Effective plastic flow surface of a porous material with two populations of voids subjected to internal pressures : constitutive modeling and 3-dimensional full-field numerical simulations

International audienceThis study is devoted to the modeling of the effective plastic flow surface of a porous materialsaturated by a fluid, typically the highly irradiated uranium dioxide (UO2) studied by the French“Institut de Radioprotection et de Sûreté Nucléaire” to investigate the response of fuel rods underaccident conditions. As a first approximation, this material exhibits two populations of cavities: (1)intragranular bubbles, almost spherical in shape with a typical diameter of a few nanometers, (2) at alarger scale, intergranular bubbles, roughly ellipsoidal in shape with a typical size of a few micronslocated at grain boundaries. These two populations of voids are subjected to internal pressures due tothe presence of fission gases. At high temperature, typically encountered in accident conditions, thisporous material is almost ductile.Approximate models for the effective plastic flow surface of such a bi-porous saturated material havebeen proposed in [1]. A three-scale homogenization procedure is performed: first, smearing out allthe small spherical bubbles (intragranular bubbles), and second, smearing out all the details of thegrain boundaries and the intergranular ellipsoidal bubbles. The main model is based on thevariational approach of Ponte Castañeda (also called the modified secant method [2]) applied to aGurson-like matrix containing randomly oriented ellipsoidal cavities. Further, a simplified version ofthese models, obtained by generalizing the approach of [3] to compressible materials, has beenrecently extended to saturated voids and corresponds to a fully closed-form model.The accuracy of this model is checked by comparison with 3-D full-field simulations using the FastFourier Transforms method [4]. More than 250 numerical simulations have been performed, varyingthe microstructures and the loadings. A typical volume element, discretized into 5123 voxels containsmore than 500 randomly oriented oblate cavities in a Gurson matrix to approach overall isotropy. Thepredictions of the model are in good agreement with the simulations. In particular, the effect of thetwo pressures in the intra and intergranular voids on the effective flow surface is accurately captured