Plastic potentials for anisotropic porous solids

The aim of this paper is to incorporate plastic anisotropy into constitutiv e equations of porous ductile metals. It is shown that plastic anisotropy o f the matrix surrounding the voids in a ductile material could have an infl uence on both effective stress-strain relation and damage evolution. Two th eoretical frameworks are envisageable to study the influence of plastic flo w anisotropy: continuum thermodynamics and micromechanics. By going through the Rousselier thermodynamical formulation, one can account for the overal l plastic anisotropy, in a very simple manner. However. since this model is based on a weak coupling between plasticity and damage dissipative process es, it does not predict any influence of plastic anisotropy on cavity growt h, unless a more suitable choice of the thermodynamical force associated wi th the damage parameter is made. Micromechanically-based models are then pr oposed. They consist of extending the famous Gurson model for spherical and cylindrical voids to the case of an orthotropic material. We derive an upp er bound of the yield surface of a hollow sphere, or a hollow cylinder, mad e of a perfectly plastic matrix obeying the Hill criterion. The main findin gs are related to the so-called 'scalar effect' and 'directional effect. Fi rst, the effect of plastic flow anisotropy on the spherical term of the pla stic potential is quantified. This allows a classification of sheet materia ls with regard to the anisotropy factor h: this is the scalar effect. A sec ond feature of the model is the plasticity-induced damage anisotropy. This results in directionality of fracture properties ('directional effect'). Th e latter is mainly due to the principal Hill coefficients whilst the scalar effect is enhanced by 'shear. Hill coefficients. Results are compared to s ome micromechanical calculations using the finite element method. (C) 2001 Editions scientifiques et medicales Elsevier SAS.