A methodology for evaluating sheet formability combining the tensile test with the M–K model

This paper proposed an approach for evaluating the sheet formability by combining the tensile test with the finite element Marciniak and Kuczynski (M–K) model. Firstly, the tensile test with a notched specimen was carried out to identify an appropriate constitutive law for an AA5086 sheet. A modified Ludwick's law was used to describe its forming behavior. A technique of digital image correlation associated with a high-speed camera was applied to evaluate specimen's surface strains during the experiments. The inverse analysis was performed to identify the parameter values in the constitutive law. The initial geometrical imperfection factor in the M–K model was determined. Then by using the commercial finite element software ABAQUS, the M–K model was simulated to evaluate numerically the sheet formability of the alloy. By means of a user-defined FORTRAN subroutine UHARD, the constitutive law was implanted into ABAQUS. Different strain states were obtained by changing displacement ratios and forming limit curves (FLCs) of the sheet were determined too. Finally, an experimental procedure based on the modified Marciniak test was carried out and the FLCs were obtained experimentally. The comparison between the numerical and experimental results showed that the approach developed in this paper could give an appropriate prediction of FLCs.

Research highlights▶ The sheet formability was improved with the increasing initial geometry imperfection factor in the M–K model. ▶ A technique of digital image correlation was properly used to measure surface strains of specimen. ▶ A good agreement between experimental and identified stress–strain data in the tensile test by the inverse method.