Comparison between the ENF and 4ENF fracture characterization tests to evaluate GIIC of bonded aluminium joints

ABSTRACT

Adhesively bonded joints have been increasingly used in structural applications over mechanical joints. Cohesive Zone Modelling (CZM) is the most widespread technique to predict the strength of these joints, and it uses the tensile fracture toughness (G_IC) and the shear fracture toughness (G_IIC). Different fracture characterization methods are available for shear loadings, among which the End-Notched Flexure (ENF) is undoubtedly the most popular. The 4-Point End-Notched Flexure (4ENF) is also available. This work consists of a detailed comparison between the ENF and 4ENF tests for the experimental estimation of G_IIC of bonded aluminium joints. Three adhesives were used: a strong and brittle (Araldite® AV138), a less strong but with intermediate ductility (Araldite® 2015) and a highly ductile (SikaForce®7752). Different data reduction methods were tested, and the comparison included the load-displacement (P-δ) curves, resistance curves (R-curves) and measured G_IIC. It was found that the ENF test presents a simpler setup and has a higher availability of reliable data reduction methods, one of these not requiring measuring the crack length (a) during its growth. For the 4ENF test, only one test method proved to be accurate, and the test geometry revealed to be highly affected by friction effects.     

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.     

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.     

Analysis of adhesively-bonded T-joints by experimentation and cohesive zone models

Within the scope of adhesively-bonded joints, one of the joint types having industrial application is the T-joint, for example, in marine applications (joining of panels to the hull and connecting the glass-fibre composite hull with anti-flood panels) and aeronautical applications (wing panels, fuselage sections). This work aims to experimentally and numerically study, by cohesive zone models (CZM), the behaviour of T-joints under peel loads. The experimentally evaluated adhesives are the Araldite^® AV138 (high ultimate strength but brittle) and Araldite^® 2015 (less stress to failure but ductile and more flexible). The joint strength is evaluated with different L-shaped adherends’ thickness (t_P2). With the numerical analysis, the stress distributions, damage evolution and strength are studied. Additionally, a purely numerical study compared joints with or without adhesive filling at the curvature of the L-shaped adherends, and an extremely ductile adhesive (Sikaforce^® 7752) was additionally evaluated. The experimental tests validated the numerical results and showed that CZM is an accurate technique for the study of T-joints. It was also shown that the geometry of the L-parts, the presence of filler adhesive and the type of adhesive have a direct influence on the joint strength. In fact, in this particular joint configuration, the ductile but with lower ultimate strength adhesive Sikaforce^® 7752 clearly outperforms the two adhesives with higher mechanical properties but less ductility.     

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.     

Numerical assessment of the Double-Cantilever Beam and Tapered Double-Cantilever Beam tests for the GIC determination of adhesive layers

ABSTRACT

Fracture mechanics-based techniques have become very popular in the failure prediction of adhesive joints. The most commonly used is cohesive zone modeling (CZM). For both conventional fracture mechanics and CZM, the most important parameters are the tensile and shear critical strain energy release rates (G_IC and G_IIC, respectively). The most common tests to estimate G_IC are the Double-Cantilever Beam (DCB) and the Tapered Double-Cantilever Beam (TDCB) tests. The main objective of this work is to compare the DCB and TDCB tests to obtain the G_IC of adhesive joints. Three adhesives with varying ductilities were used to verify their influence on the precision of the typical methods of data reduction. For both tests, methods that do not need the measurement of crack length (a) were tested. A CZM analysis was considered to reproduce the experimental load–displacement (P-δ) curves and obtain the tensile CZM laws of each tested adhesive, to test the suitability of the data reduction methods, and to study the effect of the CZM parameters on the outcome of the simulations. The CZM models accurately reproduced the experimental tests and confirmed that the data reduction methods for the TDCB test tend to underestimate G_IC for ductile adhesives.     

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.     

Modelling Damage and Failure in Adhesive Joints Using A Combined XFEM-Cohesive Element Methodology

In recent years, cohesive elements based on the cohesive zone model (CZM) have been increasingly used within finite element analyses of adhesively bonded joints to predict failure. The cohesive element approach has advantages over fracture mechanics methods in that an initial crack does not have to be incorporated within the model. It is also capable of modelling crack propagation and representing material damage in a process zone ahead of the crack tip. However, the cohesive element approach requires the placement of special elements along the crack path and is, hence, less suited to situations where the exact crack path is not known a priori. The extended finite element method (XFEM) can be used to represent cracking within a finite element and hence removes the requirement to define crack paths or have an initial crack in the structure. In this article, a hybrid XFEM-cohesive element approach is used to model cracking in the fillet area using XFEM where the crack path is not known and then using cohesive elements to model crack and damage progression along the interface. The approach is applied to the case of an aluminium–epoxy single lap joint and is shown to be highly effective.     

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.     

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.     

Comparative evaluation of the Double-Cantilever Beam and Tapered Double-Cantilever Beam tests for estimation of the tensile fracture toughness of adhesive joints

The continuous development observed in bonded joints, along with the improvements of the adhesives’ properties, are resulting in an increase of the bonded joint applications, as well as the variety of applications. Regarding the strength prediction of adhesive joints, two highly relevant methods are Fracture Mechanics and Cohesive Zone Models (CZM). By Fracture Mechanics, this is usually carried out by an energetic analysis. CZM enable the simulation of damage initiation and propagation. The tensile critical strain energy release rate (G_Ic) of adhesives is one of the most important parameters for predicting the joint strength. Two of the most commonly used tests are the Double-Cantilever Beam (DCB) and the Tapered Double-Cantilever Beam (TDCB). This work aims to assess the capability of the DCB and TDCB test to estimate the value of G_Ic of adhesive joints. Three types of adhesives with different levels of ductility are used, to study the accuracy of the typical data reduction methods under conditions that are not always consistent with Linear Elastic Fracture Mechanics (LEFM) principles. For both test protocols, methods that do not require measurement of the crack length (a) during the test are evaluated. In the DCB test, these are the Compliance Calibration Method (CCM), Corrected Beam Theory (CBT) and Compliance-Based Beam Method (CBBM). The methods used in the TDCB test are the Simple Beam Theory (SBT), CCM and CBT. With few exceptions, the results were consistent between the different methods considered for each test. The discrepancy of results is higher when comparing the two types of tests, except for the brittle adhesive. It was concluded that the data reduction methods for the TDCB test are too conservative to measure G_Ic of ductile adhesives.     

Finite element analysis of failure mechanisms in HDPE/CaCo3 particulate composite

Abstract

A finite element analysis of crack propagation in an HDPE/CaCo₃ composite was carried out using a combination of the extended finite element method (XFEM) and the cohesive zone method (CZM). A unit cell of an entire composite consisting of one particle was chosen as the study zone. The interphase was assumed as a cohesive surface between the matrix and the particle. Variable parameters were the interface adhesion, position of initial crack, volume fraction, and size of the particle. The results showed that, the energy release rate increases when increasing the particle size. Increasing the volume fraction from 5 to 10% has positive effects in decreasing the strain energy release rate; however, the effects of 10 and 15% of volume fraction on the energy release rate are almost the same. Increasing the values of interfacial adhesion strength increases the strength of composite.     

Determination of traction-separation laws on an acrylic adhesive under shear and tensile loading

Structural acrylic adhesives are of special interest because those adhesives are cured at room temperature and can be bonded to oily substrates. To use those adhesives widely for structural bonding, it is necessary to clarify the methodology for predicting strengths of bonding structures with those adhesives. Recently, cohesive zone models (CZMs) have been receiving intensive attentions for simulation of fracture strengths of adhesive joints, especially when bonded with ductile adhesives. The traction-separation laws under mode I and mode II loadings require to estimate fracture toughness of adhesively bonded joints. In this paper, the traction-separation laws of an acrylic adhesive in mode I and mode II were directly obtained from experiments using Arcan type adhesively bonded specimens. The traction-separation laws were determined by simultaneously recording the J-integral and the opening displacements in the directions normal and tangential to the adhesive layer, respectively.     

Optimization study of hybrid spot-welded/bonded single-lap joints

Joining of components with structural adhesives is currently one of the most widespread techniques for advanced structures (e.g., aerospace or aeronautical). Adhesive bonding does not involve drilling operations and it distributes the load over a larger area than mechanical joints. However, peak stresses tend to develop near the overlap edges because of differential straining of the adherends and load asymmetry. As a result, premature failures can be expected, especially for brittle adhesives. Moreover, bonded joints are very sensitive to the surface treatment of the material, service temperature, humidity and ageing. To surpass these limitations, the combination of adhesive bonding with spot-welding is a choice to be considered, adding a few advantages like superior static strength and stiffness, higher peeling and fatigue strength and easier fabrication, as fixtures during the adhesive curing are not needed. The experimental and numerical study presented here evaluates hybrid spot-welded/bonded single-lap joints in comparison with the purely spot-welded and bonded equivalents. A parametric study on the overlap length (L_O) allowed achieving different strength advantages, up to 58% compared to spot-welded joints and 24% over bonded joints. The Finite Element Method (FEM) and Cohesive Zone Models (CZM) for damage growth were also tested in Abaqus^® to evaluate this technique for strength prediction, showing accurate estimations for all kinds of joints.     

Numerical and experimental analysis of bonded joints with combined loading

The metallic materials bonding using structural adhesives has become an increasingly used process, presenting advantages when compared to other fastening methods such as screws and rivets. The aim of this paper is the numerical evaluation of bonded joints with combined loading (traction and shear) using the finite element method, comparing the results obtained with the experiments performed at the same configurations. Considering adhesive joints with the same bonded area, but with different linear dimensions, the mechanical strength may be different, which characterizes the shape factor. In this way, the analyzes considered the bonded area shape factor in nine different configurations, being modified both the height and the width of the joint, considering two points of force application for each group. For the numerical simulation, the cohesive zone models (CZM) were used, which use the concepts of linear elastic fracture mechanics (LEFM). These models consider that one or multiple interfaces or regions of fracture may be artificially introduced into the structures, which is done through the separation-traction laws. For this purpose, DCB (double cantilever beam) and ENF (end notched flexure) tests were performed, measuring this way the essential cohesive properties to the numerical modeling, especially the critical energy release in I and II modes (normal and shear, respectively). The influence of some cohesive properties on the maximum load of the bonded joint was investigated. The good numerical and experimental concordance in different configurations studied confirms that the CZM provide consistent results with the bonded joint experiments for the presented conditions of adhesive thickness, surface treatment and load application point, not only in single lap joints, but also in combined loading joints, whose investigation was done in this work.     

Mechanical characterization of adhesive joints with dissimilar substrates for marine applications

The simplicity and efficiency of the adhesive joints have increased more and more their use in many fields. In ship construction the need to join different materials, such as the bonding of the hull/deck, the sea chest, the portholes, the windshields, the panels of cabins, etc. leads to choosing increasingly the adhesive joints. In this work we have evaluated the effects of both SMP (Silyl Modified Polymer) based adhesives and sealants on single lap joints (SLJs) with dissimilar substrates. Three pairs of single lap joints were taken into account among dissimilar adherends: stainless steel (AISI 316) with PMMA (or Altuglas^®) and monolithic composite laminates bonded with glass or PMMA. Before tensile testing some SLJ samples were subjected to a three-dimensional computed tomographic analysis to evaluate how the presence of possible defects in the adhesive layer affects the failure mode. A design of experiments was defined in order to quantify the effect of the considered factors and their correlation. The obtained maximum tensile stress values confirm the data provided by the manufacturer, approximately between 2 and 2.5 MPa, showing generally cohesive fracture. Finally the considered SMP adhesives and sealants are well suited for the chosen different substrates, although special attention should be placed on the glass–GFRP joint as it is confirmed by statistical analysis.     

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.     

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.     

Effect of Adherend Recessing on the Tensile Strength of Single Lap Joints

Bonded joints are gaining importance in many fields of manufacturing owing to a significant number of advantages to the traditional methods. The single lap joint (SLJ) is the most commonly used method. The use of material or geometric changes in SLJ reduces peel and shear peak stresses at the damage initiation sites. In this work, the effect of adherend recessing at the overlap edges on the tensile strength of SLJ, bonded with a brittle adhesive, was experimentally and numerically studied. The recess dimensions (length and depth) were optimized for different values of overlap length (L _O), thus allowing the maximization of the joint's strength by the reduction of peak stresses at the overlap edges. The effect of recessing was also investigated by a finite element (FE) analysis and cohesive zone modelling (CZM), which allowed characterizing the entire fracture process and provided joint strength predictions. For this purpose, a static FE analysis was performed in ABAQUS® considering geometric nonlinearities. In the end, the experimental and FE results revealed the accuracy of the FE analysis in predicting the strength and also provided some design principles for the strength improvement of SLJ using a relatively simple and straightforward technique.     

Effect of Adhesive Ductility on Cyclic Debond Mechanism in Composite-to-Composite Bonded Joints

An investigation of an adhesively bonded composite joint with a brittle adhesive was conducted to characterize both the static and fatigue debond growth mechanism under mode I and mixed mode I-II loadings. The bonded system consisted of graphite/epoxy adherends bonded with FM-400 adhesive. Two specimen types were tested: (1) a double-cantilever-beam specimen for mode I loading and (2) a cracked-lap-shear specimen for mixed mode I-II loading. In all specimens tested, failure occurred in the form of debond growth either in a cohesive or adhesive manner. The total strain-energy-release rate is not the criterion for cohesive debond growth under static and fatigue loading in the birttle adhesive as observed in previous studies with the ductile adhesives. Furthermore, the relative fatigue resistance and threshold value of cyclic debond growth in terms of its static fracture strength is higher in the brittle adhesive than its counterpart in the ductile adhesive.