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Although drawing forming limit diagrams is a suitable tool for analyzing material formability, it can only be used when loading is proportional. In other words, when the ratio between main strains stays unaffected during the formation process. Since forming limit diagrams are strictly dependent on strain path, the significance of the limit increases. As the path of the strain changes in a formation process, the forming limit diagrams and therefore the designer's decision changes as well. In order to eliminate this issue, stress-based forming limit diagrams (SFLD) which are independent from the strain path are gaining attention. This paper gives an efficient method to determine the SFLDs and can accurately predict the location for the onset of failure, including strain rate calculations. Furthermore, introducing a damage function based on a simple continuum damage mechanics is dependent on the stress state (Triaxiality and Lode parameters). As a characterization parameter, elastic modulus is eventually chosen to measure the ductile damage in the process of plastic deformation of the material. Furthermore, a UMAT subroutine is developed in finite element simulation by ABAQUS according to original formulations, in order to analyze and link the related essential models. To examine the accuracy of the results from the present simulative study and compare with the experimental results, applicability is considered. Forming limit tests are also performed for St 13 sheets measuring the FLD and then transforming to SFLD. It should be noted that the rule of these simulative SFLDs is in good agreement with the experimental points. Results revealed that the level of the stress-based forming limit diagram for the material St 13 increases with enhancing the strain rate.

Stress-based forming limit diagrams (SFLD) considering strain rate effect and ductile damage phenomenon