Comparison of Laser Coordinate Measurements and Hierarchical Multiscale Finite Element Models for the Cup Drawing of Three Commercial Aluminum Alloys

Abstract

Cup drawing is a benchmark experiment frequently used to validate anisotropic constitutive models and multiscale crystal plasticity codes for yield locus prediction. Earing of the cup rim and thickness variation along the cup wall are sensitive to plastic anisotropy. This test was implemented on an industrial forming press and applied to 85 mm diameter disks of commercial AA1100, AA3103, and AA5005 alloy sheet. Cup geometry was determined using a laser probe coordinate measurement machine (CMM). Finite element models (FEM) were developed with ABAQUS Explicit software and a user-defined subroutine for the anisotropic yield locus based on the hierarchical multiscale model (HMS). As the coordinate cloud produced by the CMM is unrelated to the nodes of the deformed FEM-mesh, both were fitted to a polynomial-Fourier series expansion. After cleaning and correction of the CMM data, point-by-point comparison can be performed between model and experiment. For AA1100, the position of the ears was correctly identified but their magnitude was underestimated. Excellent coincidence was found for AA5005, with strong ears at 0 and 90°. The small ears at -30° and 30° and secondary ears at 90° were correctly predicted for AA3013.