Formability prediction of damageable elastic-viscoplastic media by a material stability analysis based on a linear perturbation method

The originality of the approach used here is to present stability conditions of metallic materials modeled by general phenomenological laws and to apply them to the study of the formability of thin metallic sheets. The constitutive equations are based on an elastic-viscoplastic model coupled with a classical isotropic damage model. Various classical isotropic and kinematic hardening models are considered here to reproduce the hardening behavior and the induced anisotropy, while the initial anisotropy of metallic rolled sheets is introduced by Hill’48 anisotropic yield function. Softening is taken into account by coupling the constitutive model with a scalar damage variable. This phenomenological variable is defined within the framework of continuum damage mechanics and represents the degradation of the elastic properties during the forming operations. The stability of the constitutive damageable elastic-viscoplastic system is then sought by means of linear perturbation approach. Application of this method to a mild steel and a dual phase steel leads to the determination of their formability limit diagrams. On the one hand, FLDs obtained with Rice’s criterion and with this stability criterion illustrate the theoretical relation between these criteria and on the other hand, a parametric study shows the influence of governing parameters of hardening, damage and strain rate sensitivity.