Analysis and design of adhesively bonded joints for fatigue and fracture loading: a fracture-mechanics approach

An experimental–computational fracture-mechanics approach for the analysis and design of structural adhesive joints under static loading is demonstrated by predicting the ultimate fracture load of cracked lap shear and single lap shear aluminum and steel joints bonded using a highly toughened epoxy adhesive. The predictions are then compared with measured values. The effects of spew fillet, adhesive thickness, and surface roughness on the quasi-static strength of the joints are also discussed. This fracture-mechanics approach is extended to characterize the fatigue threshold and crack growth behavior of a toughened epoxy adhesive system for design purposes. The effects of the mode ratio of loading, adhesive thickness, substrate modulus, spew fillet, and surface roughness on the fatigue threshold and crack growth rates are considered. A finite element model is developed to both explain the experimental results and to predict how a change in an adhesive system affects the fatigue performance of the bonded joint.     

Failure load prediction of structural adhesive joints Part 1: Analytical method

This paper describes an analytical method for calculating the strain energy release rate of cracked adhesive joints. The calculations proceed from a knowledge of the reactions in the adherends at the end of the joint overlap. For joints with equal adherends, a simple method exists for determining the Mode I and Mode II components of the energy release rate. The equations make it relatively easy to apply fracture mechanics failure criteria to arbitrarily loaded adhesive joints. In a subsequent paper, it is shown that by treating uncracked joints as having a crack, with the crack tip coinciding with the location of the spew fillet, the load required to propagate a crack in a cracked joint serves as a reliable conservative estimate of the load required to propagate a crack in an uncracked joint. The present method is suitable, therefore, for failure load predictions of structural adhesive joints in design applications.     

Rate effects for mixed-mode fracture of plastically-deforming,adhesively-bonded structures

Mixed-mode fracture of an adhesively-bonded structure made from a commercial adhesive and a dual-phase steel has been studied under different rates. Since mixed-mode fracture occurs along the interface between the steel and the adhesive, the cohesive parameters for the interface were required. The mode-II interfacial properties were deduced in earlier work. In this paper the mode-I interfacial toughness and the mode-I interfacial strength were determined at different rates. The mode-I interfacial strength was not affected by rate up to crack velocities at levels associated with impact conditions, and was essentially identical to the cohesive strength appropriate for crack growth within the adhesive layer. The mode-I toughness was reduced by about 40% when the crack propagated along the interface rather than within the adhesive. Furthermore, transitions to a brittle mode of failure occurred in a stochastic fashion, and were associated with a drop in interfacial toughness by a factor of about five. The mode-I interfacial parameters were combined with the previously-determined mode-II interfacial parameters within a cohesive-zone model to analyze the mixed-mode fracture of the joints which exhibited both quasi-static and unstable fracture. The mixed-mode model and the associated cohesive parameters for both quasi-static and unstable crack propagation provide bounds for predicting the behavior of the bonded joints under various rates of loading, up to the impact conditions that could be appropriate for automotive design.     

A Unified Approach for Predicting the Strength of Cracked and Non-Cracked Adhesive Joints

This paper presents an investigation of suitable failure criteria for predicting the strengths of uncracked and interfacially-cracked adhesively-bonded joints. A detailed experimental study of both bulk adhesive and adhesive joint behaviour has been carried out. The effect of both strain rate and temperature on the response of the adhesive to mechanical loading has been investigated through a series of tensile tests. The resulting data were used to construct an empirical model for the behaviour of the adhesive, A novel test method based on a four-point bend specimen has been used to investigate how the hydrostatic stress affects the response of the adhesive. Extensive tests on adhesive joints, subjected to different modes of loading and different lengths of interfacial cracks, have provided comprehensive joint strength data and insight into the site and locus of joint failure initiation. Following this, various failure criteria have been evaluated by carrying out detailed linear elastic and non-linear elasto-plastic two-dimensional analyses of the joints tested. Three-dimensional analyses provided modified loads for these two-dimensional analyses that more accurately reproduce the conditions on the plane of failure. Criteria based on critical stress or strain components at a distance from the point of singularity were investigated A procedure for accounting for the strain rate effects of the adhesive has been incorporated with the non-linear analyses. Criteria based on critical energy release rates have been evaluated from the linear elastic analyses of the joints with interfacial cracks diminishing to very small sizes. Finally, non-linear springs along a plane of failure have been used to model a line of localised damage, resulting in joint failure criteria based on a critical opening displacement. This last method provides the most physically acceptable way of predicting the strength of cracked and non-cracked joints using the same failure criterion.     

Adhesive Failure of Model Acrylic Pressure Sensitive Adhesives

An axisymmetric adhesion apparatus was used to characterize the adhesive and viscoelastic properties of acrylic block copolymer layers that behave as model pressure sensitive adhesives. The mechanisms of deformation were summarized and related to the structure and linear viscoelastic response of each model adhesive. In cases where the area between the adhesive layer and adhering surface remained circular and shrunk uniformly during detachment, the adhesive failure criterion can be quantified and compared to predictions from linear elastic fracture mechanics. The nature of adhesive failure can not be reconciled with these traditional, low-strain approaches, but is consistent with models of large strain elasticity, provided that the finite thickness of the adhesive layer is taken into account. A dimensionless ratio involving the adhesive strength, elastic modulus and adhesive layer thickness can be used to define the regime in which the adhesive failure criterion can be quantified with linear elastic fracture mechanics.     

Characterising bonded joints with a thick and flexible adhesive layer–Part 1: Fracture testing and behaviour

Adhesively bonded structural joints have increasingly found applications in automotive primary structures, joining dissimilar lighter-weight materials. Low-modulus rubbery adhesives are attracting rising interest as an alternative to conventional rigid structural adhesives due to benefits such as the excellent impact resistance they provide. This paper is the first of two parts that investigate, both experimentally and numerically, the mechanical behaviour of a rubbery adhesive and the bonded joints to be used in a lightweight automobile structure. This part 1 paper characterises the fracture behaviour of the flexible adhesive layer with thick bondlines and presents a way to reliably determine the fracture mechanics parameters under a range of loading modes. Assessment of the various fracture tests indicated that DCB and SLB should provide mode I and mixed mode fracture energies but that the conventional ENF for mode II would not be practical for such compliant adhesive layers. Instead a cracked thick adherend shear specimen was developed and used. Reliable fracture energies were obtained from these specimens and a mixed mode fracture criterion developed for application in the part 2 paper.     

Adhesive Failure of Model Acrylic Pressure Sensitive Adhesives

An axisymmetric adhesion apparatus was used to characterize the adhesive and viscoelastic properties of acrylic block copolymer layers that behave as model pressure sensitive adhesives. The mechanisms of deformation were summarized and related to the structure and linear viscoelastic response of each model adhesive. In cases where the area between the adhesive layer and adhering surface remained circular and shrunk uniformly during detachment, the adhesive failure criterion can be quantified and compared to predictions from linear elastic fracture mechanics. The nature of adhesive failure can not be reconciled with these traditional, low-strain approaches, but is consistent with models of large strain elasticity, provided that the finite thickness of the adhesive layer is taken into account. A dimensionless ratio involving the adhesive strength, elastic modulus and adhesive layer thickness can be used to define the regime in which the adhesive failure criterion can be quantified with linear elastic fracture mechanics.     

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.     

Effect of the aspect ratio of the pre-existing rectangular adhesion failure on the structural integrity of the adhesively bonded single lap joint

Non-linear three dimensional (3-D) finite element analyses (FEA) of the single lap joints (SLJs) having pre-existing rectangular adhesion failure in the interface of the strap adherend and the adhesive have been carried out. The effect of the size, the shape and the aspect ratio of the pre-existing rectangular adhesion failure on (i) the strength, (ii) the interfacial stresses and (iii) the strain energy release rates (SERRs) in the vicinity of the adhesion failure front have been presented in this research work. The SLJ is subjected to uniformly applied tensile load. The adherends are made with very high strength steels and the adhesive is a commercially available AV119. The analyses of the adhesion failure propagation have been carried out by sequentially releasing the constraints of the nodes ahead of the pre-existing adhesion failure front in finite element model. The SERR values in the vicinity of the adhesion failure fronts are computed using the virtual crack closure technique (VCCT) for assessment of the structural integrity of the SLJ. The strength of the SLJ, the interfacial stresses, and the three modes of strain energy release rates (SERRs) have been found to be significantly affected by the shape and size of adhesion failures. The SERRs and interfacial stresses along the rectangular adhesion failure front are compared with the corresponding values around the circular adhesion failure front of same area, pre-existing in the SLJ. It is observed that the circular and rectangular adhesion failures of the same area will have dissimilar growth rate and the mode II is the dominant failure mode. The total strain energy release rate and the failure strength, computed from the 3-D FEA of the SLJ is in good agreement with the experimental fracture toughness of the AV119 adhesive and the experimentally obtained failure loads, respectively.     

On the use of fracture mechanics in designing a single lap adhesive joint

The design of adhesively bonded joints is a quite difficult task, due to the stress singularity that arises at the edges of the adhesive adjacent to the loaded substrate. This stress singularity makes any design approach based on elastic stress analysis inconvenient. A more convenient design tool for an adhesive joint should be based on its mode of failure. Most of the adhesive joints fail at the adhesive/adherend interface or very close to it in the adhesive layer. Therefore, a fracture theory such as linear elastic fracture mechanics (LEFM) can be used to analyse the failure of an adhesive joint. In this paper, the design of a single lap joint using a fracture mechanics parameter, i.e. the strain energy release rate (SERR), is discussed. The SERR is extracted from a finite element model using Irwin's virtual crack closure integral. A design equation relating the lap length to the adherend thickness through some design parameters is derived.     

Mode-I adhesive fracture energy of carbon fibre composite joints with nanoreinforced epoxy adhesives

The effect of the addition of carbon nanoreinforcements to an epoxy adhesive on the strength and toughness of carbon fibre/epoxy composite joints was studied. The laminate surfaces, treated with peel ply, were characterised by profilometry, image analysis and wettability. The mechanical properties of the joints were determined by lap shear testing and double cantilever beam testing. The fracture mechanisms were studied by scanning electron microscopy.The addition of carbon nanofibres and carbon nanotubes caused an increase in the mode-I adhesive fracture energy, G_IC, of the joints while their lap shear strengths remained approximately constant. This improvement in the fracture behaviour was attributed to the occurrence of toughening mechanisms when carbon nanoreinforcements were added to the epoxy adhesive. Additionally, the use of carbon nanotubes improved the interfacial strength between the adhesive and the substrate, changing the crack growth behaviour and the macroscopic failure mode.     

Modeling of cohesive failure processes in structural adhesive bonded joints

This paper presents an approach to predicting the strength of joints bonded by structural adhesives using a finite element method. The material properties of a commercial structural adhesive and the strength of single-lap joints and scarf joints of aluminum bonded by this adhesive were experimentally measured to provide input for and comparison with the finite element model. Criteria based on maximum strain and stress were used to characterize the cohesive failure within the adhesive and adherend failure observed in this study. In addition to its simplicity, the approach described in this paper is capable of analyzing the entire deformation and failure process of adhesive joints in which different fracture modes may dominate and both adhesive and adherends may undergo inelastic deformation. It was shown that the finite element predictions of the joint strength generally agreed well with the experimental measurements.     

Characterization of fracture in adhesively bonded double-lap joints

A broad finite element study was carried out to understand the stress fields and stress intensity factors behavior of cracks in adhesively bonded double-lap joints, which are representative of loading in real aerospace structures. The interaction integral method and fundamental relationships in fracture mechanics were used to determine the mixed-mode stress intensity factors and associated strain energy release rates for various cases of interest. The numerical analyses of bonded joints were also studied for various kinds of adhesives and adherends materials, joint configurations, and thickness of adhesive and different crack lengths. The finite element results obtained show that the patch materials of low stiffness, low adhesive moduli and low tapering angles are desirable for a strong double-lap joint. In the double-lap joint, the shearing-mode stress intensity factor is always larger than that of the opening-mode and both shearing and opening mode stress intensity factors increase as the crack length increases, but their amplitudes are not sensitive to adhesive thickness. Results are discussed in terms of their relationship to adhesively bonded joints design and can be used in the development of approaches aimed at using adhesive bonding and extending the lives of adhesively bonded repairs for aerospace structures.     

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.     

Time Dependent Crack Growth and Loading Rate Effects on Interfacial and Cohesive Fracture of Adhesive Joints

Double cantilever beam fracture specimens were used to investigate rate dependent failures of model epoxy/steel adhesively bonded systems. Quasi-static tests exhibited time dependent crack growth and the maximum fracture energies consistently decreased with debond length for constant crosshead rate loading. It was also possible to cause debonding to switch between interfacial and cohesive failure modes by simply altering the loading rate. These rate dependent observations were characterized using the concepts of fracture mechanics. The time rate of change of the strain energy release rate, dG/dt, is introduced to model and predict failure properties of different adhesive systems over a range of testing rates. An emphasis is placed on the interfacial failure process and how rate dependent interfacial properties can lead to cohesive failures in the same adhesive system. Specific applications of the resulting model are presented and found to be in good agreement when compared with the experimental data. Finally, a failure envelope is identified which may be useful in predicting whether failures will be interfacial or cohesive depending on the rate of testing for the model adhesive systems.     

The effect of residual strains on the progressive damage modelling of environmentally degraded adhesive joints

This work is concerned with developing numerical modelling techniques for predicting the environmental degradation of adhesively-bonded joints. Associated experimental data are also reported. The moisture-dependent mechanical properties of the adhesive were obtained by testing bulk specimens also exposed to various moisture contents. The diffusion parameters for moisture in the adhesive were determined by carrying out gravimetric experiments on bulk adhesive samples. The moisture-dependent interfacial bond strength of the adhesive system investigated has been determined by testing a mixed mode flexure (MMF) specimen, exposed to obtain various levels of moisture content at the interface. Progressive damage in the joints was modelled with a two-parameter cohesive zone model (CZM). The CZM parameters were determined by correlating the experimental data obtained from the MMF test with results from the numerical simulation. The parameters were then used to predict the response of another configuration, the notched coating adhesion (NCA) specimen. When the residual stresses were neglected in the modelling, the predicted NCA response was seen to be in good agreement with the experimental data. However, initial simulations that included the residual stresses resulted in poor predictions of the NCA response. Creep tests on the saturated adhesive, at the ageing temperature, showed large viscoplastic deformations at low loads. Coupled diffusion-stress modelling, including viscoplastic material properties for the adhesive continuum, showed that the residual stresses for the aged specimens decreased significantly and thus did not contribute strongly to the environmental weakening. Good predictions were then obtained for the NCA tests.     

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.     

Contents Lists and Abstracts from the Journal of the Adhesion Society of Japan

Double cantilever beam fracture specimens were used to investigate rate dependent failures of model epoxy/steel adhesively bonded systems. Quasi-static tests exhibited time dependent crack growth and the maximum fracture energies consistently decreased with debond length for constant crosshead rate loading. It was also possible to cause debonding to switch between interfacial and cohesive failure modes by simply altering the loading rate. These rate dependent observations were characterized using the concepts of fracture mechanics. The time rate of change of the strain energy release rate, dG/dt, is introduced to model and predict failure properties of different adhesive systems over a range of testing rates. An emphasis is placed on the interfacial failure process and how rate dependent interfacial properties can lead to cohesive failures in the same adhesive system. Specific applications of the resulting model are presented and found to be in good agreement when compared with the experimental data. Finally, a failure envelope is identified which may be useful in predicting whether failures will be interfacial or cohesive depending on the rate of testing for the model adhesive systems.     

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.