Skip to main content
SpringerLink
Log in

Finite element analysis of combined forming processes by means of rate dependent ductile damage modelling

  • Thematic Issue: Computational Methods in Manufacturing
  • Published:
International Journal of Material Forming Aims and scope Submit manuscript

Abstract

Sheet metal forming is an inherent part of todays production industry. A major goal is to increase the forming limits of classical deep-drawing processes. One possibility to achieve that is to combine the conventional quasi-static (QS) forming process with electromagnetic high-speed (HS) post-forming. This work focuses on the finite element analysis of such combined forming processes to demonstrate the improvement which can be achieved. For this purpose, a cooperation of different institutions representing different work fields has been established. The material characterization is based on flow curves and forming limit curves for low and high strain rates obtained by novel testing devices. Further experimental investigations have been performed on the process chain of a cross shaped cup, referring to both purely quasi-static and quasi-static combined with electromagnetic forming. While efficient mathematical optimization algorithms support the new viscoplastic ductile damage modelling to find the optimum parameters based on the results of experimental material characterization, the full process chain is studied by means of an electro-magneto-mechanical finite element analysis. The constitutive equations of the material model are integrated in an explicit manner and implemented as a user material subroutine into the commercial finite element package LS-DYNA.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Akima H (1970) A new method of interpolation and smooth curve fitting based on local procedures. J ACM (JACM) 17:589–602

    Article  MATH  Google Scholar 

  2. Aretz H, Barlat F (2013) New convex yield functions for orthotropic metal plasticity. Int J Non-Linear Mech 51:97–111

    Article  Google Scholar 

  3. Bai Y, Wierzbicki T (2008) A new model of metal plasticity and fracture with pressure and lode dependence. Int J Plast 24: 1071–1096

    Article  MATH  Google Scholar 

  4. Balanethiram VS, Daehn GS (1994) Hyperplasticity: Increased forming limits at high workpiece velocity. Scr Metall Mater 30:515–520

    Article  Google Scholar 

  5. Barlat F, Gracio JJ, Lee MG, Rauch EF, Vincze G (2011) An alternative to kinematic hardening in classical plasticity. Int J Plast 27:1309 – 1327

    Article  MATH  Google Scholar 

  6. Børvik T, Hopperstad O, Berstad T, Langseth M (2001) A computational model of viscoplasticity and ductile damage for impact and penetration. European Journal of Mechanics - A/Solids 20:685–712

    Article  MATH  Google Scholar 

  7. Brünig M, Gerke S, Hagenbrock V (2013) Micro-mechanical studies on the effect of the stress triaxiality and the lode parameter on ductile damage. Int J Plast 50:49–65

    Article  Google Scholar 

  8. Byrd R, Nocedal J, Schnabel R (1994) Representations of quasi-newton matrices and their use in limited memory methods. Math Program 63:129–156

    Article  MathSciNet  MATH  Google Scholar 

  9. Caldichoury I, L’Eplattenier P (2008) Introduction of an electromagnetism module in ls-dyna for coupled mechanical thermal electromagnetic simulations. ICHSF 2008, 85–96

  10. Chaboche JL (1988) Continuum damage mechanics: Parts i and ii. J Appl Mech 55:59–72

    Article  Google Scholar 

  11. Demir OK, Kwiatkowski L, Brosius A, Tekkaya AE (2012) Exceeding the forming limit curve with deep drawing followed by electromagnetic calibration. In: Proceedings of the 5th International Conference on High Speed Forming ICHSF 2012, Dortmund, pp 277–282

  12. Engelhardt M, Klose C (2014) Experimental investigations on forming limits for aluminium alloy sheet metal at various strain rates. In: Hoon H, Tekkaya AE (eds) High Speed Forming 2014, pp 11–20

  13. Frederick CO, Armstrong PJ (2007) A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24:1–26

    Article  Google Scholar 

  14. Hill R (1948) A theory of the yielding and plastic flow of anisotropic metals. Proc R Soc Lond A 193:281–297

    Article  MathSciNet  MATH  Google Scholar 

  15. Jeunechamps PP, Ponthot JP (2013) An efficient 3d implicit approach for the thermomechanical simulation of elasticviscoplastic materials submitted to highstrain rate and damage. Int J Numer Methods Eng 94:920–960

    Article  MATH  Google Scholar 

  16. Johnson GR, Cook WH (1985) Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures. Int J Eng Fract Mech 21:31–48

    Article  Google Scholar 

  17. Kiliclar Y, Engelhardt M, Vladimirov IN, Pietryga MP, von Senden genannt Haverkamp H, Reese S, Bach FW (2012) On the improvement of formability and the prediction of forming limit diagrams at fracture by means of constitutive modelling. Key Eng Mater 504–506:29–34

    Article  Google Scholar 

  18. Kiliclar Y, Demir OK, Engelhardt M, Rozgic M, Vladimirov IN, Wulfinghofff S, Weddeling C, Klose C, Reese S, Tekkaya EA, Meier HJ, Stiemer M (2015) Experimental and numerical investigations on the process combination of a quasi-static and high-speed forming process for increasing formability. J Mater Process Technol. submitted September 2015

  19. Lemaitre J (1985) A continuous damage mechanics model for ductile fracture. J Eng Mater Technol 107:83

    Article  Google Scholar 

  20. Lemaitre J (1996) A course on damage mechanics. Springer

  21. Lemaitre J, Chaboche J (1995) Mechanics of solid materials. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  22. Lou Y, Yoon JW, Huh H (2014) Modeling of shear ductile fracture considering a changeable cut-off value for stress triaxiality. Int J Plast 54:56–80

    Article  Google Scholar 

  23. Mahnken R, Johansson M, Runesson K (1998) Parameter estimation for a viscoplastic damage model using a gradient-based optimization algorithm. Eng Comput 15:925–955

    Article  MATH  Google Scholar 

  24. Nakazima K, Kikuma T, Hasuka K (1968) Study on the formability of steel sheet. Yawata Technical Report:141–154

  25. Pietryga MP, Vladimirov IN, Reese S (2012) A finite deformation model for evolving flow anisotropy with distortional hardening including experimental validation. Mech Mater 44:163–173

    Article  Google Scholar 

  26. Psyk V, Risch D, Kinsey BL, Tekkaya AE, Kleiner M (2011) Electromagnetic forming—a review. J Mater Process Technol 211:787–829

    Article  Google Scholar 

  27. Schwarz HR, Kückler N (2009) Numerische Mathematik. Springer DE

  28. Seth M, Vohnout VJ, Daehn GS (2005) Formability of steel sheet in high velocity impact. J Mater Process Technol 168:390– 400

    Article  Google Scholar 

  29. Shutov A, Ihlemann J (2012) A viscoplasticity model with an enhanced control of the yield surface distortion. Int J Plast 39: 152–167

    Article  Google Scholar 

  30. Stoughton TB, Yoon JW (2011) A new approach for failure criterion for sheet metals. Int J Plast 27:440–459

    Article  MATH  Google Scholar 

  31. Stoughton TB, Yoon JW (2012) Path independent forming limits in strain and stress spaces. Int J Solids Struct 49:3616– -3625

    Article  Google Scholar 

  32. Tutyshkin N, Mller WH, Wille R, Zapara M (2014) Strain-induced damage of metals under large plastic deformation: Theoretical framework and experiments. Int J Plast 59:133–151

    Article  Google Scholar 

  33. Vladimirov IN, Pietryga MP, Kiliclar Y, Tini V, Reese S (2014) Failure modelling in metal forming by means of an anisotropic hyperelastic-plasticity model with damage. International Journal of Damage Mechanics 23:1096–1132

    Article  Google Scholar 

  34. Vladimirov IN, Pietryga MP, Reese S (2011) On the influence of kinematic hardening on plastic anisotropy in the context of finite strain plasticity. Int J Mater Form 4:255–267

    Article  Google Scholar 

  35. Vladimirov IN, Pietryga MP, Reese S (2009) Prediction of springback in sheet forming by a new finite strain model with nonlinear kinematic and isotropic hardening. J Mater Process Technol 209:4062–4075

    Article  Google Scholar 

  36. Wächter A, Biegler LT (2006) On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math Program 106:25–57

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

This work is based on the results of PAK343 Methods for quasi-static-dynamic combined forming processes within the projects TP1 (O. Koray Demir, Christian Weddeling and A. Erman Tekkaya), TP2 (Marco Rozgic̀ and Marcus Stiemer), TP3 (Yalin Kiliclar, Stefan Wulfinghoff and Stefanie Reese) and TP4 (Marcus Engelhardt, Christian Klose and Hans Jürgen Maier). The authors would like to thank the German Science Foundation (DFG) for its financial support.

Author information

Authors and Affiliations

  1. Institute of Applied Mechanics, RWTH Aachen University, Mies-van-der-Rohe-Str. 1, 52074, Aachen, Germany

    Y. Kiliclar, S. Wulfinghoff & S. Reese

  2. MTU Aero Engines AG, 80995, München, Germany

    I. N. Vladimirov

  3. TU Dortmund, Institute of Forming Technology and Lightweight Construction, Baroper Str. 305, 44227, Dortmund, Germany

    O. K. Demir, C. Weddeling & A. E. Tekkaya

  4. Institut für Werkstoffkunde (Materials Science), Leibniz Universität Hannover, An der Universität 2, 30826, Garbsen, Germany

    M. Engelhardt, C. Klose & H. J. Maier

  5. Theory of Electrical Engineering, Helmut Schmidt University, Holstenhof Weg 85, 22043, Hamburg, Germany

    M. Rozgic̀ & M. Stiemer

Authors
  1. Y. Kiliclar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. N. Vladimirov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Wulfinghoff
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. S. Reese
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. O. K. Demir
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. C. Weddeling
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. A. E. Tekkaya
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. M. Engelhardt
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. C. Klose
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. H. J. Maier
    View author publications

    You can also search for this author in PubMed Google Scholar

  11. M. Rozgic̀
    View author publications

    You can also search for this author in PubMed Google Scholar

  12. M. Stiemer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Y. Kiliclar.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kiliclar, Y., Vladimirov, I.N., Wulfinghoff, S. et al. Finite element analysis of combined forming processes by means of rate dependent ductile damage modelling. Int J Mater Form 10, 73–84 (2017). https://doi.org/10.1007/s12289-015-1278-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12289-015-1278-z

Keywords

Search

Navigation