Efficient and Robust Prediction of Localized Necking in Sheet Metals

The recently proposed Critical Specific Tension (CST) model is jointly used with the well-known Marciniak and Kuczyński (M-K) model to predict localized necking in anisotropic sheet metals in the regime of negative and positive minor in-plane strains, respectively. A significantly simplified method is presented to calculate the critical tensile stress required in the CST model, without the need of iterative computations. In the present work the CST/M-K model is used along with a rate-independent phenomenological elasto-plastic constitutive model as well as the known visco-plastic self-consistent (VPSC) crystal plasticity model developed by Tomé and Lebensohn. A comparison between experimental data and the limit strains predicted by means of the phenomenological constitutive model reveals a very good agreement. In order to validate the correctness of the non-trivial computational implementation of the VPSC-based CST/M-K model the predicted necking strains are compared with results obtained by using the phenomenological constitutive model. It is shown that the results of both approaches are in good agreement.