The use of the exponential Drucker-Prager material model for defining the failure loads of the mono and bi-adhesive joints

In this study, our previous experimental study was extended applying the exponential Drucker-Prager (EDP) yield criterion to define the numerical failure loads for mono and bi-adhesive single lap joints (SLJs) [Öz and Özer, 2016]. Bi-adhesive (or hybrid adhesive) joint is an alternative stress-reduction technique for adhesively bonded lap joints. The joints have two adhesives with different moduli in the overlap region. Non-linear finite element analyses were carried out for mono and bi-adhesive joints implementing the EDP material model. Distributions of EDP maximum principal stress, equivalent stress and shear stress were obtained along the middle of the adhesive thickness. Numerical failure loads were compared with our previous experimental failure loads. In addition, hydrostatic stress and equivalent plastic strain distributions for these joints under the failure loading were obtained. The general results show that experimental and numerical failure loads were in a good agreement. As a result, when bond-length ratios are selected properly and appropriate adhesives are used along the overlap length, the strength of bi-adhesive joints, compared to mono-adhesive joints, was found to increase considerably.     

Stress analysis and strength evaluation of bonded shrink fitted joints subjected to torsional loads

This paper deals with the stress analysis and strength evaluation of bonded shrink fitted joints subjected to torsion. The stress distributions in the adhesive layer of bonded shrink fitted joints are analyzed by the axisymmetric theory of elasticity when an external torsion is applied to the upper end of the shaft. The effects of the outer diameter and the stiffness of rings on the interface stress distributions are clarified by numerical calculations. Using the interface stress distributions, the joint strength is predicted. In addition, the joint strength was measured experimentally. It is seen that rupture of the adhesive layer is initiated from the upper edge of the interface when torsion is applied to the upper end of the shaft. The numerical results are in fairly good agreement with the experimental results. It was found that the joint strength of bonded shrink fitted joints is greater than that of shrink fitted joints.     

Mechanical behaviour of thick structural adhesives in wind turbine blades under multi-axial loading

Wind turbine blades are made of integrated composite parts bonded together using structural adhesives. The blades are among the most severely multi-axial fatigue loaded structures and the bonded joints play an important role in their structural integrity. For better understanding of the mechanical performance of the bonded joints, thorough knowledge is required on the multi-axial behaviour of the bulk adhesive. In this study, tubular specimens consisting of glass/epoxy bonding paste were subjected to uniaxial (tension, compression and torsion) and biaxial (tension–torsion and compression–torsion) static tests. Different biaxial ratios were used and the stress–strain responses were recorded using strain-gauges. The imposed biaxial stress ratios influenced the stress–strain behaviour of the material system, especially the compression and the shear stress–strain. A material model was developed based on the experimental observations taking into account the non-linear behaviour and the effects of the biaxial ratios and it was implemented together with a progressive damage scenario into a finite-element model. The experimental failure patterns were compared with the numerical simulations and a good match was found.     

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.     

STRENGTH OF ADHESIVE JOINTS WITH ADHEREND YIELDING: I. ANALYTICAL MODEL

A sandwich element can be isolated in all two-dimensional adhesive joints, thereby simplifying the analysis of strain and stress. An adhesive sandwich model has been developed that accommodates arbitrary loading, a bilinear adherend stress-strain response, and any form of nonlinear adhesive behavior. The model accounts for both the bending deformation and the shear deformation of the adherends. Stress and strain distributions in the adhesive were obtained by solving a system of six differential equations using a finite-difference method. For a sample adhesive sandwich, the adhesive strains and stresses from the new model were compared with those of other models. Finally, the model was coupled with an analytical solution for the detached section of an adhesive joint in peel. The stress and strain distributions in the adhesive and the root curvature of the peel adherend were then compared with finite element results. An accompanying article in this issue uses the model with experimental peel data to investigate the suitability of various adhesive failure criteria.     

Strength of adhesive joints with adherend yielding: I. Analytical model

A sandwich element can be isolated in all two-dimensional adhesive joints, thereby simplifying the analysis of strain and stress. An adhesive sandwich model has been developed that accommodates arbitrary loading, a bilinear adherend stress-strain response, and any form of nonlinear adhesive behavior. The model accounts for both the bending deformation and the shear deformation of the adherends. Stress and strain distributions in the adhesive were obtained by solving a system of six differential equations using a finite-difference method. For a sample adhesive sandwich, the adhesive strains and stresses from the new model were compared with those of other models. Finally, the model was coupled with an analytical solution for the detached section of an adhesive joint in peel. The stress and strain distributions in the adhesive and the root curvature of the peel adherend were then compared with finite element results. An accompanying article in this issue uses the model with experimental peel data to investigate the suitability of various adhesive failure criteria.     

A Stress Analysis of Adhesive Butt Joints of Dissimilar Materials Subjected to Cleavage Loads

Stress distributions are examined when an adhesive butt joint, in which two thin plates made of dissimilar materials are joined, is subjected to cleavage loads. General representations of the stress and displacement fields are given using the two-dimensional theory of elasticity. The effects of the ratios of young's modulus among two adherends and an adhesive and the thickness of the adhesive on the stress distributions of the joints are clarified by numerical calculations. In addition, the stress singularity near the edge of the interface in the load application side is evaluated. For verification, the strain distributions near the interface of each adherend were measured. The analytical results are closely consistent with the experimental ones.     

Adhesively bonded steel tubes – Part II: Numerical modelling and strength prediction

Capacity prediction of adhesively bonded joints remains challenging; this is particularly true for tubular joints composed of circular hollow sections used in civil engineering. This paper extends its companion paper, which presented experimental results of a large research campaign on full-scale tubular joints, with the aim to develop a dimensioning method. Firstly, experiments were designed to quantify the strength of the adhesive-steel connection; the results thereof were cast into the formulation of an adequate failure criterion, for each of the adhesives considered. Secondly, numerical models of all investigated joint configurations were established, from which the stress-state inside the bonded connection could be determined. A series of analyses clearly showed that stress magnitude and joint capacity did not correlate, thus indicating that a direct stress based methodology is destined to fail. Accordingly, a probabilistic method that is based on the concept of size effects was developed, and implemented. It allowed not only determining average values for joint capacities, but also estimated the expected experimental scattering thereof. The validity of the approach was tested by successfully comparing experimental and computed joint capacities.     

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.     

A two-dimensional stress analysis and strength evaluation of band adhesive butt joints subjected to tensile loads

The stresses in band adhesive butt joints, in which two adherends are bonded partially at the interfaces, are analyzed, using a two-dimensional theory of elasticity, in order to demonstrate the usefulness of the joints. In the analysis, similar adherends and adhesive bonds, which are bonded at two or three regions, are, respectively, replaced by finite strips. In the numerical calculations, the effects of the ratio of Young's moduli for adherends to that for adhesives, the adhesive thickness, the bonding area and position, and the load distribution are shown on the stress distributions at interfaces. It is seen that band adhesive joints are useful when the bonding area and positions are changed with external load distributions. Photoelastic experiments and the measurement of the adherend strains were carried out. The analytical results are in a fairly good agreement with the experimental results. In addition, a method for estimating the joint strength is proposed by using the interface stress distribution obtained by the analysis. Experiments concerning joint strength were performed and fairly good agreement is found between the estimated values and the experimental results.     

Strength prediction of epoxy adhesively bonded scarf joints of dissimilar adherends

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

Three-dimensional stress analysis of adhesive butt joints with disbonded areas and spew fillets

This paper deals with three-dimensional stress analysis of adhesive butt joints subjected to tensile loads, to help establish fracture criteria. In this analysis, the adherends and adhesive bond are replaced with finite solid culinders. Stress distributions in adhesive joints are analysed using a three-dimensional theory of elasticity. The effects of a disbonded area and a spew fillet on the principal stress distributions are shown by numerical calculation. Where a joint has a disbonded area, the stress singularity increases with a decrease in the diameter of the spew fillet, and the stress singularity decreases with an increase in the diameter of the adhesive. The analytical result is compared with that obtained by an experiment concerning the strain produced on the adherends in the case of a disbonded area. Both results are satisfactorily consistent.     

Strength Degradation of Adhesively Bonded Single-Lap Joints in a Cyclic-Temperature Environment Using a Cohesive Zone Model

Adhesively bonded joints are widely used in automotive industry. Adhesively bonded joints permit to have more uniform stress distributions, join complex shapes, and reduce the weight of the structures. The requirement to reduce the weight of automobiles is also increasing the application of composites. In this article, CFRP (carbon fiber-reinforced plastics) composite was used in experimental tests. In many cases, adverse environments cause non-negligible degradation in joints mechanical performance. So a combined experimental–numerical approach was developed to characterize the effect of cyclic-temperature environment on adhesively bonded joints. Experimental tests were carried out on single-lap joints with CFRP and steel adherend in a cyclic-temperature environment. A cohesive zone model was taken into consideration to predict the results observed during the experimental tests and an environmental degradation model was developed. Scanning electron microscopy was utilized to investigate the fracture surfaces.     

Analytical solutions for adhesively bonded composite single-lap joints under mechanical loadings using full layerwise theory

In this paper, analytical solutions for adhesively bonded composite single-lap joints (SLJs) are presented within the framework of the full layerwise theory (FLWT). The adhesively bonded composite SLJ is divided into a large number of mathematical plies through the thickness and three regions along its length. The equilibrium equations of each region are obtained using the principle of minimum total potential energy. The three sets of fully-coupled governing equations then are simultaneously solved by introducing the state space variables. The effects of adhesive thickness and loading conditions including uniaxial tension and bending moment on the interfacial peel and shear stress as well as the von Mises stress distributions along the length and through the thickness of the adhesive layer are studied. The present results, which are verified via analytical, experimental, and numerical investigations available in the literature, can be introduced as scaling solutions to verify the authenticity of other methods.     

Non-linear Modeling of Tubular Adhesive Scarf Joints Loaded in Tension

In this paper, a simple analytical model is developed to determine the adhesive shear strain distribution of a tubular adhesive scarf joint loaded in tension. The approach is an extension of the original well-recognized Volkersen's shear lag analysis for a shear loaded joint, which is frequently applied to adhesively-bonded joints. A mathematical representation consisting of linear and exponential functions is employed to model the elastic-plastic behavior commonly observed in structural adhesives. The governing equation is found to be in the form of a non-linear second-degree ordinary differential equation with variable coefficients. A numerical method required for solving this equation is also introduced. Numerical predictions of shear strain distributions are compared with results from non-linear Finite Element Analysis (FEA), utilizing the commercially available software, ANSYS 5.6, a general-purpose software system. It is shown that both the linear and non-linear approximate solutions are closely comparable with the FEA results for a 10°-scarf angle and elastic isotropic adherends. In concurrence with previous work on flat adherends, the present work demonstrates that the scarf joint develops more uniform shear stress and strain distributions with a consequent reduction in peak values than those for the conventional lap joint. In contrast, the conventional lap joint with the equivalent bonded surface area experiences a more substantial elastic trough, which can provide a more stable configuration for, sustained long term loading applications.     

Non-linear Modeling of Tubular Adhesive Scarf Joints Loaded in Tension

In this paper, a simple analytical model is developed to determine the adhesive shear strain distribution of a tubular adhesive scarf joint loaded in tension. The approach is an extension of the original well-recognized Volkersen's shear lag analysis for a shear loaded joint, which is frequently applied to adhesively-bonded joints. A mathematical representation consisting of linear and exponential functions is employed to model the elastic–plastic behavior commonly observed in structural adhesives. The governing equation is found to be in the form of a non-linear second-degree ordinary differential equation with variable coefficients. A numerical method required for solving this equation is also introduced. Numerical predictions of shear strain distributions are compared with results from non-linear Finite Element Analysis (FEA), utilizing the commercially available software, ANSYS 5.6, a general-purpose software system. It is shown that both the linear and non-linear approximate solutions are closely comparable with the FEA results for a 10°-scarf angle and elastic isotropic adherends. In concurrence with previous work on flat adherends, the present work demonstrates that the scarf joint develops more uniform shear stress and strain distributions with a consequent reduction in peak values than those for the conventional lap joint. In contrast, the conventional lap joint with the equivalent bonded surface area experiences a more substantial elastic trough, which can provide a more stable configuration for, sustained long term loading applications.     

On the von Mises elastic stress evaluations in the bi-adhesive single-lap joint: a numerical and analytical study

Bi-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 the flexible adhesive at the ends. This study is the extension of our previous paper to the von Mises stress evaluation and discusses the values and importance of the von Mises stresses in the bi-adhesive single-lap joint. Both analytical and numerical analyses were performed using three different bi-adhesive bondline configurations. The Zhao’s closed form (analytic) solution used includes the bending moment effect. In the finite element models, overlap surfaces of the adherends and the adhesives were modeled using surface-to-surface contact elements. The contribution levels of the peel and shear stresses for producing a peak von Mises stress are also studied. It is concluded that the contribution level of the shear stress at where von Mises stress becomes peak is more than that of the peel stress. Joint strength analyses were performed based on the peak elastic von Mises stresses. It is seen that joint strength can be increased using bi-adhesive bondline. The analytical and numerical results show that the appropriate bond-length ratio must be used to obtain high joint strength.     

Parametric study of adhesive joints with composites

Adhesively-bonded joints are increasingly used in aeronautical industry. Adhesive joints permit to join complex shapes and reduce the weight of structures. The need to reduce the weight of airplanes is also increasing the use of composites. Composites are very anisotropic: in the fibre directions, unidirectional composites can be very strong and stiff, whereas the transverse and shear properties are much lower. Bonded joints experience peel loading, so the composite may fail in transverse tension before the adhesive fails. That is why it is important to study these joints and try to find reliable ways to predict the strength of joints with composite adherends. The main goal of this study was to understand the failure in adhesive joints with composites, bonded with adhesives with different characteristics, and find reliable ways to predict them. Experimental tests were carried with single lap joints with composite adherends and different adhesives, brittle and ductile, with several overlap lengths. A Cohesive Zone Model (CZM) was taken into consideration to predict the results observed during the experimental tests. The experimental results were also compared with simple analytical models and the suitability of each model was evaluated for each bonded system.     

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.     

Comparison of Analytical, Numerical, and Experimental Methods in Deriving Fracture Toughness Properties of Adhesives Using Bonded Double Lap Joint Specimens

Stress and fracture analysis of bonded double lap joint (DLJ) specimens have been investigated in this paper. Numerical and analytical methods have been used to obtain shear- and peel-stress distributions in the DLJ. The generalized analytical solution for the peel stress was calculated for various forms of the DLJ geometry and, by using crack closure integral (CCI) and by means of the J-integral approach, the analytical strain energy-release rate, G, was calculated. Experimental fracture tests have also been conducted to validate the results. The specimens were made of steel substrates bonded by an adhesive and loaded under tension. Specimens with cracks on both sides and at either end of the DLJ interface were tested to compare the fracture behavior for the two crack positions where tensile and compressive peel stresses exist. Tests confirmed that the substrates essentially behave elastically. Therefore, a linear elastic solution for the bonded region of the DLJ was developed. The fracture energy parameter, G, calculated from the elastic experimental compliance for different crack lengths, was compared with numerical and analytical calculations using the experimental fracture loads. The stresses from analytical analysis were also compared with those from the finite element results. The strain energy-release rate for fracture, G_f, for the adhesive has been shown to have no R-curve resistance, was relatively independent of crack length, and compared well with those obtained from numerical and analytical solutions. However, it was found that fracture energy for the crack starter in the position where the peel stress was tensile was about 20% lower than where the crack was positioned at the side, where the peel stress was found to be compressive.