Mode-l Fracture Behaviour of Adhesive Joints. Part I. Relationship Between Fracture Energy and Bond Thickness

The fracture properties of adhesive joints of aluminium were investigated using a rubber-modified tough epoxy resin system (G_IC = 2.76 kJ/m²) as adhesive material. Compact tension (CT) adhesive joints were manufactured for a wide range of bond thickness t (from 0.05mm to 10mm) and fracture tests conducted under static load. Scanning electron microscopy (SEM) was used to examine the fracture surface morphology. A large deformation elastic- plastic finite element model was developed to evaluate the J-integral value for different bond thickness. The fracture energy, J_c , was found to be highly dependent on the bond thickness and was lower than that of the bulk adhesive. As the bond thickness was increased J_c also increased, though not monotonically, towards the fracture energy of the bulk adhesive. This result was caused by the complicated interactions between the stress and strain fields, plastic deformation of the adhesive around the crack tip, constraint from the adherends and the failure path. It was shown that values of J_c as a function of bond thickness correlated well with the variation of plastic zone height. Scanning electron micrographs from the fracture surfaces of the CT adhesive joints illustrated that the failure path was mainly cohesive through the centre-plane of the adhesive layer. Brittle fracture mechanisms were observed for thin bonds (0.04mm < t< 0.5 mm) but tough fracture mechanisms were identified for thick bonds (t > 1 mm).     

Evaluation of Mode-II Fracture Energy of Adhesive Joints with Different Bond Thickness

A study on the mode-II edge-sliding fracture behaviour of aluminium-adhesive joints was carried out. Compact pure shear (CPS) adhesive joints of different bond thickness were produced using a rubber-modified epoxy resin as the adhesive. An analytical model was developed to calculate the stress distribution along the bond line of the joint. A crack-closure technique was used to evaluate the mode-II strain energy release rate. G_II, as a function of the adhesive bond thickness. The results indicated that for a given applied load, G_II increased gradually with the bond thickness. A finite element model (FEM) was also developed to evaluate the stress state along the bond line and the strain energy release rate of the CPS specimens. Consistent results were obtained between the theoretical model and finite element analysis. Scanning electron micrographs of the fracture surface illustrated a mainly interfacial fracture path between the adherends and the adhesive for all adhesive joint specimens. The critical fracture load increased very rapidly with bond thickness in the range 0.02 mm to 0.1 mm but remained constant thereafter. However, the mode-II critical fracture energy rose more gradually as the bond thickness was increased.     

Evaluation of Mode-II Fracture Energy of Adhesive Joints with Different Bond Thickness

A study on the mode-II edge-sliding fracture behaviour of aluminium-adhesive joints was carried out. Compact pure shear (CPS) adhesive joints of different bond thickness were produced using a rubber-modified epoxy resin as the adhesive. An analytical model was developed to calculate the stress distribution along the bond line of the joint. A crack-closure technique was used to evaluate the mode-II strain energy release rate. G _II, as a function of the adhesive bond thickness. The results indicated that for a given applied load, G _II increased gradually with the bond thickness. A finite element model (FEM) was also developed to evaluate the stress state along the bond line and the strain energy release rate of the CPS specimens. Consistent results were obtained between the theoretical model and finite element analysis. Scanning electron micrographs of the fracture surface illustrated a mainly interfacial fracture path between the adherends and the adhesive for all adhesive joint specimens. The critical fracture load increased very rapidly with bond thickness in the range 0.02 mm to 0.1 mm but remained constant thereafter. However, the mode-II critical fracture energy rose more gradually as the bond thickness was increased.     

Effect of Bond Thickness on Fracture Behaviour in Adhesive Joints

To study the effects of bond thickness on the fracture behaviour of adhesive joints, experimental investigation and finite element analysis have been carried out for compact tension (CT) and double-cantilever-beam (DCB) specimens with different bond thickness. Fractography and fracture toughness exhibited apparent variations with bond thickness. Numerical results indicate that the crack tip stress fields are affected by bond thickness due to the restriction of plastic deformation by the adherends. At the same J level, a higher opening stress was observed in the joint with a smaller bond thickness (h). Beyond the crack tip region, a self-similar stress field can be described by the normalized loading parameter, J/hσ₀. The relationship between J and crack tip opening displacement, δ, is dependent on the bond thickness. The strong dependence of toughness upon bond thickness is a result of the competition between two different fracture mechanisms. For small bond thickness, toughness is linearly proportional to bond thickness due to the high constraint. After reaching a critical bond thickness, the toughness decreases with further increase of bond thickness due to the rapid opening (blunting) of the crack tip with loading. A simple model has been proposed to predict the variation of toughness with bond thickness.     

Effect of Bond Thickness on Fracture Behaviour in Adhesive Joints

To study the effects of bond thickness on the fracture behaviour of adhesive joints, experimental investigation and finite element analysis have been carried out for compact tension (CT) and double-cantilever-beam (DCB) specimens with different bond thickness. Fractography and fracture toughness exhibited apparent variations with bond thickness. Numerical results indicate that the crack tip stress fields are affected by bond thickness due to the restriction of plastic deformation by the adherends. At the same J level, a higher opening stress was observed in the joint with a smaller bond thickness (h). Beyond the crack tip region, a self-similar stress field can be described by the normalized loading parameter, J/hσ₀. The relationship between J and crack tip opening displacement, δ, is dependent on the bond thickness. The strong dependence of toughness upon bond thickness is a result of the competition between two different fracture mechanisms. For small bond thickness, toughness is linearly proportional to bond thickness due to the high constraint. After reaching a critical bond thickness, the toughness decreases with further increase of bond thickness due to the rapid opening (blunting) of the crack tip with loading. A simple model has been proposed to predict the variation of toughness with bond thickness.     

Non Linear Fracture Mechanics for Adhesive Lap Joints

The Rice Cherepanov J is calculated for a lap joint in pure shear. By choosing as a condition for fracture a critical value J_c of this quantity the fracture load of the joint is calculated for linear elastic, perfectly plastic and linear hardening behavior of the adhesive. Comparisons are given with experiments with various adhesives and overlap lengths.     

Mode I Fracture Load Predictions of Adhesive T-joints

This paper presents fracture data and a finite element analysis for adhesive T-joints, It is shown that fracture loads of T-joints, bonded with two different structural epoxies and subjected to either tensile loading or three-point bending, can be predicted using a fracture mechanics approach. Fracture loads were predicted by calculating the applied energy release rate, G, using finite element methods, and comparing that with a critical value, G_c, determined experimentally using double-cantilever-beam specimens. By recording the failure sequence of the bondline with a video camera attached to a microscope, it was seen that subcritical crack propagation took place prior to final fracture of the bondline. Accounting for the observed subcritical crack propagation in the finite element analysis gave a good agreement between the actual and the calculated fracture loads.     

Analysis of Discontinuities in Time-Dependent Adhesive Fracture

The adhesive fracture energy of a bond system consisting of a soft adhesive bonded to several elastomers has been evaluated over a wide range of temperature and rate. It was found that the shift factors used to superpose bond data at different temperatures displayed time-dependent features of both the adhesive interlayer and the elastomeric backing/substrate, indicating thermorheologically complex behavior. Individual contributions of the various bond components to the overall response of the joint have been quantitatively described in terms of their weight fractions and plateau moduli. Adhesive fracture energy mastercurves obtained by superposition of data exhibited two pronounced discontinuities. Both of these discontinuities corresponded to changes in adhesive failure mode and one was related to the rubber-to-glass transition of the adhesive. Previous researchers have described the magnitude of this later discontinuity in terms of the simple extension properties of the adhesive. In this work, it is shown that the discontinuity can be described by the thermorheologically complex behavior of the bond system as manifested by changes in the effective viscoelastic reference state.     

Asymptotic Fields in Adhesive Fracture

This paper presents the asymptotic singular fields associated with the fracture analysis of adhesive joints and the micromechanics of adhesive failure. The fracture parameters used in adhesives are examined and their validity and use in applications is evaluated. Contrary to conventional fracture mechanics of homogeneous media the asymptotic field in most adhesive fracture is a function of the following: the adhesive and adherend properties, the dimensionality of the crack geometry, and their relationship to the interface. The Finite Element Iterative Method (FEIM) is used in analyzing the asymptotic fields. The results of the singularities for interfacial cracks of various geometries and material properties are presented and discussed in relation to adhesive failures.     

Asymptotic Fields in Adhesive Fracture

This paper presents the asymptotic singular fields associated with the fracture analysis of adhesive joints and the micromechanics of adhesive failure. The fracture parameters used in adhesives are examined and their validity and use in applications is evaluated. Contrary to conventional fracture mechanics of homogeneous media the asymptotic field in most adhesive fracture is a function of the following: the adhesive and adherend properties, the dimensionality of the crack geometry, and their relationship to the interface. The Finite Element Iterative Method (FEIM) is used in analyzing the asymptotic fields. The results of the singularities for interfacial cracks of various geometries and material properties are presented and discussed in relation to adhesive failures.     

Effect of Adhesive Stiffness and Thickness on Stress Distributions in Structural Finger Joints

Environmental, political, and socioeconomic actions over the past several years have resulted in a decreased wood supply at a time when there is an increased demand for forest products. This combination of increased demand and decreased supply has forced more emphasis on engineered wood products, a varied category usually connected with adhesively-bonded end joints, of which the most common type is the finger joint. This paper presents the results of a finite-element analysis of structural finger joints, and focuses primarily on the effect of adhesive stiffness and thickness on stress distribution patterns in finger joints. Results indicate that a flexible adhesive layer concentrates adherend longitudinal and radial stresses at the finger base, whereas a stiff adhesive layer minimizes adherend stresses but increases adhesive stress levels. Results also show that a thin adhesive layer concentrates longitudinal adherend stresses at the juncture of the finger tip and flexible finger base and concentrates radial stresses at all finger bases. However, these increased longitudinal and radial stresses are balanced by reduced adhesive shear stresses.     

Adhesive Failure and Deformation Behaviour of Polymers

An instrument has been developed to determine the adhesive fracture energy as a function of the most important parameters such as temperature, contact time etc. and to study the stress-strain behaviour during bond separation. Additionally, the deformation processes during debonding were observed by high speed photography. Investigations of two high molecular weight polymers, polyisobutylene (PIB) and polyethylhexylacrylate (PEHA), showed two different types of bond separation: “brittle” behaviour with low adhesive failure energy for PIB and the formation and deformation of fibrillar structures for PEHA leading to much higher strains at break and adhesive failure energies. It follows from mechanical measurements that both polymers differ mainly by their entanglement networks. The much longer entanglement spacing for PEHA leads to the formation of fibrillar structures which, in accordance with a theory of Good, seem to be the reason for strong adhesion.     

Mode II Fracture Toughness of a Brittle and a Ductile Adhesive as a Function of the Adhesive Thickness

The main goal of this study was to evaluate the effect of the thickness and type of adhesive on the Mode II toughness of an adhesive joint. Two different adhesives were used, Araldite ® AV138/HV998 which is brittle and Araldite 2015 which is ductile. The end notched flexure (ENF) test was used to determine the Mode II fracture toughness because it is commonly known to be the easiest and widely used to characterize Mode II fracture. The ENF test consists of a three-point bending test on a notched specimen which induces a shear crack propagation through the bondline. The main conclusion is that the energy release rate for AV138 does not vary with the adhesive thickness whereas for Araldite 2015, the fracture toughness in Mode II increases with the adhesive thickness. This can be explained by the adhesive plasticity at the end of the crack tip.     

Influence of Residual Thermal Stresses on the Fracture Behavior of Hybrid Bonded Joints

The objective of this work is to study the influence of the residual thermal stresses on the fracture behavior of hybrid composite-aluminium bonded joints. A modified DCLS specimen is designed and the strain energy release rate is determined using both an analytical fracture mechanics based method and a finite element method. The residual thermal stresses, which appear in the adhesive because of the difference between the curing and the service temperatures, are evaluated with a two-ply laminate specimen. Some rupture tests are performed on the DCLS specimens at different temperatures and for different geometries and materials. The results show a good agreement between analytical calculations, numerical analysis and experiments. The residual thermal stresses are never negligible in the considered hybrid bonded joints and do influence their fracture behaviors. Although the designed specimen is not adapted to study fatigue crack propagation, it provides a simple way to study the crack initiation and thus to characterize the rupture properties of the joint.     

Adhesive Failure and Deformation Behaviour of Polymers

An instrument has been developed to determine the adhesive fracture energy as a function of the most important parameters such as temperature, contact time etc. and to study the stress–strain behaviour during bond separation. Additionally, the deformation processes during debonding were observed by high speed photography. Investigations of two high molecular weight polymers, polyisobutylene (PIB) and polyethylhexylacrylate (PEHA), showed two different types of bond separation: “brittle” behaviour with low adhesive failure energy for PIB and the formation and deformation of fibrillar structures for PEHA leading to much higher strains at break and adhesive failure energies. It follows from mechanical measurements that both polymers differ mainly by their entanglement networks. The much longer entanglement spacing for PEHA leads to the formation of fibrillar structures which, in accordance with a theory of Good, seem to be the reason for strong adhesion.     

Fatigue Growth of Cohesive Defects in T-Peel Joints

This paper uses 2D and 3D finite element models to predict the stresses within bonded and weld-bonded T-peel joints. Epoxy adhesive is modelled as a homogeneous layer providing a perfect bond between aluminium adherends. Knowledge of the critical tensile stresses enables the likely region of fatigue crack initiation to be predicted. The long term reliability and durability of a joint depend directly on its fatigue strength. This research elucidates the region of cohesive crack initiation, the subsequent direction of crack propagation and the relative duration of the different stages of fatigue crack growth. The various stages of embedded, surface and through-width fatigue growth of cohesive defects within a T-peel joint are compared. This establishes fatigue life from crack initiation to final joint fracture for typical bonded and weld-bonded T-peel joints.     

Similarity Concepts in the Fatigue Fracture of Adhesively Bonded Joints

Cyclic debond data obtained from fatigue testing of four different specimen geometries having the same adhesive is considered. Fatigue properties of the adhesive are characterized in terms of linear elastic fracture mechanics concepts whereby debond growth rates are correlated to appropriate mixed mode fracture parameters. Stress analyses of the four specimens under maximum load indicate that in most cases inclusion of geometric nonlinearities is required for the determination of the fracture parameters. For three of the specimens considered, the debond growth laws based on total energy release rate as correlating mixed-mode fracture parameter were found to be similar. A number of potential reasons for the lack of similarity in debond growth laws in all four specimens are explored.     

A Method for the Stress Analysis of Lap Joints

A theory is presented for the adhesive stresses in single and double lap joints under tensile loading, while subjected to thermal stress. The formulation includes the effects of bending, shearing, stretching and hygrothermal deformation in both the adherend and adhesive. All boundary conditions, including shear stress free surfaces, are satisfied. The method is general and therefore applicable to a range of material properties and joint configurations including metal-to-metal, metal-to-CFRP or CFRP-to-CFRP. The solution is numerical and is based on an equilibrium finite element approach. Through the use of an iterative procedure, the solution has been extended to cater for non-linear adhesive materials.     

A Two-dimensional Stress Analysis of Butt Adhesive Joints Having a Circular Hole Defect in the Adhesive Subjected to External Bending Moments

This paper deals with a two-dimensional stress analysis of butt adhesive joints, with a circular hole defect in the adhesive, subjected to external bending moments. The analysis was done using the two-dimensional theory of elasticity in order to examine the strength of the joints. It was assumed that the adherends were rigid and the adhesive was replaced with a finite strip including a hole defect. The effects of the location and size of a hole defect on the stress distributions around the hole and at the interfaces were obtained by numerical calculations. In addition, the singular stress near the edge of the interface was obtained. For verification, photoelastic experiments were performed. The analytical results were fairly consistent with the experimental results. It was seen that the principal stress around a hole becomes larger with a certain shift toward the free boundary. It was also seen that the stress concentration became larger with an increase of the size of the hole.     

A Two-dimensional Stress Analysis of Butt Adhesive Joints Having a Circular Hole Defect in the Adhesive Subjected to External Bending Moments

This paper deals with a two-dimensional stress analysis of butt adhesive joints, with a circular hole defect in the adhesive, subjected to external bending moments. The analysis was done using the two-dimensional theory of elasticity in order to examine the strength of the joints. It was assumed that the adherends were rigid and the adhesive was replaced with a finite strip including a hole defect. The effects of the location and size of a hole defect on the stress distributions around the hole and at the interfaces were obtained by numerical calculations. In addition, the singular stress near the edge of the interface was obtained. For verification, photoelastic experiments were performed. The analytical results were fairly consistent with the experimental results. It was seen that the principal stress around a hole becomes larger with a certain shift toward the free boundary. It was also seen that the stress concentration became larger with an increase of the size of the hole.