Forming limit of AZ31B magnesium alloy under in-plane complex biaxial loading paths with cruciform specimens

This paper focused on the forming limit curves (FLC) of the AZ31B magnesium alloy sheet metal under different complex loading paths in-plane. Compared with simple loading paths, the study of forming limit of sheet metal under complex loading paths was more practical. In this study, biaxial tensile test of the cruciform specimen was utilized to acquire the FLC after the cruciform specimen was subjected to uniaxial pre-tensile process along rolling direction, which experimentally characterize the forming limits under different pre-strain values of 1.15%, 2.34%, 4.0%, and 5.4%. Subsequently, based on the constitutive model, Hill48 yield criterion and shear failure criterion, the theoretical FLCs of AZ31B magnesium alloy sheet metal was be calculated. Meanwhile, the normal biaxial tensile tests were also simulated by Abaqus to obtain the limit strains by Finite Element Analysis (FEA). Extracting limit strains from the fracture region in FEA model when the first derivative of the strain difference with respect to time reached the maximum value between the first principal strain of necked element and the first principal strain of the element adjacent to the necked zone. As a result, the experimental FLCs was qualitatively consistent with the result of theoretical model and FEA model. In addition, the FLCs of AZ31B magnesium alloy sheet moved to the upper left of forming limit diagram with the increase of the pre-strain, which indicated that the pre-strain process along the rolling direction could significantly improve the formability of the sheet metal.