Couplage d'une loi d'adhésion à une loi de contact avec frottement pour l'étude de la décohésion dans les matériaux composites

In this thesis, an original law of adhesion is developed and then coupled to the classical law of unilateral contact with threshold friction, in order to study the phenomenon of fibre/matrix debonding in composite materials. This tribological law is developed within the framework of standard generalized materials adapted to interfaces. Thus, the law is derived from a free energy potential ψc and a dissipation potential Φc. The adhesive interface is interpreted as a bundle of links connecting the two contact surfaces. Each link is assumed to have a plastic behavior with softening and damage, caused by stretching, to represent the loss of adhesion. An internal variable ga measuring an irreversible adhesive gap is introduced and associated by energetic duality to an adhesive stress pa. The ranges of ga and pa are limited by two characteristic constants of adhesion, gM and pM respectively. pM is the maximum adhesive tension below which the links remain elastic. Above this limit, debonding and damage of the links occur as ga increases. Once ga reaches the value gM, total rupture of the adhesive bond occurs. This adhesion law is then mounted in parallel to the contact and friction laws into a unique law. The law is regularized using either the approximate penalty method or the exact augmented Lagrangian method, in option. The regularized laws are implemented in a node-to-node contact element of the finite element code TACT. The adhesive force is computed by means of a predictor-corrector with projection algorithm for integrating the evolution of ga, and the relevant Jacobian tensors required for the resolution of non-linearities by the iterative scheme of Newton are calculated. This is accomplished for the penalty and the augmented Lagrangian regularizations. A traction test of a glass/epoxy interface in the normal direction is designed and used to experimentally determine the parameters pM and gM of such an interface (pM directly and gM indirectly). Numerical simulations of adhesion between a rigid punch and an elastic half-space enable the comparison of the proposed model of adhesion to the classical theories of adhesion. A numerical simulation of the standard pull-out test of a fibre embedded in a matrix is then performed, and the numerical shear distribution along the interface is compared to the analytical one existing for this experiment. The results are in good agreement with existing ones. Finally, a crack propagation in a fibrous composite is simulated.

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