International Journal of Material Forming

, Volume 10, Issue 5, pp 707–716 | Cite as

On the benefits of a stress criterion for the simulation of cup drawing process

  • Yann Jansen
  • Roland E. Logé
  • Pierre-Yves Manach
  • Gabriel Carbuccia
  • Marc Milesi
Original Research


Experimental and numerical cup drawing process has been investigated on 0.65 mm zinc sheets. The cup exhibits anisotropic earrings due to the material microstructure. The material formability is studied through elliptical bulge tests in the rolling, diagonal and transverse direction. High anisotropy of the formability is observed. The numerical simulation of cup drawing is then made and demonstrates the correct fitting with experimental results. A stress formability criterion developed by Jansen et al. [14] is then implemented into a finite element method software and applied to predict the material rupture observed for some process conditions. The risk zone of the cup is subjected to some strain path changes according to the simulation whereas the strain value does not explain the rupture according to the experimental formability measured by the bulge tests. It has been shown that the rupture is due to some critical stresses, which are reached in the risk zone of the cup. The use of the stress criterion and its non-dependence on the strain path change allows the fracture prediction. Finally, the numerical fracture propagation by the “kill element method”, as briefly discussed by Bouchard et al. [4], is used and shows a good similarity with the experience.


Anisotropy Zinc Cup drawing Stress criterion 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. 1.
    Adams KH (1965) Dislocation mobility and density in zinc single crystals. California Institute of TechnologyGoogle Scholar
  2. 2.
    Arrieux R, Bedrin C, Boivin M (1982) Determination of an intrinsic forming limit stress diagram for isotropic metal sheets, In: Proceedings of the 12th Biennial Congress of the IDDRG:61–71Google Scholar
  3. 3.
    Arrieux R, Boivin M, Le Maître F (1987) Determination of the forming limit curve for anisotropic sheets. Annals of the CIRP 25:195–198CrossRefGoogle Scholar
  4. 4.
    Bouchard PO, Bernacki M, El Khaoulani R, Milesi M (2009) On the role of particles distribution on damage and fatigue mechanisms. Int J Mater Form 2(1):935–938CrossRefGoogle Scholar
  5. 5.
    Bramley AN, Mello PB (1968) Plastic anisotropy of titanium and zinc sheet-I. Int J Mech Sci 10:211–219CrossRefGoogle Scholar
  6. 6.
    Cazacu O, Plunkett B, Barlat F (2006) Orthotropic yield criterion for hexagonal closed packed metals. Int J Plast 22:1171–1194CrossRefMATHGoogle Scholar
  7. 7.
    Coër J (2014) Mise en forme par emboutissage en température d'un alliage d'aluminium A5754-O, PhD, University of Bretagne-SudGoogle Scholar
  8. 8.
    Fundenberger JJ, Philippe MJ, Wagner F, Esling C (1997) Modelling and prediction of mechanical properties for materials with hexagonal symmetry (zinc, titanium and zirconium alloys. Acta Mater 45:4041–4055CrossRefGoogle Scholar
  9. 9.
    Graf A, Hosford W (1994) The influence of strain-path changes on forming limit diagrams of A1 6111 T4. Int J Mech Sci 36:897–910CrossRefGoogle Scholar
  10. 10.
    Haberfield AB, Boyles MW (1973) Laboratory determined forming limit diagrams. Sheet Met Ind 50:400–405 & 411Google Scholar
  11. 11.
    He M, Li F, Wang Z (2011) Forming limit stress diagram of aluminum alloy 5052 based on GTN model parameters determined by in situ tensile test. Chin J Aeronaut 24:378–386CrossRefGoogle Scholar
  12. 12.
    Hill R (1948) A theory of the yielding and plastic flow of anisotropic metals. Proceedings of the Royal Society a: mathematical. Phys Eng Sci 193:281–297CrossRefMATHGoogle Scholar
  13. 13.
    Inagaki H, Kohara S (1991) Cup drawing of strongly textured titanium sheets. ISIJ Int 31:820–826CrossRefGoogle Scholar
  14. 14.
    Jansen Y, Logé RE, Milesi M, Massoni E (2013) An anisotropic stress based criterion to predict the formability and the fracture mechanism of textured zinc sheets. J Mater Process Technol 213:851–855CrossRefGoogle Scholar
  15. 15.
    Jansen Y, Logé RE, Milesi M, Masson, E (2012) Using cross stamping to test zinc sheets formability, Key Eng Mater 504–506:65–70Google Scholar
  16. 16.
    Keeler SP, Backhofen WA (1964) Plastic instability and fracture in sheet stretched over rigid punches. ASM Trans 56:25–48Google Scholar
  17. 17.
    Lankford WT, Low JR, Gensamer M (1947) The Plastic Flow Of Aluminum Alloy Sheet Under Combined Loads, in: Metals Technology Vol. XIV:31Google Scholar
  18. 18.
    Milesi M, Chastel Y, Hachem E, Bernacki M, Logé RE, Bouchard PO (2010) A multi-scale approach for high cycle anisotropic fatigue resistance: application to forged components. Mater Sci Eng A 527:4654–4663CrossRefGoogle Scholar
  19. 19.
    Philippe MJ, Fundenberger JJ, Galledou Y, Humbert M, Wegria J, Esling C (1991) Influence of texture on low temperature bendability of Zn alloys. Textures and Microstructures 14:471–476CrossRefGoogle Scholar
  20. 20.
    Philippe MJ, Wagner F, Mellab FE, Esling C, Wegria J (1994) Modelling of texture evolution for materials of hexagonal symmetry-I. Application to zinc alloys. Acta Metall Mater 42:239–250CrossRefGoogle Scholar
  21. 21.
    Rojek J, Lumelskyy D, Pęcherski R, Grosman F, Tkocz M, Chorzępa W (2013) Forming limit curves for complex strain paths. Arch Metall Mater 58Google Scholar
  22. 22.
    Signorelli JW, Serenelli MJ, Bertinetti MA (2012) Experimental and numerical study of the role of crystallographic texture on the formability of an electro-galvanized steel sheet. J Mater Process Technol 212:1367–1376CrossRefGoogle Scholar
  23. 23.
    Stoughton TB (2000) A general forming limit criterion for sheet metal forming. Int J Mech Sci 42:1–27CrossRefMATHGoogle Scholar
  24. 24.
    Von Mises R (1928) Mechanics of plastic deformation of crystals. Appl Math Mech 592:161–185Google Scholar
  25. 25.
    Yoshida K, Kuwabara T, Kuroda M (2007) Path-dependence of the forming limit stresses in a sheet metal. Int J Plast 24:118–139CrossRefMATHGoogle Scholar
  26. 26.
    Zhalehfar F, Hosseinipour SJ, Nourouzi S, Gorji AH (2013) A different approach for considering the effect of non-proportional loading path on the forming limit diagram of AA5083. Mater Des 50:165–173CrossRefGoogle Scholar

Copyright information

© Springer-Verlag France 2016

Authors and Affiliations

  • Yann Jansen
    • 1
  • Roland E. Logé
    • 1
    • 3
  • Pierre-Yves Manach
    • 4
  • Gabriel Carbuccia
    • 2
  • Marc Milesi
    • 2
  1. 1.Center for Material Forming (CEMEF), Mines Paristech, UMR CNRS 7635Sophia-Antipolis CedexFrance
  2. 2.Umicore Building Products FranceLes mercurialesBagnoletFrance
  3. 3.Laboratory of Thermomechanical Metallurgy – PX Group ChairEcole Polytechnique Fédérale de Lausanne (EPFL)NeuchâtelSwitzerland
  4. 4.Université de Bretagne-SudLorientFrance

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