A Theoretical Study on Forming Limit Diagram Predictions Using Viscoplastic Polycrystalline Plasticity Models
The Forming Limit Diagrams (FLDs) of textured polycrystalline sheet metals were investigated using micro-macro averaging and two types of grain-interaction models: Full-Constraint (FC) and Self-consistent (SC) schemes, in conjunction with the Marciniak–Kuczynski (MK) approach. By referring to previous FLD studies based on the FC-Taylor model ─ Wu and coworkers [Effect of an initial cube texture on sheet metal formability, Materials Science and Engineering A, 364:182–7, 2004] and Inal and coworkers [Forming Limit comparison for FCC and BCC sheets, International Journal of Plasticity, 21:1255-1266, 2005] ─ we found that the MK-FC strategy leads to unrealistic results. In the former case, the researchers found that an increasing spread about the cube texture produces unexpectedly high limit strains. In the latter work, Inal et al. predicted a remarkably low forming-limit curve for a FCC material and an extremely high forming-limit curve for a BCC material, in the biaxial-stretching range. Our investigations show that simulations performed with the MK-VPSC approach successfully predict more reliable results. For the BCC structure, the MK-VPSC predictions do not give the extreme values predicted when calculations are carried out with the MK-FC approach. In the FCC case, with decreasing textural intensity ─ from the ideal cube texture, through dispersions around the cube texture with increasing cut-off angles, to a random texture ─ a smooth transition in increasing limit strains was obtained. Furthermore, these results suggest that the selected constitutive model is critical for predicting the behavior of materials that exhibit a qualitative change in crystallographic texture, and hence, evolve anisotropically during mechanical deformation.
J.R. Duflou, R. Clarke, M. Merklein, F. Micari, B. Shirvani and K. Kellens
M. Serenelli et al., "A Theoretical Study on Forming Limit Diagram Predictions Using Viscoplastic Polycrystalline Plasticity Models", Key Engineering Materials, Vol. 473, pp. 327-334, 2011