Résumé
This work is devoted to the modeling of the effective elastic behavior of nanoporous materials containing both spherical and ellipsoidal in shape bubbles, typically the irradiated uranium dioxide (UO2) studied by the French “Institut de Radioprotection et de Sûreté Nucléaire” to investigate the response of fuel rods under reactivity initiated accident (RIA) conditions. As a first approximation, this material exhibits at least two populations of bubbles: (1) intragranular bubbles, almost spherical in shape with a typical diameter of a few nanometers, (2) intergranular bubbles, roughly lenticular in shape whose size ranges from tens to several hundred nanometers. Molecular dynamics results of [Colbert, 2012] and [Jelea et al., 2011] show the existence of a non-neglectible surface effect on the effective elastic behavior for UO2 at the intragranular bubbles scale, particularly when the surface/volume ratio of these bubbles increases.Analytical micromechanical models ([Duan et al., 2005], [Brisard et al., 2010]) concerning materials with an isotropic distribution of nano-sized spherical inclusions have been extended to the case of materials with two populations of pressurized bubbles, one relative to spherical bubbles and the other relative to ellipsoidal bubbles. The proposed model follows the general framework of the so-called ‘morphologically representative pattern-based approach’ of [Stolz and Zaoui, 1991] and is compared to existing models (with or without surface effects). The relevance of the analytical model has been assessed by comparison with finite elements simulations. A preliminary study has been performed on the evolution of the elastic moduli of the irradiated UO2 fuel obtained from this model during a RIA test condition.