Keywords: stress analysis, edge effects, non-associated elasto-visco-plastic model, finite element analysis, joint design.

This study is concerned with increasing the performance of adhesively bonded structures. The experimental and numerical analyses of the mechanical behaviour of bonded joints are particularly made difficult by the edge effects. Stress singularities can contribute to the initiation and the propagation of cracks in adhesive joints. Therefore, understanding the stress distribution in an adhesive joint can lead to improvements in adhesively-bonded assemblies and to develop reliable experimental tests in order to analyse the non-linear behaviour of an adhesive in an assembly.

Starting from the usual single lap shear specimen, the influence of some parameters on the stress distribution through the adhesive joint thickness is presented. The three main parameters are the geometry of the substrate close to the adhesive joint, the local geometry of the joint near the edge and the thickness of the adhesive joint. Moreover the numerical determination of how stresses evolve through the thickness of the adhesive allows us to analyse the differences between the results of two experimental devices: a modified Arcan fixture, designed in order to strongly limit the influence of the edge effects, and the standardised fixture TAST. The experimental results, obtained from the proposed modified Arcan, underline various aspects of the non-linear behaviour of the adhesive for radial loadings, and are useful to develop accurate numerical models for the behaviour of the adhesive in an assembly.

A two-dimensional non-asssociated elasto-viscoplastic model is developed according to the interface finite elements formalism to represent the non linear evolution of the relative displacement of both extremities of the joint with respect to the stress state. This type of model can be justified when the thickness of the joint is not too large and by the observation of an homogeneous deformation in the thickness of the adhesive joint. As numerical simulations, performed under linear assumptions, have shown a non uniform stress state in the adhesive joint, inverse techniques are used to identify the parameters of the model. A coupling method between a finite element code and an optimization one is also presented. The proposed model represents accurately the different experimental responses for proportional traction/compression-shear loadings and for a large range of deformation rates.

Moreover, studies are underway in order to extend the proposed modelling strategy to three-dimensional applications using a pressure-dependent constitutive model. The use of the data base of experimental results from tensile-shear tests allows the identification of the so-called initial yield function in the hydrostatic stress - von Mises equivalent stress plane. The first results, underline the possibilities of three-dimensional Drucker-Prager type constitutive relations, for modelling the behaviour of an adhesive in an assembly.

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