Application of Drucker–Prager plasticity to predict fracture in rectangular cup drawing of AZ31 alloy sheet

The formability in three-dimensional rectangular cup drawing of AZ31 magnesium alloy sheet is successfully predicted by the Drucker–Prager plasticity (DP model). Numerical results show that the punch corner shoulder is under the condition of high tension bending and the die corner shoulder is on pure bending regardless of constitutive models. The failure is attributed to the competition between the biaxial tension bending induced fracture on the punch corner shoulder and the through-thickness shear induced fracture on other shoulders in the sheet forming. Taking the yield surface asymmetry into consideration, in a way of the friction angle in the coordinate of compressive and tensile strengths in the DP model, the accuracy of plastic strain is improved remarkably. The fracture locates on the punch corner shoulder where the strain reaches its fracture limit earlier than the die corner shoulderʹs. The predictions of forming limit and fracture locus in the DP model simulation are in good agreement with the experimental results.