International Journal of Material Forming

, Volume 6, Issue 2, pp 267–279 | Cite as

Modified maximum force criterion, a model for the theoretical prediction of forming limit curves

  • P. Hora
  • L. Tong
  • B. Berisha
Original Research


In order to perform the theoretical evaluation of Forming Limit Curves (FLC), the Modified Maximum Force Criterion (MMFC) has been proposed. This paper investigates the mechanism of the fracture of ductile sheet metals and introduces the MMFC model. The evaluation process and the simplified formulations are presented. The influences of hardening behavior and the yield loci are discussed as well. Comparisons with the experimental data of different materials showed generally satisfactory agreement.


FLC MMFC Sheet forming Failure prediction 


  1. 1.
    Keeler SP (1965) Determination of forming limit in automotive stamping. Soc Automot Engineering Nr. 650 535:1–9Google Scholar
  2. 2.
    Marciniak Z, Kuczynski K (1967) Int J Mech Sci 9:609–620CrossRefGoogle Scholar
  3. 3.
    Hill R (1952) On discontinuous plastic states, with special references to localized necking in the sheets. J Mech Phys Solid 1:19–30CrossRefGoogle Scholar
  4. 4.
    Swift HW (1952) Plastic instability under plane stresses. J Mech Phys Solid 1:1–18CrossRefGoogle Scholar
  5. 5.
    Hutchinson JW, Neale KW (1977) Influence of strain-rate sensitivity on necking under uniaxial tension. Acta Metall 25:839–846CrossRefGoogle Scholar
  6. 6.
    Hill R, Hutchinson JW (1975) Bifurcation phenomena in the plane tension test. J Mech Phys Solid 23:239–264MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Hora P et al (1996) A prediction method for ductile sheet metal failure using FE-simulation. NUMISHEET, Dearborn, pp 252–256Google Scholar
  8. 8.
    Hora P, et al (2003) Mathematical prediction of FLC using macroscopic instability criteria combined with micro structural crack propagation models, Plasticity, Quebec, Canada, pp. 364–366Google Scholar
  9. 9.
    Hora P, Tong L (2006) Numerical prediction of FLC using the enhanced modified maximum force criterion (eMMFC), FLC-Zurich 06, pp. 31–36Google Scholar
  10. 10.
    Krauer J, Hora P, Tong L (2007) Forming limits prediction of metastable materials with temperature and strain induced martensite transformation. In: Proceedings of the 9th International Conference on Numerical Methods in Industrial Forming Processes (NUMIFORM 2007), Porto, Portugal, pp. 1263–1268Google Scholar
  11. 11.
    Hora P, Tong L (2008) Theoretical prediction of the influence of curvature and thickness on the enhanced modified maximum force criterion, In: Proceedings of the 7th International Conference and Workshop on Numerical Simulation of 3D Sheet Metal Forming Processes (NUMISHEET 2008), Interlaken, Switzerland, pp. 205–210Google Scholar
  12. 12.
    Hora P, Eberle B, Volk W (2009) Numerical methods for a robust user-independent evaluation of Nakajima test for the FLC determination. In: Proceedings of the International Deep Drawing Research Group 2009 (IDDRG 2009), Golden CO, USA, pp.437–44Google Scholar
  13. 13.
    Banabic D, et al (2007) Anisotropy and formability, advances in material forming. Springer Verlag, pp. 143–173Google Scholar
  14. 14.
    Barlat F et al (2003) Plane stress yield function for aluminum alloy sheets–Part 1: theory. Int J Plast 19:1297–1319zbMATHCrossRefGoogle Scholar
  15. 15.
    Ghosh AK (1980) A physically-based constitutive model for metal deformation. Acta Metall 28:1443–1465CrossRefGoogle Scholar
  16. 16.
    Hockett JE, Sherby OD (1975) Large strain deformation of poly crystalline metals at low homologous temperatures. J Mech Phys Solids 23:87–98CrossRefGoogle Scholar
  17. 17.
    Hill R (1979) Theoretical plasticity of textured aggregates. Math Proc Cambridge Philosophical Soc 85:179–191zbMATHCrossRefGoogle Scholar
  18. 18.
    Aretz H (2004) Numerical restrictions of the modified maximum force criterion for prediction of forming limits in sheet metal forming. Model Simulat Mater Sci Eng 12:677–692CrossRefGoogle Scholar
  19. 19.
    Barlat F, Lian J (1989) Plastic behaviour and stretchability of sheet metal (Part 1): a yield function for orthotropic sheet under plane stress conditions. Int J Plast 5:51–56CrossRefGoogle Scholar
  20. 20.
    Comsa DS, et al (2011) Prediction of the forming limit band for steel sheets using a new formulation of Hora’s criterion (MMFC), AIP Conference Proceedings, vol. 1315 (AMPT 2010), pp 425–430Google Scholar
  21. 21.
    Banabic D, Soare S (2009) Assessment of the modified maximum force criterion for Aluminum metallic sheets. Key Engineer Mate 410:511–520CrossRefGoogle Scholar
  22. 22.
    Numisheet Benchmark 1 (2008) Virtual prediction of ductile material failure, Numisheet, Interlaken, SwitzerlandGoogle Scholar

Copyright information

© Springer-Verlag France 2011

Authors and Affiliations

  1. 1.Institute of Virtual ManufacturingETH ZurichZurichSwitzerland

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