An Anisotropic Gurson Yield Criterion for Porous Ductile Sheet Metals with Planar Anisotropy

The influence of plastic anisotropy on the plastic behavior of porous ductile materials is investigated by a three-dimensional finite element analysis. A unit cell of cube containing a spherical void is modeled. The Hill quadratic anisotropic yield criterion is used to describe the matrix anisotropy including planar anisotropy. The matrix material is first assumed to be elastic perfectly plastic. Macroscopically uniform displacements are applied to the faces of the cube. The finite element computational results are compared with those based on the closed-form anisotropic Gurson yield criterion (Liao et al., 1997) in terms of an average anisotropy parameter. Three fitting parameters are used in the closed-form anisotropic Gurson yield criterion to fit the results of finite element computations. When the strain hardening of the matrix is considered, the computational results of the macroscopic stress-strain behavior are in agreement with those based on the closed-form anisotropic Gurson yield criterion under selected monotonically increasing loading conditions.