Keywords: damage mechanics, contact, friction, interfaces, cohesive-zone models.

With the increasing use of adhesives in structural applications, the interest in modelling adhesively bonded joints and assemblies has increased as well. Adhesive bonding has several advantages compared to mechanical fastening, i.e. high corrosion and fatigue resistance and superior strength properties that often allow structures that are mechanically equivalent to, or even stronger than, conventional assemblies to be built at lower weight and cost.

As for most structural components consisting of the assembly of individual elements, failure of adhesive joints due to damage growth at bonded interfaces is one of the most important failure modes and for its simulation the cohesive-zone approach can be usefully resorted to. This is mainly motivated by the consideration that prior to the development of macroscopic fractures there exists a zone in a state of progressive damage located in front of the crack, the so-called cohesive process zone, where an interaction across the crack sides precedes the formation of traction-free surfaces. When compressive forces act at the interface, the adhesive response is accompanied by a frictional contact behaviour on the damaged area; this typically occurs in mode delamination tests where friction effects, besides being among the causes of the poor reproducibility of values of the measured fracture energy [1], can also appreciably modify the load-deflection response.

In this work the progressive interface de-cohesion is modelled via the damage mechanics approach developed by the authors in [2], relying upon the use of a single scalar damage indicator and a consistently defined work-conjugate damage energy release rate. Normal contact forces on the damaged surface are such that the contacting bodies are strictly prevented from penetration while the corresponding frictional effects, regarded as completely independent from the adhesive relationship, are introduced by analogy to classical plasticity, i.e. via an additive decomposition of the displacement jump and a modified Coulomb law allowing for small elastic tangential displacements during frictional sliding.

Under compressive loading the cohesive relationship described by the damage model is combined with the frictional model by assuming that friction acts only on the damaged portion of the interface, i.e. on the contact area. To the best of authors' knowledge, this idea appears to have been first suggested by Raous and Monerie [3] in order to obtain a progressive transition from adhesion to frictional contact behaviour. The same approach is also used by Alfano and Sacco [4], where a fully local formulation of frictional contact behaviour is exploited based on a penalty formulation of the contact constraint and the damage variable is understood as the area ratio during debonding, in accordance with the classical interpretation given to it in isotropic damage models.

The developed interface model has been implemented as a part of the general-purpose finite element (FE) code CAST3M [5]; the results of finite element analyses have been compared with the experimental results obtained for the three-point end-notched flexure (ENF) test, for which through-the-thickness compression induces friction effects between the crack faces. The comparison between experimental and numerical results shows that, if friction is neglected, the peak load is not well captured and the part of the experimental curve corresponding to the crack propagation phase tends to intersect the one obtained via FE analysis. On the contrary, no intersection is likely to occur for the frictional case, thus showing that, even with the present basic modelling of friction, an improved prediction of the experimental response is obtained.

1

X. Sun and B. D. Davidson. Numerical evaluation of the effects of friction and geometric nonlinearities on the energy release rate in three- and four-point bend end-notched flexure tests. Engineering Fracture Mechanics, 73(10):1343-1361, 2003. doi:10.1016/j.engfracmech.2005.11.007

2

N. Valoroso and L. Champaney. A damage-mechanics-based approach for modelling decohesion in adhesively bonded assemblies. Engineering Fracture Mechanics, 2006.
in press. doi:10.1016/j.engfracmech.2006.04.029

3

M. Raous and Y. Monerie. Unilateral contact, friction and adhesion: 3d cracks in composite materials. In J.A.C. Martins and M.D.P. Monteiro Marques, editors, Contact Mechanics, pages 333-346. Kluwer Academic publishers, The Netherlands, 2002.

4

G. Alfano and E. Sacco.
Combining interface damage and friction in a cohesive-zone model. International Journal for Numerical Methods in Engineering, 2006. in press. doi:10.1002/nme.1728

5

CEA, http://www-cast3m.cea.fr/cast3m. CAST3M - User Manual, 2003.

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