazing system. Typical crack propagation of adhesives, relations between compressive load (stress) and displacement (creep strain) are examined experimentally. It is shown that the test specimen with adhesives featured by lower hardness and higher elongation at break exhibit notable crack distribution concentrated in the middle of the crack surface. The compressive behaviour consists of three regions as initial elastic, nonlinear transition and post linear, in which the latter has notable strength increase with the increase of compressive deformation. The secant compressive modulus are measured based on compressive stress and creep strain relations. It is demonstrated that the joint has higher secant compressive modulus due to less crack propagation. All test joints exhibit significant degradation of strength and energy absorption, which can be well fitted in similar exponential forms with normalized cycle numbers for test joints with different adhesives.     

The Strength of Joints Combining an Adhesive with a Bolt

In this paper, discussion is made on the strength of joints combining adhesives with bolts. The stress distributions in adhesives and the variation in bolt axial force are analyzed when an external load is applied to the combination joint. The joint consists of two hollow cylinders clamped by a bolt and a nut with an initial clamping force after they are joined by an adhesive. The analytical result is almost consistent with the experimental result, therefore the strength of the combination joints can be estimated. The strength of the combination joint is greater than that of the adhesive joint. In addition the variation in bolt axial force in the combination joint is less that that in the bolted joint. The characteristics and the availability of combination joints are made clear.     

Experimental analysis of the behavior of adhesively bonded joints under tensile/compression–shear cyclic loadings

Adhesive bonding is an interesting structural assembling technique which requires accurate numerical models in order to optimize the design of high-tech applications. In this paper, following the strategy previously developed for monotonic loadings, crack initiation in adhesively-bonded joints, under various tensile/compression–shear cyclic loadings is analyzed using a modified Arcan device with a single bonded joint designed to strongly limit stress concentrations. Moreover, such a system is associated with the maximum stress state in the center of the adhesive, and thus, allows the analysis of some influences of the stress triaxiality. Experimental results, for a ductile adhesive, under cyclic loadings are presented for different load amplitudes and mean loads; they underline that the evolutions of viscous deformations and of damage depend on the loading type.     

Through-the-width delamination damage propagation characteristics in single-lap laminated FRP composite joints

Three-dimensional non-linear finite element analyses have been carried out to study the effects of through-the-width delaminations on delamination damage propagation characteristics in adhesively bonded single-lap laminated FRP composite joints. The delaminations have been presumed either to pre-exist or to get evolved due to coupled stress failure criteria in the laminated FRP composite adherends near the overlap ends beneath the ply adjacent to the overlap region. The out-of-plane stresses in the adhesive layer, the interlaminar stress distributions along the delamination fronts and the strain energy release rates (SERRs) corresponding to the three individual modes have been evaluated for varying positions of the delaminations pre-embedded in either of the adherends. A good matching between the present 3D results and experimental and analytical solution of the literature has been established for the undamaged and a damaged model. A significant difference in the interlaminar stresses and the SERR values has been observed and is largely dependent on the adherends (bottom or top) possessing the through-the-width delamination damages. Also, the interlaminar stresses and SERR values along the two corresponding delamination fronts are different. Accordingly, it can be concluded that the positions of the through-the-width delaminations significantly influence the delamination damage propagation behaviour vis-a-vis the performance of the composite joint.