Finite element calculations of hole expansion in a thin steel sheet with polynomial yield functions of four and six degrees

Abstract

A three-dimensional finite element simulation was used to study the anisotropic plasticity behavior of sheet metal forming. Both Gotoh's (fourth order) yield function and the more flexible sixth order polynomial yield functions with an associated flow rule were implemented as user material subroutines in the FE code ABAQUS. Parameter values in the yield functions were decided by fitting the yield stresses and plastic strain ratios along various directions of uniaxial and biaxial tension. To verify the FE implementation and to evaluate the modeling capabilities of the developed yield functions that were certified to be convex, the hole expansion experiment by Kuwabara et al.[1] was considered as the target example. The simulation results using the sixth order yield function showed a better agreement with the experimental results than those of lower order yield functions such as Hill's second order or Gotoh's fourth order yield functions.