On the Combined Effect of Pressure and Third Invariant on Yielding of Porous Solids With von Mises Matrix

Oana Cazacu (1) , Benoît Revil-Baudard (2) , Ricardo A. Lebensohn (3) , Mihail Garajeu (4)

1 MAE - Department of Mechanical and Aerospace Engineering [Shalimar]
2 UF|MAE - Department of Mechanical and Aerospace Engineering [Gainesville]
3 Materials Science and Technology Division
4 LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]

In this paper, a new plastic potential for porous solids with von Mises perfectly-plastic matrix containing spherical cavities is derived using a rigorous limit analysis approach. For stress-triaxialities different from 0 and ±∞, the dilatational response depends on the signs of the mean stress and the third invariant of the stress deviator. The classic Gurson potential is an upper-bound of the new criterion. A full-field dilatational viscoplastic Fast Fourier Transform (FFT)-based approach is also used to generate numerical gauge surfaces for the porous material. The numerical calculations confirm the new features of the dilatational response, namely: a very specific dependence with the signs of the mean stress and the third invariant that results in a lack of symmetry of the yield surface.

Mots clés: coupled mean stress third-invariant effect; porous ductile solids; tension-compression asymmetry; limit analysis

Domaines: Mécanique des solides [physics.class-ph]; Mécanique des matériaux [physics.class-ph]

Oana Cazacu, Benoît Revil-Baudard, Ricardo A. Lebensohn, Mihail Garajeu. On the Combined Effect of Pressure and Third Invariant on Yielding of Porous Solids With von Mises Matrix. Journal of Applied Mechanics, 2013, 80 (6), ⟨10.1115/1.4024074⟩. ⟨hal-01656806⟩