Numerical formability assessment in single crystals of magnesium

In this paper a rate-sensitive elastic–viscoplastic crystal plasticity constitutive model (CPCM) together with the Marciniak–Kuczynski (M–K) approach have been used to assess the formability of a magnesium single crystal sheet by simulating the forming limit diagrams (FLDs). Sheet necking is initiated from an initial imperfection in terms of a narrow band. A homogeneous deformation field is assumed inside and outside the band, and conditions of compatibility and equilibrium are enforced across the band interfaces. Thus, the CPCM only needs to be applied to two regions, one inside and one outside the band. The FLDs have been simulated under two conditions: (a) the plastic deformation mechanisms are basal, pyramidal 〈c + a〉, and prismatic slip systems, and (b) the plastic deformation mechanisms are basal, pyramidal 〈c + a〉, and prismatic slip systems, as well as extension and contraction twinning systems. The FLDs have been generated for two grain orientations. In the first orientation pyramidal 〈c + a〉 and extension twinning systems, and in the second orientation basal and pyramidal 〈c + a〉 slip systems, as well as contraction twinning systems have favourable orientation for activation. The effects of shear strains outside the necking band, strain rate sensitivity, and c/a ratio on the simulated FLDs in the two grain orientations have been individually explored.