On the prediction of the forming-limit diagram of sheet metals

Models for predicting the formability of sheet metals which take into account a single mode of strain localization have not yet led to accurate predictions. In the present work an attempt is made to include some important experimentally determined parameters in the model, i.e. surface roughness, void growth, sheet thickness, grain size, strain-hardening exponent, strain-rate sensitivity index, and normal anisotropy. In this model, which is based on the Marciniak-Kuczynski (M-K) hypothesis, the initial size of the imperfection is determined by the surface roughness. Two possible concurrent modes of flow localization, viz. necking and shear-band formation, are assumed to contribute to the final failure. The solutions of equations resulting from the M-K theory and the Hutchinson-Tvergaard analysis for plane strain are combined in two ways to obtain the prediction equations for the formability of orthotropic, isotropically hardening materials. A reasonably good correlation with the experimental results is demonstrated