A yield function to simulate earing in the deep drawing of aluminium

Bibliography: leaves 76-77.Deep drawing of metal sheeting is a commercially significant manufacturing process and as with all metal forming processes is subject to geometric defects. One defect of particular concern, termed earing, is characterised by an uneven edge to the drawn article. This work covers the implementation of a suitable constitutive model in a general purpose finite element code ABAQUS Version 5.4 to simulate this earing phenomenon in aluminium can body stock. Earing is caused by plastic anisotropy of the blank material and anisotropy induced during the drawing process. It is the result of crystallographic textures or preferred grain orientations that develop during the sheet rolling process. In polycrystalline materials it may be modelled via either crystallographic texture models or phenomenological yield surface models. Crystallographic models have the advantage over phenomenological ones in that they are able to describe both initial and evolving anisotropy. However, they are very demanding in terms of computational power and are reported to over predict the plastic strain ratios in anisotropic materials. A phenomenological yield surface model proposed by Karafillis and Boyce was consequently selected as a suitable constitutive model to investigate the earing phenomenon. This model can describe the elasto-plastic behaviour of both isotropic and anisotropic three dimensional polycrystalline materials. It is a pressure independent yield surface which is convex in stress space and assumes an associated flow rule. It was implemented in ABAQUS as a FORTRAN 77 User-Material Subroutine. An Euler Backward integration scheme was adopted and a consistent tangent modulus used. Four axisymmetric cupping operations were simulated: two with the model's parameters set to represent the aluminium alloy under consideration and two to investigate the effect of the yield surface on earing. For comparison purposes, a fifth case was run using the Hill (1948) anisotropic material model