Le principe d'élaboration microstructurale des céramiques à base d'alumine repose sur la dispersion des zones sphériques relativement larges (10–50 μm) dans une matrice céramique (Claussen et Petzow, 1982–1984 [[1]]). Lors du refroidissement, ces zones avec des quantités variables en ZrO₂, se dilatent par rapport à la matrice. Cette dilatation peut être complète ou partielle et engendre dans tous les cas des contraintes. Ces dernières peuvent être :

The microstructural design concept of bio-ceramics is based on relatively large (10–100 μm) spherical zones dispersed in a ceramic matrix. These zones contain variable fractions of ZrO₂ particles. On cooling from the fabrication temperature they expand relative to the matrix either completely during cooling or at first partially and then continue by stress induction. Compressive stresses are developing within and radially around zones. Tensile hoop stresses are created tangentially around the zones.

The objective of these spherical zones is to preserve stress of rupture of the matrix at a high value and to support the deviation and the cracks bifurcation. The reinforcement in these materials is related to the interaction between the stress field in crack face and the residual stress fields around the spherical zones.

In this article, we propose a study of the stress field around spherical inclusions using the finite elements method. These results are compared with those found analytically.