Approximate Yield Criterion for Anisotropic Porous Sheet Metals and its Applications to Failure Prediction of Sheet Metals Under Forming Processes

Abstract

An approximate anisotropic yield criterion for anisotropic sheet metals containing spherical voids is validated using a three-dimensional finite element analysis. An aggregate of periodically arranged cubes containing spherical voids is modeled using a unit cell method. Hill’s quadratic anisotropic yield criterion is used to describe the normal anisotropy and planar isotropy of the matrix. The metal matrix is first assumed to be elastic perfectly plastic and incompressible. The results of the finite element analysis can be in good agreement with those based on the proposed yield criterion by introducing three fitting parameters in the yield criterion. This modified yield criterion is adopted in a failure prediction methodology that can be used to determine the failure of sheet metals under forming operations. The material imperfection approach is employed to predict failure/plastic localization by assuming a slightly higher void volume fraction inside randomly oriented imperfection bands. Finally, the failure prediction methodology is applied to predict the failure of a mild steel sheet metal in a fender forming process.