Journal of Mechanical Science and Technology

, Volume 26, Issue 2, pp 345–352 | Cite as

Application of the GTN model to predict the forming limit diagram of IF-Steel

  • Mahmoud AbbasiEmail author
  • Mohammad A. Shafaat
  • Mostafa Ketabchi
  • Davoud F. Haghshenas
  • Mohammad Abbasi


Forming limit diagrams (FLDs) are extensively used in industries, particularly the auto industry. The establishment of these diagrams using a predictive approach can lead to reduction in both cost and time. In the present work, Gurson-Tvergaard-Needleman (GTN), a porosity-based model, was used to predict the FLD of an interstitial-free steel via finite element simulation. Optimum values of the GTN model were obtained by applying a response surface methodology (RSM) based on central composite design. Results show that RSM is a good method for an appropriate determination of the GTN model parameters, such as initial void volume fraction, effective void volume fraction, critical void volume fraction, and final void volume fraction. Furthermore, the experimental FLD of the specimen steel was considerably predicted using the obtained GTN model parameters.


Ductile fracture Forming limit diagram GTN model Response surface methodology 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    F. Ozturk and D. Lee, Experimental and numerical analysis of out-of-plane formability test, J. Mater. Process. Technol., 170 (2005) 247–253.CrossRefGoogle Scholar
  2. [2]
    A. Menhaj, M. Abbasi, M. Sedighi and M. Ketabchi, A new concept in obtaining forming limit diagram of tailor welded blank, J. Strain Analysis, 46 (2011) 740–748..CrossRefGoogle Scholar
  3. [3]
    M. Aghaie-khafri, R. Mahmudi and H. Pishbin, Role of yield criteria and hardening laws in the prediction of forming limit diagrams, Metall Mater Trans A, 33 (2002) 1363–1371.CrossRefGoogle Scholar
  4. [4]
    S. E. Jones and P. P. Gillis, An analysis of biaxial stretching of a flat sheet, Metall Mater Trans A, 15 (1984) 133–138.CrossRefGoogle Scholar
  5. [5]
    C. Zhiying and D. Xianghuai, The GTN damage model based on Hill’48 anisotropic yield criterion and its application in sheet metal forming, Comp. Mater. Sci., 44 (2009) 1013–1021.CrossRefGoogle Scholar
  6. [6]
    M. Brunet, F. Morestin and H. Walter, Damage identification for anisotropic sheet-metals using a non-local damage model, Int. J. Damage. Mech., 13 (2004) 35–57.CrossRefGoogle Scholar
  7. [7]
    M. Abbasi, M. Ketabchi, H. Izadkhah, D. F. Haghshenas and A. N. Aghbash, Identification of GTN model parameters by application of response surface methodology, Procedia Eng., 10 (2011) 415–420.CrossRefGoogle Scholar
  8. [8]
    M. Springmann and M. Kuna, Determination of ductile damage parameters by local deformation fields: measurement and simulation, Arch. Appl. Mech., 75 (2006) 775–797.zbMATHCrossRefGoogle Scholar
  9. [9]
    M. Brunet, S. Mguil and F. Morestin, Analytical and experimental studies of necking in sheet metal forming processes, J. Mater. Process. Technol., 80–81 (1998) 40–46.CrossRefGoogle Scholar
  10. [10]
    L. Fratini, A. Lombardo and F. Micari, Material characterization for the prediction of ductile fracture occurrence: an inverse approach, J. Mater. Process. Technol., 60 (1996) 311–316.CrossRefGoogle Scholar
  11. [11]
    G. B. Broggiato, F. Campana and L. Cortese, Identification of material damage model parameters: an inverse approach using digital image processing, Meccanica, 42 (2007) 9–17.zbMATHCrossRefGoogle Scholar
  12. [12]
    D. C. Montgomery, Design and analysis of experiments, John Wiley & Sons, New York, USA (2006).Google Scholar
  13. [13]
    M. Abbasi, B. Bagheri, M. Ketabchi and D. F. Haghshenas, Application of response surface methodology to drive GTN model parameters and determine the FLD of tailor welded blank, Comp. Mater. Sci., 53 (2012) 368–376.CrossRefGoogle Scholar
  14. [14]
    A. L. Gurson, Continuum theory of ductile rupture by void nucleation and growth. Part I: yield criteria and flows rules for porous ductile media, J. Eng. Mater. Technol., 99 (1977) 2–15.CrossRefGoogle Scholar
  15. [15]
    A. K. Gupta and D. R. Kumar, Formability of galvanized interstitial-free steel sheets, J. Mater. Process. Technol., 172 (2006) 225–237.CrossRefGoogle Scholar
  16. [16]
    ASTM Standards, Standard test methods for tension testing of metallic materials, ASTM E8-E8M, 2009.Google Scholar
  17. [17]
    Abaqus/6.9 Software, Abaqus Analysis User’s Manual (6.9), Porous metal plasticity, 2009.Google Scholar
  18. [18]
    M. Abbasi, Analysis of wrinkling and tearing of tailor welded blank during deep drawing process, Ph. D. Thesis, Amirkabir University of Technology, Tehran, Iran (2011).Google Scholar
  19. [19]
    Abaqus/6.9 Software, Dassault Systèmes Simulia Corp., Providence, RI, USA (2009).Google Scholar
  20. [20]
    Z. Chen and X. Dong, The GTN damage model based on Hill’48 anisotropic yield criterion and its application in sheet metal forming, Comp. Mater. Sci., 44 (2009) 1013–1021.CrossRefGoogle Scholar
  21. [21]
    J. Rojek, E. Onate and E. Postek, Application of explicit FE codes to simulation of sheet and bulk metal forming processes, J. Mater. Process. Technol., 80–81 (1998) 620–627.CrossRefGoogle Scholar
  22. [22]
    D. Banabic, H. J. Bunge, K. Pöhlandt and A. E. Tekkaya, Formability of metallic materials, Springer-Verlag, Berlin, Germany (2000).Google Scholar
  23. [23]
    A. Seireg, Friction and lubrication in mechanical design, Mechanical Engineering Series, Marcel Dekker Pub. (1998).Google Scholar
  24. [24]
    M. A. Shafaat, M. Abbasi and M. Ketabchi, Investigation into wall wrinkling in deep drawing process of conical cups, J. Mater. Process. Technol. (2011), DOI: 10.1016/j.jmatprotec.2011.05.026.Google Scholar
  25. [25]
    N. Amjadi and A. Shirzadi, Unit commitment using a new integer coded genetic algorithm, Eur. T. Electr. Power, 19 (2009) 1161–1176.CrossRefGoogle Scholar
  26. [26]
    W. F. Hosford and R. M. Caddell, Metal formingmechanics and metallurgy, Cambridge University Press, Cambridge (2007).CrossRefGoogle Scholar

Copyright information

© The Korean Society of Mechanical Engineers and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Mahmoud Abbasi
    • 1
    Email author
  • Mohammad A. Shafaat
    • 1
  • Mostafa Ketabchi
    • 1
  • Davoud F. Haghshenas
    • 1
  • Mohammad Abbasi
    • 2
  1. 1.Department of Mining and MetallurgyAmirkabir University of TechnologyTehranIran
  2. 2.Faculty of Aerospace EngineeringSharif University of TechnologyTehranIran

Personalised recommendations