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
Résumé
This study is devoted to the modeling of the effective plastic flow surface of a porous material saturated 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 under
accident 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 a larger scale, intergranular bubbles, roughly ellipsoidal in shape with a typical size of a few microns located at grain boundaries. These two populations of voids are subjected to internal pressures due to the presence of fission gases. At high temperature, typically encountered in accident conditions, this porous material is almost ductile.
Approximate models for the effective plastic flow surface of such a bi-porous saturated material have been proposed in [1]. A three-scale homogenization procedure is performed: first, smearing out all the small spherical bubbles (intragranular bubbles), and second, smearing out all the details of the grain boundaries and the intergranular ellipsoidal bubbles. The main model is based on the variational approach of Ponte Castañeda (also called the modified secant method [2]) applied to a Gurson-like matrix containing randomly oriented ellipsoidal cavities. Further, a simplified version of these models, obtained by generalizing the approach of [3] to compressible materials, has been
recently 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 Fast Fourier Transforms method [4]. More than 250 numerical simulations have been performed, varying the microstructures and the loadings. A typical volume element, discretized into 5123 voxels contains more than 500 randomly oriented oblate cavities in a Gurson matrix to approach overall isotropy. The predictions of the model are in good agreement with the simulations. In particular, the effect of the two pressures in the intra and intergranular voids on the effective flow surface is accurately captured.