Skip to main content
SpringerLink
Log in

On the identification of kinematic hardening material parameters for accurate springback predictions

  • Thematic Issue: Twente
  • Published:
International Journal of Material Forming Aims and scope Submit manuscript

Abstract

An experimental method that frequently has been used for the determination of material hardening parameters is the three-point bending test. The advantage of this test is that it is simple to perform, and standard test equipments can be used. The disadvantage is that the material parameters have to be determined by some kind of inverse approach. The test has then been simulated by means of the Finite Element Method, and the material parameters have been determined by finding a best fit to the experimental results by means of a Response Surface Methodology. An alternative method is the tensile/compression test of a sheet strip. In practice such a test is very difficult to perform, due to the tendency of the strip to buckle in compression. In spite of these difficulties some successful attempts to perform cyclic tension/compression tests have been reported in the literature. However, a few writers have reported that there are substantial differences between hardening parameters determined from bending tests and those determined from tensile/compression tests. The purpose of the present study is to try to understand the background of these differences, to find out the influence on predicted springback, and to determine which of the two methodologies for hardening parameter identification is the most suitable one.

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
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  1. Eggertsen PA, Mattiasson M (2009) On the modelling of the bending-unbending behavior for accurate springback predictions. Int J Mech Sci 51:547–563

    Article  Google Scholar 

  2. Eggertsen PA, Mattiasson M (2010) An efficient inverse approach for material hardening parameter identification from a three-point bending test. Eng Comput 26:159–170

    Article  Google Scholar 

  3. Eggersten PA (2009) Prediction of springback in sheet metal forming, with emphasis on material modelling. Licentiate thesis, Chalmers University of Technology

  4. Eggertsen PA, Mattiasson M (2010) On constitutive modeling for springback analysis. Int J Mech Sci 52:804–818

    Article  Google Scholar 

  5. Yoshida F, Uemori T, Fujiwara K (2002) Elastic-plastic behavior of steel sheets under in-plane cyclic tension-compression at large strain. Int J Plast 18:633–659

    Article  MATH  Google Scholar 

  6. Lee MG, Kim D, Kim C, Wenner ML, Wagoner RH, Chung K (2005) Spring-back evaluation of automotive sheets based on isotropic-kinematic hardening laws and non-quadratic anisotropic yield functions. Part II: characterization of material properties. Int J Plast 21:883–914

    MATH  Google Scholar 

  7. Balakrishnan V (1999) Measurements of in-plane Bauschinger effect in metal sheets. Master’s thesis, The Ohio state university

  8. Kuwabara T (2007) Advances in experiments on metal sheets and tubes in support of constitutive modeling and forming simulations. Int J Plast 23:385–419

    Article  MATH  Google Scholar 

  9. Zhao KM, Lee JK (2001) Generation of cyclic stress-strain curves for sheet metals. J Eng Mater Technol 123:291–397

    Google Scholar 

  10. Omerspahic E, Mattiasson K, Enqvist B (2006) Identification of material hardening parameters by the three-point bending of metal sheets. Int J Mech Sci 48:1525–1532

    Article  Google Scholar 

  11. Yoshida F, Urabe M, Toropov VV (1998) Identification of material parameters in constitutive model for sheet metals from cyclic bending tests. Int J Mech Sci 40:237–249

    Article  Google Scholar 

  12. Carbonnière J, Thuillier S, Sabourin F, Brunet M, Manach PY (2009) Comparison of the work hardening of metallic sheets in bending-unbending and simple shear. Int J Mech Sci 51:122–130

    Article  Google Scholar 

  13. Kessler L, Gerlach J, Aydin MS. Proceedings of IDDRG (2008) Does the measurement of more material data necessarily result in higher forming simulation accuracy, Olofström. pp 441–452

  14. Geng L, Shen Y, Wagoner RH (2002) Anisotropic hardening equations derived from reverse-bend testing. Int J Plast 18:743–767

    Article  MATH  Google Scholar 

  15. Kessler L, Gerlach J, Aydin MS (2008) Proceedings of the German LS-Dyna user forum. Springback simulation with complex hardening material models. Bamberg

  16. Banabic D, Aretz H, Comsa DS, Paraianu L (2005) An improved analytical description of orthotropy in metallic sheets. Int J Plast 21:493–512

    Article  MATH  Google Scholar 

  17. Barlat F, Brem JC, Yoon JW, Chung K, Dick RE, Lege DJ, Pourboghrat F, Choi SH, Chu E (2003) Plane stress yield function for aluminum alloy sheets—Part I: theory. Int J Plast 19:1297–1319

    Article  MATH  Google Scholar 

  18. Aretz H (2005) A non-quadratic plane stress yield function for orthotropic sheet metals. J Mater Process Technol 168:1–9

    Google Scholar 

  19. Mattiasson K, Sigvant M (2008) An evaluation of some recent yield criteria for industrial simulation of sheet forming proceses. Int J Mech Sci 50:774–787

    Article  Google Scholar 

  20. Hodge PG (1957) A new method of analyzing stresses and strains in work hardening solids. J Appl Mech 24:482–483

    MathSciNet  Google Scholar 

  21. Crisfield MA (1997) More plasticity and other material non-linearity-II. In: Crisfield MA (ed) Non-linear finite element analysis of solids and structures, vol 2. Wiley, Chichester, pp 158–187

    Google Scholar 

  22. Armstrong PJ, Frederick CO (1966) A mathematical representation of the multiaxial bauschinger effect. G.E.G.B. report RD/B/N 731

  23. Geng L, Wagoner RH (2000) Springback analysis with a modified hardening model. SAE paper No. 2000-01-0768, SAE, Inc

  24. Boger R.K (2006). Non-Monotonic strain hardening and its constitutive representation, Dissertaion, The Ohio state University

  25. Yoshida F, Uemori T (2002) A model of large-strain cyclic plasticity describing the Baushinger effect and work hardening stagnation. Int J Plast 18:661–686

    Article  MATH  Google Scholar 

  26. Yoshida F, Uemori T (2003) A model of large-strain cyclic plasticity and its application to springback simulation. Int J Mech Sci 45:1687–1702

    Article  MATH  Google Scholar 

  27. LS-DYNA keyword user’s manual (2007) Volume I, Version 971, Livermore Software technology corporation (LSTC)

  28. Ortiz M, Simo JC (1986) An analysis of a new class of integration algorithms for elastoplastic constitutive relations. Int J Numer Methods Eng 23:353–366

    Article  MathSciNet  MATH  Google Scholar 

  29. Prager W (1956) A new method of analysing stresses and strains in work hardening plastic solids. J Appl Mech 23:493–496

    MathSciNet  MATH  Google Scholar 

  30. Ziegler H (1959) A modification of Prager’s hardening rule. Quart Appl Math 17:55–65

    MathSciNet  MATH  Google Scholar 

  31. Bathe KJ, Montáns FJ (2004) On modeling mixed hardening in computational plasticity. Comput Struct 82:535–539

    Article  Google Scholar 

  32. Chaboche JL (1986) Time-independent constitutive theories for cyclic plasticity. Int J Plast 2:149–188

    Article  MATH  Google Scholar 

  33. Chaboche JL (1989) Constitutive equations for cyclic plasticity and cyclic viscoplasticity. Int J Plast 5:247–302

    Article  MATH  Google Scholar 

  34. Mróz Z (1967) On the description of anisotropic work hardening. J Mech Phys Solids 15:163–175

    Article  Google Scholar 

  35. Dafalias YF, Popov EP (1976) Plastic internal variables formalism of cyclic plasticity. J Appl Mech 98:645

    Article  Google Scholar 

  36. Yoshida F, Uemori T, Fujiwara K (2002) Elastic-plastic behavior of steel sheets under in-plane cyclic tension-compression at large strain. Int J Plast 18:633–659

    Article  MATH  Google Scholar 

  37. Sigvant M, Mattiassson K, Vegter H, Thilderkvist P (2009) A viscous pressure bulge test for the determination of a plastic hardening curve and equibiaxial material data. Int J Mater Form 4:235–242

    Article  Google Scholar 

  38. Zhao KM, Lee JK (2002) Finite element analysis of the three-point bending of sheet metals. J Mater Process Technol 122:6–11

    Article  Google Scholar 

  39. Stander N, Roux W, Eggleston T, Craig K (2007) LS-OPT user’s manual, Version 3.2. Livermore Software technology corporation (LSTC)

  40. Mattiasson K, Strange A, Thilderkvist P, Samuelsson A (1995) Simulation of springback in sheet metal forming. In: Simulation of materials processing: theory, methods and applications 115-24

  41. Logan RW, Hosford WF (1980) Upper-bound anisotropic yield locus calculations assuming (111)-pencil glide. Int J Mech Sci 27:419–430

    Article  Google Scholar 

Download references

Acknowledgements

The characterization of the materials used in this study was conducted by Per Thilderkvist and Jörgen Hertzman at the Industrial Development Center in Olofström, Sweden. The three-point bending tests were performed by Bertil Enquist at Växjö University. Their contribution to this work is gratefully acknowledged.

Financial support has been provided by Vinnova through the FFI research program (Strategic Vehicle Research and Innovation).

Author information

Authors and Affiliations

  1. Division of Material and Computational Mechanics, Department of Applied Mechanics, Chalmers University of Technology, 412 96, Göteborg, Sweden

    Per-Anders Eggertsen & Kjell Mattiasson

  2. Department 91430, PV22, Volvo Cars Safety Centre, 405 31, Göteborg, Sweden

    Kjell Mattiasson

Authors
  1. Per-Anders Eggertsen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kjell Mattiasson
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kjell Mattiasson.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Eggertsen, PA., Mattiasson, K. On the identification of kinematic hardening material parameters for accurate springback predictions. Int J Mater Form 4, 103–120 (2011). https://doi.org/10.1007/s12289-010-1014-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12289-010-1014-7

Keywords

Search

Navigation