Analytical Method for Forming Limit Diagram Prediction with Application to a Magnesium ZEK100-O Alloy

A significant barrier to broader implementation of magnesium alloys is their poor room temperature formability, a consequence of the anisotropic response of the Mg hexagonal closed-packed (hcp) crystal structure. Additions of rare earth (RE) elements, such as in the ZEK100 alloys, weaken the texture and improve formability. Room temperature forming limit analyses of RE-containing Mg alloys, particularly Mg ZEK100, have not been explored to any significant extent in the literature. In this paper, strain-based forming limit diagrams (FLDs) are derived for an Mg ZEK100-O alloy (Zn1.34Zr0.23Nd0.182, wt.%) using an analytical method that combines the vertex theory of Storen and Rice (J Mech Phys Solids, 23:421-441, 1979), the anisotropic yield criterion of Barlat and Lian (Int J Plast, 5:51-66, 1989), and a hardening law. The method does not rely on assumptions about pre-existing defects, is broadly applicable to sheet alloys exhibiting in-plane anisotropy requiring a higher-order yield criterion, and requires only minimal experimental inputs. Results from the analytical method are compared with experimentally derived FLDs based upon the well-known Nakajima test and tensile deformation, and with predictions from an existing analytical method for FLDs. Close agreement between the experimentally derived FLDs and the present theoretical method was obtained. Sheet materials where the theoretical method does not apply are also discussed.