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Computational Science, Engineering & Technology Series
ISSN 1759-3158
Edited by: B.H.V. Topping, G. Montero, R. Montenegro
Chapter 11

Numerical Modelling of Non-Linear Behaviour in Adhesively-Bonded Assemblies

J.Y. Cognard*, R. Créac'hcadec*, L. Sohier+ and P. Davies#

*Mechanics of Naval and Offshore Structures, ENSIETA, Brest, France
+Laboratoire d'Ingénierie Mécanique et Electrique, UBO, Brest, France
#Materials and Structures Group, IFREMER Brest Centre, Plouzané, France

Full Bibliographic Reference for this chapter
J.Y. Cognard, R. Créac'hcadec, L. Sohier, P. Davies, "Numerical Modelling of Non-Linear Behaviour in Adhesively-Bonded Assemblies", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Innovation in Computational Structures Technology", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 11, pp 225-247, 2006. doi:10.4203/csets.14.11
Keywords: adhesion, composite, marine structures, Arcan fixture, finite element, non-linear behaviour.

This paper presents the contributions of numerical modelling for the optimization of adhesively-bonded assemblies for marine and underwater applications. Such assemblies offer many advantages and major aerospace projects have addressed their use in aircraft structures, but a lack of confidence currently limits the marine use of this technology. If applications are to be extended it must be clearly demonstrated that the strength of adhesively bonded structures can be predicted accurately. There are several approaches to the strength analysis of bonded joints [1], but the analysis of the mechanical behaviour is made difficult, in particular by the stress singularities due to edge effects [2,3]. This work is part of an ongoing project aimed at developing numerical tools for adhesively bonded marine structures.

Difficulty in modelling the failure of even simple joints (lab shear specimens) highlighted the need for more reliable constituent input data. The first objective was to define an experimental methodology enabling the adhesives of interest to be characterised up to failure. A modified Arcan fixture [4] has been designed, using several numerical simulations, in order to enable compression or tension to be combined with shear loads [5,6]. Numerical simulations in linear elasticity, for bi-material structures, show that the use of a special geometry for the substrate (a beak close to the adhesive joint) makes it possible to strongly limit the contribution of the singularities due to edge effects. The numerical determination of the evolution of the stresses through the thickness of the adhesive joint requires very refined meshes, especially for large material heterogeneity of the structure. It has been numerically shown that another important parameter is the geometry of the joint near the edge; this parameter can be difficult to control during manufacturing. Moreover non-linear simulations taking into account the fixing system of the substrates onto the supporting fixture were used to optimize the design of the complete fixture in order to prevent pre-loading of the adhesive joint. For the epoxy resin VanticoTM Redux 420 the fracture envelope in the normal stress-shear stress plane has been reached; we note that compression increases the shear stress at failure significantly. Moreover, this study makes it possible to obtain an elastic envelope which is useful for rapid industrial-type design. Furthermore, the results obtained with steel or aluminium substrates and with mixed assemblies involving composites show similar behaviour of the adhesive using the procedure suggested [7].

The second aim of this work was to model the non-linear behaviour of the adhesive joint in order to allow us to achieve more precise dimensioning. Therefore, non-contact extensometry has been used to enable the full non-linear stress-strain behaviour to be determined. The geometry of the experimental fixture and the low thickness of the adhesive film (nearly 0.4 mm) led us to study the displacements of both substrates in order to obtain the relative displacements of both ends of the adhesive joint. An optimization technique has been developed in order to get the best displacement field of the substrates [7]. This technique can take into account the strains of the substrates associated with tension and shear stresses. The results underline different types of non-linear behaviour of the thin adhesive film with respect to the loading conditions (tension/compression-shear). This study allows us to work with the following variables: the applied load on the specimen and the displacement of both extremities of the adhesive joint. Viscoplastic behaviour of the adhesive joint is observed [6]; the non-linear behaviour is characterised by an important evolution of the strain of the adhesive joint. Moreover an anisotropic behaviour of the plastic evolution of the relative displacement of the two ends of the bonded joint is observed.

A further step was the development of a model to represent the evolution of the displacement of both extremities of the adhesive joint with respect to the stress state. This type of model can be justified by the observation of a homogeneous deformation in the thickness of the adhesive joint [8]. As the numerical simulations performed for linear behaviour of constituents have shown a non-uniform evolution of the state of stress in the adhesive joint, inverse type techniques are used to identify the parameters of the model, taking into account different experimental data.

To reduce the numerical cost of simulations of the non-linear behaviour of adhesively-bonded assemblies, the use of interface elements is proposed. Within this framework, which simplifies the identification procedure, a first version of an elastoplastic model with isotropic hardening was proposed in the case of monotonic loadings. The use of an inverse identification technique made it possible to determine the so-called elastic yield surface, which was represented by an elliptical function for two-dimensional problems. The feasibility of the proposed approach was evaluated starting from numerical examples.

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Goncalves J.P.M., Moura M.F.S.F., De Castro P.M.S.T., "A three-dimensional finite element model for stress analysis of adhesive joints", Inter. J. Adhesion et Adhesives; 22, 357-365, 2002. doi:10.1016/S0143-7496(02)00015-5
Arcan L., Arcan M., Daniel I., "SEM fractography of pure and mixed mode interlaminar fracture in graphite/epoxy composites", ASTM Special Tech. Publ., 948, pp. 41-67, 1987.
Cognard J.Y., Davies P., Gineste B.,"Conception et optimisation d'assemblages collés pour structures sous-marines en composites", 4ème Conférence internationale sur la conception et la fabrication intégrée en mécanique, cdrom, 2002.
Cognard J.Y., Davies P., Gineste B., Sohier L., "Development of an improved adhesive test method for composite assembly design", Composite Science and Technology, Vol 65, pp 359-368, 2005. doi:10.1016/j.compscitech.2004.09.008
Cognard J.Y., Davies P., Sohier L., "Design and Evaluation of bonded composite assemblies", 4th European Congress on Computational Methods in Applied Sciences and Engineering, cdrom, 2004.
Allix O., Corigliano A., "Geometrical and interfacial non-linearities in the analysis of delamination in composites", Int. J. of Solids and Structures, 36, pp. 2189-2216, 1999. doi:10.1016/S0020-7683(98)00079-1

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