Skip to main content
SpringerLink
Log in

Modeling of the elastic modulus evolution in unloading-reloading stages

  • Original Research
  • Published:
International Journal of Material Forming Aims and scope Submit manuscript

Abstract

It was already stated that springback in sheet metal forming strongly depends on the elastic properties. Several experimental investigations have revealed that the elastic modulus decreases as the plastic strain increases. Two approaches have been separately employed to explain this phenomenon: dislocations rearrangements and damage. These approaches are considered in a proposed elastoplastic model coupled with damage based on Lemaitre type isotropic ductile damage law. In addition, a hysteresis aspect, which is experimentally observed during unloading-reloading stages, is also considered. Uniaxial tension tests have been used and the predicted results agree well with published experimental data. The proposed model is intended to be implemented in FEM codes for reliable results in forming processes including springback.

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

Similar content being viewed by others

References

  1. Yamaguchi K, Adachi H, Takakura N (1998) Effects of plastic strain path on Young’s modulus of sheet metals. Metals Mater 4:420–425

    Google Scholar 

  2. Yang M, Akiyama Y, Sasaki T (2004) Evaluation of change in material properties due to plastic deformation. J Mat Proc 151:232–236

    Article  Google Scholar 

  3. Cleveland RM, Ghosh AK (2002) Inelastic effects on springback in metals. Int J Plast 18:769–785

    Article  MATH  Google Scholar 

  4. Benito JA, Manero JM, Jorba J, Roca A (2005) Change of Young’s modulus of cold-deformed pure iron in a tensile test. Metall Mater Trans A 36:3319

    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. 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 

  7. Yu HY (2009) Variation of elastic modulus during plastic deformation and its influence on springback. Mater Des 30:846–850

    Article  Google Scholar 

  8. Eggertsen PA, Mattiasson K (2009) On the modelling of the bending–unbending behaviour for accurate springback predictions. Int J Mech Sci 51:547–563

    Article  Google Scholar 

  9. Halilovič M, Vrh M, Štok B (2009) Prediction of elastic strain recovery of a formed steel sheet considering stiffness degradation. Meccanica 44:321–338

    Article  MATH  Google Scholar 

  10. Vrh M, Halilovič M, Starman B, Štok B (2009) Modelling of springback in sheet metal forming. Int J Mater Form 2:825–828

    Article  Google Scholar 

  11. Vrh M, Halilovič M, Štok B (2011) The evolution of effective elastic properties of a cold, formed stainless steel sheet. Exp Mech 51:677–695

    Google Scholar 

  12. Hambli R, Mkaddem A, Potiron A (2003) Damage prediction in L-bending processes using FEM. Int J Adv Manuf Technol 22:12–19

    Article  Google Scholar 

  13. Yilamu K, Hino R, Hamasaki H, Yoshida F (2010) Air bending and springback of stainless steel clad aluminum sheet. J Mater Process Technol 272–278

  14. Ghaei A, Green DE, Taherizadeh A (2010) Semi-implicit numerical integration of Yoshida–Uemori two-surface plasticity model. Int J Mech Sci 52:531–540

    Article  Google Scholar 

  15. Ghaei A, Green DE (2010) Numerical implementation of Yoshida–Uemori two-surface plasticity model using a fully implicit integration scheme. Comput Mater Sci 48:195–205

    Article  Google Scholar 

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

    Article  Google Scholar 

  17. Kubli W, Krasovskyy A, Sester M (2008) Modeling of reverse loading effects including workhardening stagnation and early replastification. Int J Mater Form (Suppl 1):145–148, doi 10.1007/s12289-008-0012-5

  18. Eggertsen PA, Mattiasson K (2010) On the modeling of the unloading modulus for metal sheets. Int J Mater Form 3:127–130

    Article  Google Scholar 

  19. Bonora N, Gentile D, Pirondi A, Newaz G (2005) Ductile damage evolution under triaxial state of stress: theory and experiments. Int J Plast 21:981–1007

    Article  MATH  Google Scholar 

  20. Lemaître J, Chaboche J-L (1985) Mécanique des matériaux solides, Dunod Eds, Paris

  21. Badreddine H, Saanouni K, Dogui A (2010) On non-associative anisotropic finite plasticity fully coupled with isotropic ductile damage for metal forming. Int J Plast 26:1541–1575

    Article  MATH  Google Scholar 

  22. Celentano DJ, Chaboche J-L (2007) Experimental and numerical characterization of damage evolution in steels. Int J Plast 23:1739–1762

    Article  MATH  Google Scholar 

  23. Chatti S, Hermi N (2011) The effect of non-linear recovery on springback prediction. Comput Struct 89:1367–1377

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratory of Mechanical Engineering, Higher Institute of Applied Science and Technology of Sousse, ISSAT, Cité Taffala (Ibn Khaldoun), 4003, Sousse, Tunisia

    S. Chatti

Authors
  1. S. Chatti
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Chatti.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chatti, S. Modeling of the elastic modulus evolution in unloading-reloading stages. Int J Mater Form 6, 93–101 (2013). https://doi.org/10.1007/s12289-011-1075-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12289-011-1075-2

Keywords

Search

Navigation