Macroscopic Yield Criterion for Ductile Materials Containing Randomly Oriented Spheroidal Cavities

This study is devoted to a micromechanical approach of the macroscopic yield criterion of ductile porous materials made up of a perfectly plastic von Mises matrix and randomly oriented spheroidal voids (with a same shape ratio, prolate or oblate including penny-shaped crack). The approach is based on recent results established by Monchiet et al. [Monchiet, V., Charkaluk, E. and Kondo, D. (2007). An Improvement of Gurson-type Models of Porous Materials by using Eshelby-like Trial Velocity Fields, Comptes Rendus Mecanique, 335: 32–41.] for a unit cell containing a single family of spheroidal cavities. By adopting an approximation introduced by previous authors and which consists in embedding each void family in a medium submitted to the macroscopic stress, we provide for the studied class of materials closed-form expressions of the isotropic macroscopic yield function. The established results are compared with existing ones, and their interest is clearly shown.