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.