Prediction of stress- and strain-based forming limits of automotive thin sheets by numerical, theoretical and experimental methods

Forming limit is a complex concept of limit values related to the onset of local necking in the sheet metal. In cold sheet metal forming, major and minor limit strains are influenced by the sheet thickness, strain path (deformation history) as well as material parameters and microstructure. Forming Limit Curves are plotted in ε1 – ε2 coordinate system providing the classic strain-based Forming Limit Diagram (FLD). Using the appropriate constitutive model, the limit strains can be changed into the stress-based Forming Limit Diagram (SFLD), irrespective of the strain path. This study is about the effect of the hardening model parameters on defining of limit stress values during Nakazima tests for automotive dual phase (DP) steels. Five limit strain pairs were specified experimentally with the loading of five different sheet geometries, which performed different strain-paths from pure shear (−2ε2=ε1) up to biaxial stretching (ε2=ε1). The former works of Hill, Levy-Tyne and Keeler-Brazier made possible some kind of theoretical strain determination, too. This was followed by the stress calculation based on the experimental and theoretical strain data. Since the n exponent in the Nádai expression is varying with the strain at some DP steels, we applied the least-squares method to fit other hardening model parameters (Ludwik, Voce, Hockett-Sherby) to calculate the stress fields belonging to each limit strains. The results showed that each model parameters could produce some discrepancies between the limit stress states in the range of higher equivalent strains than uniaxial stretching. The calculated hardening models were imported to FE code to extend and validate the results by numerical simulations.