The finite element implementation, validation and verification of a plane stress yield criterion for use in sheet metal forming analysis

The Leacock 2006 orthotropic yield criterion, previously developed and experimentally verified by Leacock [1], was implemented as a rate independent, elastoplastic user material subroutine (UMAT) within the commercial finite element software PAM-STAMP 2G™. This paper focuses on the implementation and the computational and experimental validation of the Leacock UMAT. The UMAT architecture incorporates the Associated Flow Rule (AFR), and the Cutting Plane Algorithm for the integration of the elastoplastic constitutive equations. The UMAT driven simulations of deep drawing and stretching operations were compared to data collected from laboratory performed experimental deep drawing of AA2024-O and AA6451-T4, and stretching of AA2024-T3 under the action of a hemispherical punch. The Hill family of yield criteria provided a relative comparison. The Leacock 2006 UMAT provided an accurate prediction of the punch force versus displacement, and in the prediction of the experimental major and minor strain in the stretching of AA2024-T3. The Leacock 2006 UMAT provided an acceptable accuracy of the earing profile and the experimental punch force versus displacement during the deep drawing of the aluminium alloys 2024-O and 6451-T4.