Study on forming limit diagrams prediction using a phenomenological and a physical approach of plasticity theory

Abstract
In the present work a study on the prediction of the Forming Limit Diagrams is developed, by using a phenomenological and a physical approach of the plasticity theory. Two advanced constitutive models of the plastic anisotropy are considered, namely the Yld'96 Barlat phenomenological yield function and a combined model of texture and strain-path-induced anisotropy. The studied material is a bake-hardened steel sheet. The experimental FLDs were determined for linear and complex strain paths. The necking phenomenon was modeled using the Marciniack-Kuczinsky theory. The YLD'96 predicted Lankford coefficients and normalized yield distributions were investigated and compared with experimental data. The effect of the hardening model on the FLDs is analyzed by using several hardening laws, namely Swift law, Voce law and the strain-path-induced anisotropy model. In proportional loading a successful correlation is observed between the experimental FLDs and the computed limit strains when the shape of yield locus is described by Yld'96 criterion and the hardening law represented either by Swift law or by using the combined model of texture and strain-path-induced anisotropy. As the strain-path induced anisotropy is more evident for the steels, the physical model can provide a better accuracy than the phenomenological one for the forming limits involving two-stage strain paths.