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.     

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.     

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.     

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 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.     

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.     

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.     

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.     

Estimation of static strength of adhesively bonded single lap joints with an acrylic adhesive under tensile shear condition based on cohesive zone model

In this study, the tensile shear and bending tests of adhesively bonded single lap joints with the acrylic adhesive was evaluated experimentally and numerically. In the previous paper, the traction-separation laws in mode 1 and mode 2 for an acrylic adhesive were directly obtained from the observation of failure process using Arcan type adhesively bonded specimens: simultaneous measurements of the J-integral and the opening displacements in the directions normal, δ_n and tangential to the adhesive layer, δ_s respectively. The experimental results were compared with numerical simulations conducted in ABAQUS including cohesive damage model. The cohesive laws obtained in the previous paper were simplified to trapezoidal shape from the experimentally obtained ones which were indicated in the previous paper. A good agreement was found between the experimental and numerical results. Then, to investigate the damage evolution in the adhesive layer for some lap joints, microscopic video observation was conducted near the end of the adhesive layer, and the video image have been compared with the contours of damage variable obtained by FEM corresponding to the video images. The observed damage evolution also agrees with the trend of damage variable.     

Strength prediction of adhesively bonded ferrite pillar–tin bronze plate under axial shear loading

Abstract

With the fast development of electronic, automotive and aerospace engineering in recent years, ferrite material has been widely used in devices including inductor, voltage transformer, filter and choke coil, etc. The proper characterisation on the mechanical capacity of the connection between ferrite and traditional metals has become a key issue for both industrial and academic fields. This work focused on the mechanical performance as well as fracture behaviour of adhesively bonded ferrite–tin bronze plate (FTBP), subjected to axial shear loading through experimental and numerical approaches. In the process, a new set of Arcan testing methods was developed for mechanical parameter determination of high flow epoxy adhesives. The material parameters of the epoxy adhesive connecting the ferrite pillar and bronze were experimentally determined. Curing mould was designed for the manufacture of the selected adhesive with high flowability in dumbbell tensile testing and Arcan testing under 0° and 90° loading directions. Quasi-static shear loading test was then conducted on bonded FTBP with a specially designed jig, and the failure surface was studied through optical microscopy and scanning electron microscopy (SEM) observations. Finite element (FE) modelling was carried out to simulate the loading process up to failure, where the crack propagation in the adhesive layer was modelled using cohesive zone model (CZM) with a bilinear traction-separation response. The experimentally measured and numerically simulated results of the adhesively bonded FTBP were compared with each other, proving the validity of the strength prediction approach developed in this work.

Abbreviation: FTBP: Ferrite - Tin Bronze Plate; SEM: Scanning Electron Microscope; FE: Finite Element; CZM: Cohesive Zone Model; CIR: Cold In-place Recycling; DIC: Digital Image Correlation; DCB: Double Cantilever Beam; ENF: End-notched Flexure; PTFE: Polytetrafluoroethylene; CTOD: Crack Tip Opening Displacement; SDEG: Scalar Stiffness Degradation Variable; DOF: Degree of Freedom.     

Effect of creep on the mode II residual fracture energy of adhesives

Viscous flow that often occurs in adhesive materials leads to a permanent deformation when adhesives are subjected to creep loading. Creep loading has a significant influence on the strength of bonded structures. Due to the viscous behavior, the fracture energy also may change with time for joints that experience creep loading in service. In this work the effects of two creep parameters (creep load and time) on the residual mode II fracture energy of an adhesive was investigated using end notched flexure (ENF) specimens. To achieve this, ENF samples were subjected to different creep loading levels at different creep times followed by quasi static tests to obtain the residual shear fracture energy of the adhesive. Experimental results showed that pre-creep loading of the bonded structures can significantly improve the fracture energy and the static strength of the joints.     

Adhesive Selection for Single Lap Bonded Joints: Experimentation and Advanced Techniques for Strength Prediction

The integrity of multi-component structures is usually determined by their unions. Adhesive-bonding is often used over traditional methods because of the reduction of stress concentrations, reduced weight penalty, and easy manufacturing. Commercial adhesives range from strong and brittle (e.g., Araldite® AV138) to less strong and ductile (e.g., Araldite® 2015). A new family of polyurethane adhesives combines high strength and ductility (e.g., Sikaforce® 7888). In this work, the performance of the three above-mentioned adhesives was tested in single lap joints with varying values of overlap length (L_O). The experimental work carried out is accompanied by a detailed numerical analysis by finite elements, either based on cohesive zone models (CZM) or the extended finite element method (XFEM). This procedure enabled detailing the performance of these predictive techniques applied to bonded joints. Moreover, it was possible to evaluate which family of adhesives is more suited for each joint geometry. CZM revealed to be highly accurate, except for largely ductile adhesives, although this could be circumvented with a different cohesive law. XFEM is not the most suited technique for mixed-mode damage growth, but a rough prediction was achieved.     

Assessments for impact of adhesive properties: modeling strength of metallic single lap joints

Adhesively bonded joints are widely used in a variety of industrial and engineering activities. Their overall strength is dependent on the properties of the adhesives. In the present research, assessments of adhesive properties were performed systematically through defining both strength mixity and energy rate mixity and using them to characterize the overall strength of metallic single lap joints. By means of the cohesive zone model, the adhesive strength mixity was defined as the ratio of the shear and tensile separation strength, and the energy rate mixity was defined as the ratio of the area below the shear cohesive curve and the area below the tensile cohesive curve. For each specified group of mixity parameters, corresponding to the properties of a specified adhesive, the overall strengths and the critical displacements of bonded joints were characterized. A series of strength and energy rate mixities were taken into account in the present calculations. A comparison of the present calculations with some existing experiments was carried out for both brittle and ductile adhesives. Finally, in the calculations presented here, damage initiation and evolution of the adhesive layer were also undertaken. The results showed that the overall strength of the joints was significantly depended on the adhesive properties, which were characterized by the strength and energy rate mixities of the adhesive. Furthermore, the shear adhesive stress components played a dominate role in both the damage initiation and evolution in the adhesives, which were also affected by the overlap length of the 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.     

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.     

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.     

Failure behavior of adhesively bonded joints with a rubber modified epoxy adhesive under tensile-shear combined cyclic loading

Rubber-modified epoxy adhesives are used widely as structural adhesive owing to their properties of high fracture toughness. In many cases, these adhesively bonded joints are exposed to cyclic loading. Generally, the rubber modification decreases the static and fatigue strength of bulk adhesive without flaw. Hence, it is necessary to investigate the effect of rubber-modification on the fatigue strength of adhesively bonded joints, where industrial adhesively bonded joints usually have combined stress condition of normal and shear stresses in the adhesive layer. Therefore, it is necessary to investigate the effect of rubber-modification on the fatigue strength under combined cyclic stress conditions. Adhesively bonded butt and scarf joints provide considerably uniform normal and shear stresses in the adhesive layer except in the vicinity of the free end, where normal to shear stress ratio of these joints can cover the stress combination ratio in the adhesive layers of most adhesively bonded joints in industrial applications.

In this study, to investigate the effect of rubber modification on fatigue strength with various combined stress conditions in the adhesive layers, fatigue tests were conducted for adhesively bonded butt and scarf joints bonded with rubber modified and unmodified epoxy adhesives, wherein damage evolution in the adhesive layer was evaluated by monitoring strain the adhesive layer and the stress triaxiality parameter was used for evaluating combined stress conditions in the adhesive layer. The main experimental results are as follows: S–N characteristics of these joints showed that the maximum principal stress at the endurance limit indicated nearly constant values independent of combined stress conditions, furthermore the maximum principal stress at the endurance limit for the unmodified adhesive were nearly equal to that for the rubber modified adhesive. From the damage evolution behavior, it was observed that the initiation of the damage evolution shifted to early stage of the fatigue life with decreasing stress triaxiality in the adhesive layer, and the rubber modification accelerated the damage evolution under low stress triaxiality conditions in the adhesive layer.     

Effect of silicon carbide nanoparticles on the adhesion strength of steel–epoxy composite joints bonded with acrylic adhesives

This paper reports a study on the effect of silicon carbide nanoparticles on the adhesion strength of steel–glass/epoxy composite joints bonded with two-part structural acrylic adhesives. The introduction of nanosilicon carbide in the two-part acrylic adhesive led to a remarkable enhancement in the shear and tensile strength of the composite joints. The shear and tensile strengths of the adhesive joints increased with adding the filler content up to 1.5?wt%, after which decreased with adding more filler content. Also, addition of nanoparticles caused a reduction in the peel strength of the joints. DSC analysis revealed that Tg values of the adhesives rose with increase in the nanofiller content. The equilibrium water contact angle was decreased for adhesives containing nanoparticles. SEM micrographs revealed that addition of nanoparticles altered the fracture morphology from smooth to rough fracture surfaces.     

Adhesive strength of steel–epoxy composite joints bonded with structural acrylic adhesives filled with silica nanoparticles

This paper reports a study on the effect of silica nanoparticles on the adhesion strength of steel–glass/epoxy composite joints bonded with two-part structural acrylic adhesives. The introduction of nano-silica in the two-part acrylic adhesive led to a remarkable enhancement in the shear and tensile strength of the composite joints. The shear and tensile strengths of the adhesive joints increased with addition of the filler content up to 1.5 wt%, after which decreased with addition of more filler content. Also, addition of nanoparticles caused a reduction in the peel strength of the joints. Differential scanning calorimeter analysis revealed that T_g values of the adhesives rose with increasing the nanofiller content. The equilibrium water contact angle was decreased for adhesives containing nanoparticles. Scanning electron microscope micrographs revealed that addition of nanoparticles altered the fracture morphology from smooth to rough fracture surfaces.     

Steel-Epoxy Composite Joints Bonded with Nano-TiO2 Reinforced Structural Acrylic Adhesive

This article reports a study on the effect of TiO₂ nanoparticles on the adhesion strength of steel–glass/epoxy composite joints bonded with two-part structural acrylic adhesives. The introduction of nano-TiO₂ in the two-part acrylic adhesive led to a remarkable enhancement in the shear and tensile strength of the composite joints. The shear and tensile strengths of the adhesive joints increased with adding the filler content up to 3 wt.%, after which it decreased with adding more filler content. Also, addition of nanoparticles caused a reduction in the peel strength of the joints. Differential scanning calorimeter analysis revealed that glass transition temperature (T_g) values of the adhesives rose with increasing the nano-filler content. The equilibrium water contact angle decreased for adhesives containing nanoparticles. Scanning electron microscope micrographs revealed that addition of nanoparticles altered the fracture morphology from smooth to rough fracture surfaces.