Document Type : Research Paper


School of Mechanical Engineering, Shahrood University of Technology, Shahrood 3619995161, Iran


This paper investigates the earing phenomenon in deep drawing of AA3105 aluminum alloy, experimentally and numerically. Earing defect is mainly attributed to the plastic anisotropy of sheet metal. In order to control such defect, predicting the evolution of ears in sheet metal forming analyses becomes indispensable. In this regard, the present study implements the advanced yield criterion BBC2003. Based on this yield function and the associated flow rule of plasticity, the constitutive model is derived. Accordingly, a user material VUMAT subroutine is developed and adopted in the commercial finite element software ABAQUS/Explicit. Several plane stress loading problems are designed, through which, the accuracy of the developed subroutine is verified. In addition, cylindrical cups of AA3105 aluminum alloy are fabricated using a deep drawing die. The earing defect was clearly observed on the recovered parts. Using the experimentally obtained constants of BBC2003 yield criterion for this alloy in VUMAT, deep drawing of the cylindrical cups was simulated. The results demonstrate that the earing profile can successfully be predicted using BBC2003 yield function.

Graphical Abstract

Prediction of earing in deep drawing of anisotropic aluminum alloy sheet using BBC2003 yield criterion


Main Subjects

[1]     D. Banabic, Sheet metal forming processes: constitutive modelling and numerical simulation, Springer Science & Business Media, pp. 45-120, (2010).
[2]     M. Vrh, M. Halilovič, B. Starman, B. Štok, D.-S. Comsa, and D. Banabic, “Capability of the BBC2008 yield criterion in predicting the earing profile in cup deep drawing simulations”, Eur. J Mech. A-Solid, Vol. 45, pp. 59-74, (2014).
[3]     K. Chung, and K. Shah. “Finite element simulation of sheet metal forming for planar anisotropic metals”, Int. J. Plasticity, Vol. 8, No. 4, pp. 453-476, (1992).
[4]     J. W. Yoon, F. Barlat, R. E. Dick, and M.
E. Karabin, “Prediction of six or eight ears in a drawn cup based on a new anisotropic yield function”, Int. J. Plasticity, Vol. 22, No. 1, pp.174-193, (2006).
[5]     J. Gawad, D. Banabic, A.Van Bael, D.S. Comsa, M. Gologanu, P. Eyckens, P. Van Houtte, and D. Roose, “An evolving plane stress yield criterion based on crystal plasticity virtual experiments”, Int. J. Plasticity, Vol. 75, pp.141-169, (2015).
[6]     D. Banabic, H. Aretz, D. S. Comsa, and L. Paraianu, “An improved analytical description of orthotropy in metallic sheets”, Int. J. Plasticity, Vol. 21, No. 3, pp. 493-512, (2005).
[7]     M. Vrh, M. Halilovič, and B. Štok. “Improved explicit integration in plasticity”, Int. J. Numer. Meth. Eng., Vol. 81, No. 7, pp. 910-938 (2010).
[8]     M. Halilovič, M. Vrh, B. Štok, “NICEh: a higher-order explicit numerical scheme for integration of constitutive models in plasticity”, Eng. Comput., Vol 29, No. 1, pp. 55−70, (2013).
[9]     K. Lange, Handbook of metal forming,  McGraw-Hill Book Company, pp. 20.16-20.19, (1985).
[10]   S. Izadpanah-Najmabad, M. Gerdooei, S. H. Ghaderi, “Determination of BBC2003 yield criterion constants for anisotropic aluminum alloy sheets based on plane strain tensile test”, Modares Mech. Eng., Vol. 15 , No. 11, pp. 127-135, (2015).
[11]   B. Starman, M. Vrh, M. Halilovič, and B. Štok, “Advanced modelling of sheet metal forming considering anisotropy and Young’s modulus evolution”, Stroj. Vestn. J. Mech. E., Vol. 60, No. 2, pp. 84-92, (2014).