Porous materials with two populations of voids under internal pressure: I. Instantaneous constitutive relations
Titre de la revue : International Journal of Solids and Structures
Volume : 46
N° : 3-4
Pagination : 480-506
Date de publication : 01/02/2009
This study is devoted to the mechanical behavior of uranium dioxide (UO2) which
is a porous material with two populations of voids of very different size subjected
to internal pressure. The smallest voids are intragranular and spherical in shape
whereas the largest pores located at the grain boundary are ellipsoidal and randomly
oriented. In this first part of the study, attention is focused on the effective
properties of these materials with fixed microstructure. In a first step the poroelastic
properties of these doubly voided materials are studied. Then two rigorous
upper bounds are derived for the effective poro-plastic constitutive relations of these
materials. The first bound, obtained by generalizing the approach of Gologanu et al.
(1994) to compressible materials, is accurate at high stress-triaxiality. The second
one, which derives from the variational method of Ponte Castaneda (1991), is accurate
when the stress triaxiality is low. A N-phase model, inspired by Bilger et al.
(2002), is proposed which matches the best of the two bounds at low and high triaxiality.
The effect of internal pressures is discussed. In particular it is shown that
when the two internal pressures coincide, the effective flow surface of the saturated
biporous material is obtained from that of the drained material by a shift along the
hydrostatic axis. However, when the two pressures are different, the modifications
brought to the effective flow surface in the drained case involve not only a shift
along the hydrostatic axis but also a change in shape and size of the surface.