Keywords: cylindrical joint, adhesion, stress concentration, finite element analysis, joint design.

The use of adhesive for the design of assemblies can reduce the cost and the weight of structures, especially in the case of assembling dissimilar material or of composite materials, but a lack of confidence limits the current use of this technology. Thus, the optimisation of the design of adhesively-bonded assemblies requires accurate numerical tools which have to take into account the possible stress singularities due to edge effects. Stress singularities can contribute to the initiation and the propagation of cracks in the adhesive. Various simplified models have been proposed in order to describe the behavior of some bonded joints using one or two-dimensional models, but often such models are not able to describe the effect of stress singularities which often have an influence on the maximum load transmitted by the bonded assemblies. Therefore, understanding the stress distribution in an adhesive joint can lead to improvements in adhesively-bonded assemblies; for instance, the design of assemblies which strongly limit the edge effects can be very interesting.

The aim of this paper is first to analyse the stress concentrations in the case of cylindrical joints under axial loading starting from refined finite element computations assuming elastic behaviour of the materials. Such problems can be solved using axisymmetric models which are less costly than three-dimensional models. It has been shown, for other geometries of bonded joints, on the one hand, that it is necessary to strongly limit the influence of edge effects, starting form computation under linear elasticity, in order to limit the risk of first rupture near the edge of the joint; and on the other hand, that the non-linear behaviour of the adhesive (plasticity) does not seem to limit the influence of the edge effects. The influence of various geometrical parameters, such as joint thickness, overlap length and tubular thickness, on the stress distribution are analysed. Secondly, geometries which strongly limit the influence of edge effects are proposed. An optimisation of the maximum transmitted load of cylindrical joints is proposed using a pressure-dependent elastic limit of the adhesive defined from the two stress invariants, hydrostatic stress and von Mises equivalent stress; such models are often used to model the behaviour of polymers.

Those numerical results provide some rules for manufacturing conditions in order to optimise bonded cylindrical joints under tensile loading. Assuming elastic behaviour, the key point is to strongly limit the influence of edge effects in order to increase the load transmitted. An optimisation of the geometrical parameters of the two proposed geometries (beaks and inverse beaks) can improve the behaviour the assemblies.

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