On the use of stress-based forming limit curve for forming and fracture

The forming limit curve (FLC) or diagram illustrates the major and minor strains expected on the surface of a deforming sheet material at the onset of local necking. Since determining forming limits experimentally is costly and time consuming, it is desirable to develop a theoretical model. In this work, the equal biaxial strain hardening behavior and the anisotropic yield function Yld2000-2d (Barlat et al. [4]) are used as input to the model that calculates forming limits according to the Marciniak-Kuczynski (M-K) imperfection theory for strain localization. The resultant strain-based forming limit curves are mapped to stress-based FLC in stress space. The mapping procedure from strain space to stress space was explained in detail for a general nonquadratic yield function. A solution to the challenge of assessing formability in stress space is proposed by using a single parameter which indicates the necking based on plastic state variables. The necking parameter was utilized for the simulation including the forming of an automotive part and the fracture in a beverage can end.