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.     

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.     

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.     

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.     

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.     

The simulation of a double cantilever beam test using the virtual crack closure technique with the cohesive zone modelling

The fracture of an adhesively bonded joint is a complicated process of crack nucleation and propagation. In this work, a method for modelling the fracture process with separate nucleation and propagation phases is presented. The method combines the virtual crack closure technique (VCCT) with the cohesive zone modelling (CZM) on the finite element basis to take into account the development of fracture toughness. The method is applied to simulate a double cantilever beam (DCB) test as an example. Experiments using a butt joint specimen are carried out to support the adhesive characterization. The analysis focuses on the physical validity of the VCCT-CZM coupling and on the determination of applicable simulation parameter values. By using experimental data as a reference, the simulation results are compared to the results of traditional CZM and VCCT simulations. The comparison indicates that the applied combined CZM-VCCT method reproduces the DCB test cycles more accurately than the CZM and VCCT models.     

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.     

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.     

Improvement of the Adhesive Fracture Toughness of Bonded Aluminum Joints Using E-Glass Fibers at Cryogenic Temperature

Fracture toughness and crack resistance of aluminum adhesive joints were measured at the cryogenic temperature of ?150°C, with respect to the orientation and volume fraction of the E-glass fibers in the epoxy adhesive. Cleavage tests on the DCB (Double Cantilever Beam) adhesive joints were performed using two different test rates of 1.67 × 10^?2 and 8.33 × 10^?4 mm/s to observe the crack propagation trends. From the experiments, it was found that the DCB joints bonded with the epoxy adhesive reinforced with E-glass fibers not only showed a stable crack propagation with a low crack propagation speed, but also higher fracture toughness and crack resistance than those of the DCB joints bonded with the unreinforced epoxy adhesive at a cryogenic temperature of ?150°C.     

Mechanics of crack growth in epoxide resins

Experiments have been conducted employing tapereddouble-cantilever-beam joints with different epoxide adhesives. Depending on the adhesive employed, crack propagation occurred either (a) in a continuous stable manner with crack propagation velocities in the range 10^?4 to 5 m/s and values of the adhesive fracture energy, G_Ic, being almost independent of the crack velocity, or (b) intermittently in an unstable manner when the initial crack velocity was never less than about 20 m/s and, in some instances, rose to about 450 m/s; values of G_Ic (initiation) increased rapidly with increasing velocity. It is proposed that the amount of localized plastic deformation arising from shear yielding that occurs at the crack tip prior to crack propagation is controlling. Secondly, the longterm strength of stressed, structural adhesive joints has been investigated. The fracture of these joints over eight decades of time is uniquely described by a critical plastic zone size developed at the crack tip at failure.     

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.     

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.     

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.     

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.     

Elastoplastic Fracture Behavior of Structural Adhesives Under Monotonic Loading

Elastic-plastic fracture behavior of a structural adhesive in the bulk and bonded forms is discussed. The model adhesive chosen, Metlbond 1113 (with scrim carrier cloth) and 1113-2 (neat resin) solid film adhesives exhibit a relatively brittle material behavior to justify the use of LEFM methods.

The solid film adhesives are first cast in the form of tensile coupons to determine the bulk fracture properties with the use of single-edge-cracked specimen geometry. K_Ic evaluation is done using the procedure suggested by the ASTM standard. A K-calibration method based on application of boundary collocation procedure to the William's stress function is utilized to relate the measured critical loads to the K_Ic values. The yield stresses and elastic moduli values in the bulk tensile mode are also evaluated. The availability of K_Ic à _y E and v (Poisson's ratio) values makes the calculation of crack tip plastic zone radii (r_yc ) and fracture energy (G_Ic ) values possible on the basis of Irwin's theory. The bulk casting procedure is done under different cure (temperature, time and cool-down) conditions to determine optimum properties.

The fracture behavior of the same adhesives in the bonded form is studied with the use of Independently Loaded Mixed Mode Specimen (ILMMS) geometry. This specimen allows independent measurement of P_I and P_II (and consequently G_I and G_II ) values. Since the fracture energy values are affected by the thickness of the adherend and the bondline, an experimental program is executed first by varying these geometrical parameters to determine the plane strain conditions. The relationship between the bondline thickness and the crack tip plastic zone radius values calculated earlier is also studied. Expressions developed on the basis of LEFM assumptions are utilized to calculate G_Ic and G_IIC values in the bonded form. The G_IC values obtained in this manner are compared to the bulk G_IC values obtained earlier.

With the availability of P_I and P_II (G_I and G_II ) values that result in failure in the bonded form, the fracture condition (i.e. the fracture failure criterion) in mixed mode (modes I and II) loading is determined for adhesively bonded joints. The use of both 1113 and 1113-2 adhesives also reveals the effects of the carrier cloth on the mechanical phenomena cited above.     

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.     

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.