A.D. Crocombe

Elastic analysis and engineering design formulae for bonded joints

Abstract The general elastic plane strain problem of adhesively bonded structures which consist of two different adherends is considered. To facilitate a truly general approach the adhesive joint is modelled as an adherend-adhesive sandwich with any combination of tensile, shear and moment loading being applied at the ends of both adherends. A full elastic analysis is presented which calculates the adhesive shear and tensile stresses in the overlap region, this analysis has been validated for a range of load cases using a finite element program. Basic design approaches are outlined and explicit expressions are developed which enable the simple evaluation of the stress distributions in the adhesive overlap. Simplified two parameter design formulae are also produced which accurately describe the peak stresses at the ends of the adhesive overlap in both the transverse and longitudinal shear directions. In all of the analyses the adherends are assumed to behave as linear elastic cylindrically bent plates with the adhesive forming an elastic interlayer between them. In the simplified analyses only one component of adhesive stress is considered, while in the full elastic analysis two components of stress are considered with a consequent increase in the complexity of the required solution method, but also an increase in accuracy over the simplified analyses for a wider range of joint configurations.

Global yielding as a failure criterion for bonded joints

Abstract This paper is concerned with predicting failure in adhesively bonded joints. After reviewing various methods that have been used for this purpose one technique is presented that in three independent studies has given reliable predictions of joint strength. This is based on a concept termed global yielding, which applies when a path of adhesive along the overlap region reaches the state in which it can sustain no further significant increase in applied load. Using an analysis technique such as the finite element method it is possible to ascertain the load at which this occurs fairly readily; this gives a good estimate of failure load. The three studies cited consist of experimental and analytical programmes on different types of joint. The first is concerned with the single lap joint, where this technique actually demonstrates why the strength of a joint increases with decreasing adhesive thickness. The second study is concerned with failure in double lap joints and the third with a new type of test termed the compressive shear test where it can be shown that loads considerably in excess of those expected can be sustained by eliminating the transverse tensile adhesive stresses.

Non-linear adhesive bonded joint design analyses

Abstract The general plane strain problem of adhesively bonded structures which consist of two different adherends is considered. The adhesive joint is modelled as an adherend-adhesive sandwich allowing the application of any combination of tensile, shear and moment loading at the adherend ends. The adherends are assumed to behave as linearly elastic cylindrically bent plates with the adhesive forming a non-linear interlayer between them. The deformation theory of plasticity is used to model the stress-strain characteristics of the adhesive, with the stress-strain curve itself being approximated by any continuous mathematical function. In this case both a Ramberg-Osgood curve and a hyperbolic tangent approximation were used. Unlike some approaches to this problem both the adhesive shear and the transverse direct stresses contribute to the yield of the adhesive, and the non-linear response of both is modelled. The adhesive yield can be modelled using either a simple or modified von Mises yield criterion. The latter is formulated for adhesives taking into account hydrostatic stresses as well as deviatoric stresses. Force and moment balance equations for an elemental length of sandwich overlap are presented. Simple adherend bending is assumed and the differential deformations in the upper and lower adherends in both the shear and transverse directions are related to the corresponding strains in the adhesive layer. The problem is then reduced to a set of six first-order non-linear differential equations, which, in conjunction with the chosen stress-strain properties of the adhesive, are solved using a boundary-value finite-difference method. Both the stress and strain results in the shear and transverse directions for various load cases have been compared with the results of a non-linear finite element analysis and agree favourably, even for high levels of adhesive non-linearity. Finally the analysis has been used to study the effect of adhesive thickness on lap joint strength and it is shown that this effect can only be modelled using a non-linear analysis.

The effect of environment on the fatigue of bonded composite joints, part 1: testing and fractography

In this work, the effect that test environment and pre-conditioning had on the fatigue behaviour of CFRP/epoxy lap–strap joints was investigated. It was shown that the fatigue resistance of the lap–strap joints did not vary significantly until the glass transition temperature, Tg, was approached, at which point a considerable reduction in the fatigue threshold load was observed. It was also noted that absorbed moisture resulted in a significant reduction in the Tg of the adhesive. This must be taken into account when selecting an adhesive to operate at elevated temperatures. The locus of failure of the joints was seen to be highly temperature dependent, transferring from primarily in the composite adherend at low temperatures to primarily in the adhesive at elevated temperatures. It was also seen that as the crack propagated along the lap–strap joint, the resolution of the forces at the crack tip tended to drive it into the strap adherend, which could result in complex mixed mode fracture surfaces.

Prediction of fatigue thresholds in adhesively bonded joints using damage mechanics and fracture mechanics

The prediction of fatigue threshold in composite adhesively bonded joints using continuum damage mechanics (CDM) and fracture mechanics (FM) approaches has been investigated. Two joint types were considered in this study: double lap (DL) and lap strap (LS) joints. The substrates, which were made of uni-directional (UD) or multi-directional (MD) composite laminates, were bonded together using an epoxy film adhesive. The joints were tested under fatigue loading with a load amplitude ratio of 0.1 at various test temperatures. Damage evolution laws were derived using thermodynamics principles. The number of cycles to failure was then expressed in terms of the stresses in the adhesive layer and material constants. The stresses were calculated from non-linear finite element analyses, considering both geometrical and material non-linearities. The damage laws generated for the UD/DL joint data were then used to predict the fatigue crack initiation thresholds for the MD/DL, UD/LS, and MD/LS joints. The FM approach uses the crack closure integral method to compute the strain energy release rate at the threshold load (G th) from the results of geometrical non-linear finite element analysis. The G th value for an inherent crack size at the centre of the bondline in the UD/LS joint is used as the failure criterion in order to predict the fatigue threshold for the MD/LS, UD/DL, and MD/DL joints. It was found that the predictions using CDM were slightly more accurate than those obtained using the FM approach. In general, when predicting the fatigue thresholds of the LS joints using the DL joints data, or vice versa, good agreement was obtained between the measured and predicted thresholds at ambient and low temperatures, but poor agreement was seen at the high test temperature. This was attributed to the deleterious effect of creep, which was greater in the DL joints than in the LS joints.

Investigating fatigue damage evolution in adhesively bonded structures using backface strain measurement

Predicting the service life of adhesive joints under fatigue loading remains a major challenge. A significant part of this task is to develop laws that govern the crack initiation phase. This paper contributes to this area through the development and application of the backface strain technique. A numerical study was carried out to investigate the effect of key parameters on the technique and to determine optimum gauge specification and location. Calibration curves were then produced relating the change in strain to the extent of damage. These numerical studies were then validated by undertaking a series of fatigue tests on both aluminium and GRP (glass-reinforced polymer)-bonded joints. Following various degrees of predicted damage the joints were carefully sectioned, polished, and studied using optical microscopy. The predicted and observed damage showed close correlation. The fatigue tests have also indicated that, for unmodified joints (intact fillets), even at high loads (50% static failure load) there was an initiation phase that accounted for about half the fatigue life of the joint. Removal of the adhesive fillet has been found to eliminate the initiation phase and consequently reduce fatigue life.

Environmental degradation of the interfacial fracture energy in an adhesively bonded joint

The mixed mode flexure and notched coating adhesion tests have been carried out in order to characterise interfacial fracture for a range of environmental exposure conditions and to find a meaningful interfacial strength parameter using a fracture mechanics approach. The moisture uptake of the adhesive was accelerated using an open-faced configuration. The critical loading to cause interfacial fracture was measured and was used in conjunction with finite element analysis (FEA) to determine the fracture energy under various exposure conditions. Moisture dependent material properties were incorporated in the FEA. Scanning electron microscopy was used to characterise the nature of the failure surface. Significant degradation of the fracture energy of the interface was found and this was matched by observed changes to the failure surface. The fracture energies were found to be largely independent of test method, exposure environment and time and was primarily related only to the moisture concentration.

Numerical prediction of fatigue crack propagation lifetime in adhesively bonded structures

Abstract In this short paper, a generalised numerical procedure using finite element (FE) analysis for prediction of the fatigue lifetime of adhesively bonded structures is proposed. The number of cycles to failure (Nf) is calculated by integrating a fatigue crack growth law between initial and final crack lengths. This crack growth law is formulated in terms of the strain energy release rate (SERR), which is determined, at any crack length, from an FE analysis. This complete process is implemented within the FE code, enabling automated calculation of the fatigue life for a given set of boundary conditions. This is a development of the approach outlined for single-lap joints [Int. J. Fract., 103 (2000) 41]. However, being fully implemented within an FE code it is not limited by the approximations of the simplified analytical expressions and furthermore can be applied to any structural configuration. The procedure was evaluated by application to a single-lap joint and good results were obtained in comparison with those using other methods. Furthermore, the use of the total SERR (GT) and mode I SERR (GI) as crack-propagation-controlling parameters are investigated and briefly discussed.

Durability modelling concepts and tools for the cohesive environmental degradation of bonded structures

Abstract This paper presents a framework that has been developed to enable the environmentally degraded response of bonded structures to be assessed. This framework includes both interfacial and cohesive weakening. Numerical tools are outlined which enable the implementation of this framework for structures where cohesive (rather than interfacial) weakening determines the degraded structural response. The application of these tools is illustrated for the case of a single-lap joint. Initially, the effect of the adhesive fillet on the kinetics of moisture diffusion through the joint is quantified and an approximate analytical model presented. This is followed by assessing the residual strength of an aluminium (2024-T3) lap joint bonded with FM 1000 that has been exposed to 30 days immersion in water. This modelling approach is based on a coupled mechanical-diffusion analysis which has been solved by using finite element analysis principles. Coupled non-linear finite element analyses of both dry and wet joints are undertaken. Appropriate diffusion data and moisture-dependent adhesive material properties have been used in the wet joint analysis to determine the spatial variation of moisture and hence the variation in material response throughout the adhesive layer. It is shown that the wet and dry joint strengths can be predicted from known adhesive failure strains and further that failure would initiate at the centre of the wet joint.

Analysing structural adhesive joints for failure

Abstract This paper addresses the problem of adhesive joint design by linking various joint analyses with potential criteria of joint failure in order to give a facility for joint strength prediction that is accessible to a design engineer. The paper is thus split into two sections, the first outlining various approaches to joint analysis, some established and others completely new, white the second part uses these techniques to address the problem of actual joint failure. The main part of the analysis section is devoted to a summary of a design analysis approach that increases in complexity from linear elastic design formulae to a full adhesive-adherend non-linear analysis. This is compared with the finite element method which is viewed as a research rather than design tool. In the joint failure section all of the approaches to joint analysis have been used to predict the strength of a wide range of adhesive joints. The application of fracture mechanics to the singularities found at joint bimaterial interfaces has also been discussed. As a result of this work relevant failure criteria are proposed.