Validation of pure tensile and shear cohesive laws obtained by the direct method with single-lap joints

Joining with structural adhesives in the aeronautical industry dates back to some decades, although only more recently this technique has been implemented to load bearing parts in other industries. This technique enables joining steel with aluminium or fibre-reinforced composites, with a major weight advantage. Cohesive Zone Models (CZM) are an accurate design method for bonded structures but, depending on the adhesive type and specimen's geometry, the accuracy of the strength predictions may be highly compromised by the choice of the cohesive laws. This work presents a validation of tensile and shear CZM laws of three adhesives obtained by the direct method applied to Double-Cantilever Beam (DCB) and End-Notched Flexure (ENF) tests, respectively. The validation is carried out by considering a mixed-mode bonded geometry (the single-lap joint) with different overlap lengths (L_O) and adhesives of distinct ductility. Initially, the precise shape of the cohesive law in tension and shear of the adhesives is estimated, followed by their simplification to parameterized triangular, trapezoidal and linear-exponential CZM laws. Validation of the CZM laws was accomplished by direct comparison of the load-displacement (P-δ) curves and maximum load (P_m) of the single-lap joints as a function of the tested L_O values. The strength predictions were accurate for a CZM law shape consistent with the adhesive type, although the differences between CZM shapes were not too significant.     

Accuracy of cohesive laws with different shape for the shear behaviour prediction of bonded joints

The use of adhesive bonding as a joining technique is increasingly being used in many industries because of its convenience and high efficiency. Cohesive Zone Models (CZM) are a powerful tool for the strength prediction of bonded joints, but they require an accurate estimation of the tensile and shear cohesive laws of the adhesive layer. This work evaluated the shear fracture toughness (J_IIC) and CZM laws of bonded joints for three adhesives with distinct ductility. The End-Notched Flexure (ENF) test geometry was used. The experimental work consisted of the shear fracture characterization of the bond by the J-integral. Additionally, by this technique, the precise shape of the cohesive law was defined. For the J-integral, digital image correlation was used for the evaluation of the adhesive layer shear displacement at the crack tip during the test, coupled to a Matlab sub-routine for extraction of this parameter automatically. Finite Element Method (FEM) simulations were carried out in Abaqus® to assess the accuracy of triangular, trapezoidal and linear-exponential CZM laws in predicting the experimental behaviour of the ENF tests. As output of this work, fracture data is provided in shear for the selected adhesives, allowing the subsequent strength prediction of bonded joints.     

Strength Prediction of Adhesively Bonded Single Lap Joints Under Salt Spray Environment Using a Cohesive Zone Model

The aim of this research was to develop an experimental–numerical approach to characterize the effect of salt spray environment on adhesively bonded joints and predict the degradation in joint strength. Experiments were conducted on bulk adhesive specimens and single lap joints (SLJs) under salt spray condition and the corresponding experimental results were reported. The environment degradation factor, Deg, was incorporated into a bilinear cohesive zone model (CZM) to simulate the degradation process of the joints. The degraded CZM parameters, determined from static tests on bulk adhesive, were imported into the CZM using an approximate moisture concentration gradient approach. The reduction in residual strength of SLJ under salt spray environment was successfully predicted through comparing the experimental and numerical results.     

Fatigue Analysis of Adhesive Joints Under Vibration Loading

Adhesively bonded joints have been used extensively for many structural applications. However, one disadvantage usually limiting the service life of adhesive joints is the relatively low strength for peel loading, especially under dynamic cyclic loading such as impulsive or vibrational forces. Moreover, accurately predicting the fatigue life of bonded joints is still quite challenging. In this study, a combined experimental–numerical approach was developed to characterize the effect of the cyclic-vibration-peel (CVP) loading on adhesively bonded joints. A damage factor is introduced into the traction-separation response of the cohesive zone model (CZM) and a finite element damage model is developed to evaluate the degradation process in the adhesive layer. With this model, the adhesive layer stress states before and after being exposed to various CVP loading cycles are investigated, which reveals that the fatigue effect of the CVP loading starts first in the regions close to the edges of the adhesive layer. A good correlation is achieved when comparing the simulation results to the experimental data, which verifies the feasibility of using the proposed model to predict the fatigue life of adhesively bonded joints under the CVP type of loading.     

Predicting the Strength of Adhesively Bonded T-joints Under Cyclic Temperature using a Cohesive Zone Model

The objective of this study is to analyze the effect of cyclic-temperature environment on adhesively bonded T-joints. Experiments on steel and aluminum T-peel joints were conducted to illustrate the influence of cyclic temperature on the ultimate load of T-joints. An environmental degradation factor Deg was utilized in conjunction with a cohesive zone model (CZM) to simulate the strength of T-joints caused by temperature variation. The experimental results showed that long-term cyclic-temperature exposure caused significant degradation on the ultimate load of the T-joints. And with the increase of the temperature cycles experienced, the ultimate load of the T-joints gradually decreased. In order to model the adhesive layer between joint components and simulate the damage propagation in the interface, a CZM implemented in the finite element code ABAQUS was used. Comparison between the experimental and numerical results proved the adopted modeling procedure be successful and effective.     

Experimental and numerical analysis on fatigue durability of single-lap joints under vibration loads

Fatigue is one of the most common yet complicated failures that can cause damage to mechanical structures. Structural adhesively bonded joints are not exempt from this deleterious phenomenon and have to be assessed under vibration loads. In this work, fatigue characteristics of single-lap joints (SLJ) made of steel and carbon fibre reinforced plastic (CFRP) laminates under vibration loads are primarily investigated by experiments. The aim of this work is to analyze the changes in the ultimate load of the SLJ under vibration loads. The experimental results showed that SLJ will face cohesive failure after the uniaxial tensile loading test. In addition to the increase of vibration cycles, the ultimate load and failure displacement gradually decrease. In order to model the adhesive between joint components and simulate the damage propagation, a new traction–separation law called the embedded process zone (EPZ) and a damage factor are introduced and developed within the framework of cohesive zone Modeling (CZM) techniques. Meanwhile, the stress variations in the adhesive layer of SLJ in different vibration cycles are researched using the finite element method in ABAQUS.     

Modelling adhesive joints with cohesive zone models: effect of the cohesive law shape of the adhesive layer

Adhesively-bonded joints are extensively used in several fields of engineering. Cohesive Zone Models (CZM) have been used for the strength prediction of adhesive joints, as an add-in to Finite Element (FE) analyses that allows simulation of damage growth, by consideration of energetic principles. A useful feature of CZM is that different shapes can be developed for the cohesive laws, depending on the nature of the material or interface to be simulated, allowing an accurate strength prediction. This work studies the influence of the CZM shape (triangular, exponential or trapezoidal) used to model a thin adhesive layer in single-lap adhesive joints, for an estimation of its influence on the strength prediction under different material conditions. By performing this study, guidelines are provided on the possibility to use a CZM shape that may not be the most suited for a particular adhesive, but that may be more straightforward to use/implement and have less convergence problems (e.g. triangular shaped CZM), thus attaining the solution faster. The overall results showed that joints bonded with ductile adhesives are highly influenced by the CZM shape, and that the trapezoidal shape fits best the experimental data. Moreover, the smaller is the overlap length (L_O), the greater is the influence of the CZM shape. On the other hand, the influence of the CZM shape can be neglected when using brittle adhesives, without compromising too much the accuracy of the strength predictions.     

Testing different cohesive law shapes to predict damage growth in bonded joints loaded in pure tension

ABSTRACT

Adhesive bonding is a widely used joining method because of specific advantages compared to the traditional fastening methods. Cohesive zone modelling (CZM) is currently the most widely used technique for strength prediction. CZM supposes the characterization of the CZM laws in tension and shear. This work evaluated the tensile fracture toughness (G_IC) and CZM laws of bonded joints with three adhesives by the double-cantilever beam (DCB) test. The experimental work consisted of the adhesives’ tensile fracture characterization by the J-integral technique. As the main novelty of this work, the precise shape of the cohesive law of adhesives ranging from brittle to highly ductile was defined by the direct method, using a digital image correlation method to evaluate the tensile relative displacement (δ_n) of the adhesive layer at the crack tip and adherends’ rotation at the crack tip (?_o). Moreover, finite element (FE) simulations permitted assessing the accuracy of triangular, trapezoidal and linear-exponential CZM laws in predicting the experimental behaviour of the DCB bonded joints with markedly distinct behaviours. As output of this work, fracture data and information regarding the applicability of these CZM laws to each type of adhesive is provided, allowing the subsequent strength prediction of bonded joints.     

Direct determination of a new mode-dependent cohesive zone model to simulate metal-to-metal adhesive joints

In this paper, a new mode-dependent cohesive zone model for the simulation of metal to metal adhesive joints is directly determined. Three consecutive steps have been taken into account for this end. First, double cantilever beam (DCB) and end-notched flexure (ENF) specimens are utilized for the direct experimental extraction of the traction-separation laws (TSLs) for adhesive bonded joints subjected to pure mode I and mode II, respectively. Next, the results are implemented to obtain the relative cohesive zone parameters for defining the simplified Park-Paulino-Roesler cohesive zone model (S-PPR CZM). Finally, mixed-mode characteristics parameters are derived for an arbitrary mode-mixity ratio based on pure mode TSLs. The model is further implemented in ABAQUS® commercial software to be verified against the experimental results of pure mode loadings which leads to the direct extraction of TSLs. The experiments conducted on the strength of single lap joint (SLJ) and scarf joint (SJ) specimens, commonly tested for mixed-mode loading, confirm the accuracy of the developed mixed-mode S-PPR model for different mode-mixity conditions.     

Improving the mechanical behavior of the adhesively bonded joints using RGO additive

In this research, Araldite 2011 has been reinforced using different weight fractions of Reduced Graphene Oxide (RGO). Fourier Transform Infrared Spectroscopy (FTIR), Scanning Electron Microscopy (SEM) and Transmission Electron Microscopy (TEM) analyses were conducted and it has been shown that introduction of the RGO greatly changes the film morphology of the neat adhesive. Uni-axial tests were carried out to obtain the mechanical characteristics of the adhesive-RGO composites. It has been observed that introducing 0.5 wt% RGO enhances the ultimate tensile strength of the composites by 30%. In addition, single lap joints using neat adhesive and adhesive-RGO composites were fabricated to investigate the effect of the added RGO on the lap shear strength of the joints. Results show that the joints with added 0.5 wt RGO exhibited 27% higher lap shear strength compared to the joints bonded with neat adhesive. Finally, Finite Element (FE) numerical solutions using Cohesive Zone Modeling (CZM) have been carried out to simulate the failure behavior of the joints, and it has been shown that the FE models can predict the joint’s failure load.     

Evaluation of different modelling conditions in the cohesive zone analysis of single-lap bonded joints

Cohesive Zone Models (CZM) are widely used for the strength prediction of adhesive joints. Different simulation conditions, such as damage initiation and growth criteria, are available for use in CZM analyses to provide the mixed-mode behaviour. Thus, it is highly relevant to understand in detail their influence on the simulations’ outcome. This work studies the influence of different conditions used in CZM simulations to model a thin adhesive layer in single-lap joints (SLJ) under a tensile loading, for an estimation of their influence on the strength prediction under diverse geometrical and material conditions. Validation with experimental data is considered. Adhesives ranging from brittle to highly ductile and overlap lengths (L_O) between 12.5 and 50 mm were considered. Different studies were considered: Variation of the elastic stiffness of the cohesive laws, different mesh refinements, study of the element type, and evaluation of several damage initiation and growth criteria. The analysis carried out in this work confirmed the known suitability of CZM for static strength prediction of bonded joints and pointed out the best set of numerical conditions for this purpose. Inaccurate results can be obtained if the choice of the modelling conditions is not the most suitable for the problem.     

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.     

A Method of Estimating the Strength of Adhesive Bonded Joints of Metals

The strength of adhesive bonded joints is investigated both analytically and experimentally. The deformed states of lap joints under tensile shear loading are analysed by the finite element method on the assumption of elastic deformation. A method of using the adhesive strength law is proposed to estimate the joint strength. The adhesive strength law is experimentally determined by subjecting butt joints of two thin-walled tubes to combined axial load and torsion. The strength of lap joints is determined by adopting the adhesive strength law to the adhering interface as well as the strength law of adherend and adhesive resin. The calculated strain distribution and strength of the joints are compared with the experimental results. The effects of the joint configurations on the deformation and strength are discussed. It is shown that the proposed method is useful to predict the joint strength.     

A Method of Estimating the Strength of Adhesive Bonded Joints of Metals

The strength of adhesive bonded joints is investigated both analytically and experimentally. The deformed states of lap joints under tensile shear loading are analysed by the finite element method on the assumption of elastic deformation. A method of using the adhesive strength law is proposed to estimate the joint strength. The adhesive strength law is experimentally determined by subjecting butt joints of two thin-walled tubes to combined axial load and torsion. The strength of lap joints is determined by adopting the adhesive strength law to the adhering interface as well as the strength law of adherend and adhesive resin. The calculated strain distribution and strength of the joints are compared with the experimental results. The effects of the joint configurations on the deformation and strength are discussed. It is shown that the proposed method is useful to predict the joint strength.     

Analysis of an adhesively bonded single lap joint subjected to eccentric loading

A new experimental test is proposed, which allows the contribution of Mode I, II and III fracture modes to the failure of the adhesive layer of bonded joints aiming at achieving the realistic conditions often occurring during loading of practical joints. The main objective of this test is benchmarking of computational tools. The test is based on a Single Lap Joint subjected to Eccentric Loading (SLJ-EL). The basic concept that lies behind this configuration is that the applied in-plane tensile load leads the adhesive layer to develop normal stresses, in-plane and out-of-plane shear stresses, which correspond to Mode I, II and III loading and fracture. These tests were designed so that the metal substrates do not enter plasticity and the adhesive achieves a mode mixity ratio between Mode II and Mode III not lower than 0.5. The experiments were simulated in a 3-dimensional finite element space and a previously developed mixed-mode model is utilized for the adhesive layer, under the framework of Cohesive Zone Modeling (CZM) techniques. The numerical results are in very good agreement with the corresponding experimental measurements, as regards both the linear and non-linear region, and the attained strength. It is concluded that in the early stages of loading the contribution of Mode III is 150% higher than that of Mode II.     

Strength prediction of T-peel joints by a hybrid spot-welding/adhesive bonding technique

The need of joining methods that best meet the design requirements has led to the increased use of adhesive joints at the expense of welding, fastening and riveting. Hybrid weld-bonded joints are obtained by combining adhesive bonding with a welded joint, providing superior strength and stiffness, and higher resistance to peeling and fatigue. In the present work, an experimental and numerical study of welded, adhesive and hybrid (weld-bonded) T-peel joints under peeling loads is presented. The brittle Araldite® AV138, the moderately ductile Araldite® 2015 and the ductile Sikaforce® 7752 were the considered adhesives. An analysis of the experimental values and a comparison of these values with Finite Element Method (FEM) results in Abaqus® were carried out, which included a stress analysis in the adhesive and strength prediction by Cohesive Zone Models (CZM) considering failure simulation of both the adhesive layer and weld-nugget. It was found that the Sikaforce® 7752 performs best in the bonded and hybrid configurations. The good agreement between the experimental and numerical results enabled the validation of CZM to predict the strength of adhesive and hybrid T-peel joints, giving a basis for reducing the design time and enabling the optimization of these joints.     

Fracture and fatigue behavior of scrim cloth adhesively bonded joints with and without rivet holes

_—Tensile and fatigue disbond propagation studies on scrim cloth structural adhesive lap joints without and with rivet holes were performed. The geometry of the rivet holes is similar to that in a fuselage part of an aircraft. The joints were cycled in tension-tension fatigue at a frequency of 3 Hz and a maximum load, below the linear limit of the joint, which was obtained from the tensile tests of similar joints. The disbond length at each corner of the joint was viewed using a travelling optical microscope attached to a video camera. It was found that the static-tensile behavior of both types of joints (without and with rivet holes) consists of three stages: a linear stage followed by a region of increased non-linearity and then a 'yield' region. It is within this yield region that the rivet holes affect the strength of the joint. Stress analysis of the disbond problem under static loading revealed a strong mixed mode between the opening and shear mode stress intensity factors for both types of joints. The fatigue disbond kinetics of adhesively bonded joints without and with rivet holes were found to display an S-shaped curve with three stages of the disbond propagation rate. Failure analysis of the fatigue failed joints (without and with rivet holes) revealed three distinct regions on each half of the failed joint: an interfacial region with bare metal, a cohesive region, and an interfacial region with the adhesive adhered to the substrate. Scanning electron microscopic analysis of the disbond surface showed that the cohesive region of the fatigue fractured joints is more tortuous compared with the statically failed joints.     

Determination of Traction Separation Law for Interfacial Failure in Adhesive Joints at Different Loading Rates

Cohesive zone modeling (CZM) has been extensively used in recent years to simulate failure in adhesive joints. Accurate determination of the traction–separation law (TSL) (or parameters of the CZM) is very crucial to the success of this approach. Recent experimental investigations have indicated that loading rate influences the TSL/CZM parameters. In this work we have attempted to measure the TSL using two different approaches for an adherend/adhesive system which always fails by interfacial failure. In the first approach, the TSL is obtained by differentiating the experimentally measured J integral by the opening displacement. The second, an inverse approach, involves a finite element (FE) analysis in which the adhesive layer is also modeled and cohesive elements are used to model the interfacial failure. The TSL is then obtained iteratively by matching the numerical load–displacement data to that obtained in experiments. We show that the first approach yielded TSLs which are dependent on both adhesive layer thickness and the loading rate, whereas the second approach yielded a TSL which is independent of the adhesive layer thickness and the loading rate. Therefore, the TSL obtained from the second approach is intrinsic to the adhesive/adherend pair and in that sense is unique.     

Stress Analysis of Generally Asymmetric Single Lap Adhesively Bonded Joints

An analysis is presented that predicts shear and peel stresses in an adhesively bonded single lap joint having general asymmetric configuration. The single lap joint is under tension loading together with moments induced by geometric eccentricity. Because these eccentricity moments are the key elements of this analysis, a general relationship between the eccentricity moments and simple geometric moments has been determined with the aid of finite element analysis (FEA). Example calculations show that the shear- and peel-stress profiles from the closed-form model are well matched to FEA results except in the small regions near the free ends of the joints, because of the shear lag basis of the model. For asymmetric joints, the model predictions are more accurate for the case of modulus eccentricity than thickness eccentricity. Elastic-limit load predictions accounting for both shear and peel stress in the adhesive have been used to find optimal joint configurations between asymmetric adherends.     

Impact strength of joints bonded with high-strength pressure-sensitive adhesive

The impact strength of joints bonded with a double-coated high-strength pressure-sensitive adhesive (PSA) was experimentally investigated. PSA has recently been used to join parts of mobile devices such as smart-phones, which are often subjected to drop impacts. Consequently, the impact strength of PSA bonded joints has become important.Two types of specimens, butt joint specimens and double cantilever beam (DCB) specimens bonded with adhesives were utilized for the experiments. Quasi-static tests and impact tests of the specimens were carried out using a mechanical testing machine and an impact testing machine. The PSA layers in the specimens were observed using a high-speed digital camera. The deformation and strain distribution in the adherends of the DCB specimens were also measured using a novel high-speed digital camera with photoelastic imaging capability.Though the strength of the butt joints increased as the loading rate increased, the critical fracture energy of the DCB specimens decreased at high loading rates. This may be attributed to the transition to the brittle nature of the PSA in the loading range in which no cavitation occurred. To verify the critical fracture energy obtained with the DCB tests, finite element analyses (FEA) based on the cohesive zone model (CZM) were carried out, and the load–displacement curves of the DCB tests were simulated. The predicted results showed good agreements with the experimental results.