Formability prediction of ductile materials using a non-associative plasticity model and bifurcation-based criteria

Abstract

Plastic instabilities such as diffuse or localized necking may occur during sheet metal forming processes, thus limiting sheet metal formability, which is detrimental to industry. The formability of sheet metals is usually characterized by the concept of forming limit diagram (FLD), which was first proposed by Keeler and Backofen and Goodwin . The FLD reports combinations of in-plane major and minor strains, thus delimiting the plane into two zones: a safe zone and a critical one located above the FLD. It remains however that the experimental determination of FLDs is difficult, time consuming and involving non-negligible costs. To overcome these drawbacks, significant efforts have been devoted in the literature to develop theoretical criteria able to predict the formability limits of sheet metals, which are associated with the occurrence of diffuse or localized necking. For reliable predictions of sheet metal formability, one of the requirements is to develop an integrated approach coupling advanced constitutive models, capable of accurately reproducing the key physical phenomena that occur during forming processes, with theoretically well-founded necking criteria. In this work, a non-associative elastic‒plastic model, with Hill'48 anisotropic plastic yield surface, is coupled with the continuum damage mechanics theory based on the Lemaitre isotropic damage model. The resulting constitutive model is then combined with four bifurcation-based criteria, namely: General Bifurcation (GB) and Limit-Point Bifurcation (LPB) , for the prediction of diffuse necking, and Loss of Ellipticity (LE) and Loss of Strong Ellipticity (LSE), for the prediction of localized necking. The complete approach is implemented into the finite element code ABAQUS/Standard, within the framework of large strains and plane-stress conditions. A comparative study of the above bifurcation criteria is carried out on a mild steel, in order to classify them with respect to their order of prediction of critical necking strains.