A homogenized anisotropic constitutive model of perforated sheets for numerical simulation of stamping

Abstract

Perforated sheets exhibit strong anisotropy related to the arrangement of holes during plastic deformation, which poses significant challenges for accurate prediction of the macroscopic plastic behavior in stamping. Addressing this, unit cell simulations were conducted to determine the homogenized yielding and hardening behaviors of perforated sheets with hexagonal or square arrays of circular holes under in-plane loading conditions. The local deformation mode, which determines the macroscopic anistropy, is unveiled. A mechanism-motivated homogenized yield criterion was proposed based on the local deformation modes, which provides a concise yet unified approach to modeling complex material anisotropic behavior with high accuracy. Additionally, a mixed hardening strategy was developed to capture the evolution of yield loci in term of size and shape. The proposed constitutive model demonstrates precise predictions of flow stress variations and the apparent r-value with loading angles during uniaxial tension. Furthermore, it successfully forecasts two distinct types of earing profiles in the deep drawing of perforated sheets with square arrays of circular holes at different hole fractions. This modeling approach provides a feasible way for predicting the deformation behavior of perforated sheets during stamping with high computational efficiency.