Skip to main content
SpringerLink
Log in

Numerical approach to the evaluation of forming limit curves for zircaloy-4 sheet

  • Article
  • Published:
Journal of Materials Research Aims and scope Submit manuscript

Abstract

The forming limit strains (FLSs) of zircaloy-4 sheets are studied. After having obtained the true stress–strain curve of zircaloy-4 using the weighted-average method, limit dome height (LDH) tests are performed to establish experimental FLSs. We summarize related theoretical forming limit curves (FLC) and discuss their limitations. Two finite element (FE) models are established for determining FLSs; an LDH test FE model for the negative minor strain sector, and a biaxial tensile FE model for the positive minor strain sector. The numerical FLSs are found to agree well with experimental data. Since the numerical FLC gives the strain at the onset of local thinning (whereas the experimental FLC provides the strain between local necking and ductile fracture), resulting FE FLS values are slightly lower than the experimental ones so that results can be regarded as conservative. Our FE approach substitutes the expensive and time-demanding experimental LDH tests.

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
FIG. 14
FIG. 15
FIG. 16
FIG. 17
FIG. 18
FIG. 19
FIG. 20
FIG. 21
FIG. 22

Similar content being viewed by others

References

  1. S.P. Keeler: Determination of forming limits in automotive stampings. Sheet Metal. Ind. 42, 683–691 (1965).

    Google Scholar 

  2. G.M. Goodwin: Application of strain analysis to sheet metal forming problems in the press shop. Metall. Ital. 60, 764–774 (1968).

    Google Scholar 

  3. R. Arrieux, C. Bedrin, and M. Boivin: Determination of an intrinsic forming limit stress diagram for isotropic metal sheets. In Proceedings of the 12th Biennial Congress IDDRG; Genoa, Italy, 1982; pp. 61–71.

  4. J. He, Z. Xia, X. Zhu, D. Zeng, and S. Li: Sheet metal forming limits under stretch–bending with anisotropic hardening. Int. J. Mech. Sci. 75, 244–256 (2013).

    Article  Google Scholar 

  5. K. Inal, K.W. Neale, and A. Aboutajeddine: Forming limit comparisons for FCC and BCC sheets. Int. J. Plast. 21, 1255–1266 (2005).

    Article  Google Scholar 

  6. W. Lee, K.H. Chung, D. Kim, J. Kim, C. Kim, K. Okamoto, R.H. Wagoner, and K. Chung: Experimental and numerical study on formability of friction stir welded TWB sheets based on hemispherical dome stretch tests. Int. J. Plast. 25, 1626–1654 (2009).

    Article  CAS  Google Scholar 

  7. J. Liu, W. Liu, and W. Xue: Forming limit diagram prediction of AA5052/polyethylene/AA5052 sandwich sheets. Mater. Des. 46, 112–120 (2013).

    Article  CAS  Google Scholar 

  8. R.G. Narayanan and K. Narasimhan: Predicting the forming limit strains of tailor-welded blanks. J. Strain Anal. Eng. Des. 43, 217–227 (2008).

    Article  Google Scholar 

  9. F. Ozturk and D. Lee: Analysis of forming limits using ductile fracture criteria. J. Mater. Process. Technol. 147, 397–404 (2004).

    Article  Google Scholar 

  10. T. Pepelnjak and K. Kuzman: Numerical determination of the forming limit diagrams. J. Achiev. Mater. Manuf. Eng. 20, 375–378 (2007).

    Google Scholar 

  11. A. Petek, T. Pepelnjak, and K. Kuzman: An improved method for determining a forming limit diagram in the digital environment. J. Mech. Eng. 51, 330–345 (2005).

    Google Scholar 

  12. D.Y. Seong, M.Z. Haque, J.B. Kim, T.B. Stoughton, and J.W. Yoon: Suppression of necking in incremental sheet forming. Int. J. Solids Struct. 51, 2840–2849 (2014).

    Article  Google Scholar 

  13. L.M. Smith, R.C. Averill, J.P. Lucas, T.B. Stoughton, and P.H. Matin: Influence of transverse normal stress on sheet metal formability. Int. J. Plast. 19, 1567–1583 (2003).

    Article  Google Scholar 

  14. C. Zhang, L. Leotoing, D. Guines, and E. Ragneau: Theoretical and numerical study of strain rate influence on aa5083 formability. J. Mater. Process. Technol. 209, 3849–3858 (2009).

    Article  CAS  Google Scholar 

  15. L. Zhang and J. Wang: Modeling the localized necking in anisotropic sheet metals. Int. J. Plast. 39, 103–118 (2012).

    Article  Google Scholar 

  16. A. Graf and W.F. Hosford: Effect of changing strain paths on forming limit diagram of Al 2008-T4. Metall. Mater. Trans. A 24, 2503–2512 (1993).

    Article  Google Scholar 

  17. T.B. Stoughton and X. Zhu: Review of theoretical models of the strain-based FLD and their relevance to the stress-based. Int. J. Plast. 20, 1463–1486 (2004).

    Article  Google Scholar 

  18. Y. Seo, H.C. Hyun, H. Lee, and N. Kim: Forming limit diagrams of zircaloy-4 and zirlo sheets for stamping of spacer grids of nuclear fuel rods. Trans. Korean Soc. Mech. Eng. A 35, 889–897 (2011). [In Korean].

    Article  Google Scholar 

  19. R. Hill: On discontinuous plastic state, with special reference to localized necking in thin sheets. J. Mech. Phys. Solids 1, 19–30 (1952).

    Article  Google Scholar 

  20. H.W. Swift: Plastic instability under plane stress. J. Mech. Phys. Solids 1, 1–16 (1952).

    Article  Google Scholar 

  21. Z. Marciniak and K. Kuczynski: Limits strains in the processes of stretch-forming sheet metal. Int. J. Mech. Sci. 9, 609–620 (1967).

    Article  Google Scholar 

  22. S. Stören and J.R. Rice: Localized necking in thin sheets. J. Mech. Phys. Solids 23, 421–441 (1975).

    Article  Google Scholar 

  23. P.W. Bridgman: Studies in Large Plastic Flow and Fracture (McGraw Hill, New York, 1952).

    Google Scholar 

  24. Y. Ling: Uniaxial true stress-strain after necking. AMP. J. Technol. 5, 37–48 (1996).

    Google Scholar 

  25. Abaqus: Abaqus User’s Manual: Version 6.12 (Dassault Systemes, Providence, RI, 2012).

  26. H.C. Hyun, M. Kim, S. Bang, and H. Lee: On acquiring true stress-strain curves for sheet specimen using tensile test and fe analysis based on a local necking criterion. J. Mater. Res. 29, 695–707 (2014).

    Article  CAS  Google Scholar 

  27. S.S. Hecker: A simple forming limit curve technique and results on aluminum alloys. In Proceedings of the 7th Biennial Congress IDDRG; Amsterdam, Netherlands, 1972; pp. 5.1–5.8.

  28. Z. Marciniak: Stability of plastic shells under tension with kinematic boundary condition. Arch. Mech. Stosow. 17, 577–592 (1965).

    Google Scholar 

  29. W. Hotz: European Efforts in Standardization of FLC (ETH Zürich, Zürich, Switzerland, 2006); pp. 24–25.

    Google Scholar 

  30. A.K. Ghosh: The effect of lateral draw-in on stretch formability. Met. Eng. Q 15, 53–64 (1975).

    CAS  Google Scholar 

  31. R.A. Ayres, W.G. Brazier, and V.F. Sajewski: Evaluating the GMR-limiting dome height test as a new measure of press formability near plane strain. J. Appl. Metalwork 1, 41–49 (1978).

    Article  Google Scholar 

  32. A. Bragard, J.C. Baret, and H. Bonnarens: A simplified technique to determine the FLD at onset of necking. Rapport du Centre de Recherches Mettallurgiques 33, 53–63 (1972).

    Google Scholar 

  33. H. Liebertz, A. Duwel, R. Illig, W. Hotz, S. Keller, A. Koehler, A. Kroeff, M. Merklein, J. Rauer, L. Staubwasser, G. Steinbeck, and H. Vegter: Guideline for the determination of forming limit curves. In Proceedings of the IDDRG Conference; Sindelfingen, Germany, 2004; pp. 216–224.

  34. ISO 12004: Metallic Materials-sheet and Strip-Determination of the Forming Limit Curves. Part 2: Determination of Forming Limit Curves in the Laboratory (ISO, Geneva, 2006).

    Google Scholar 

  35. V. Hasek: Research and theoretical description concerning the influences on the FLDs. Blech, Rohre, Profile 25, 213–220 (1978). [In German].

    Google Scholar 

Download references

ACKNOWLEDGMENTS

This work was supported by the Nuclear Power Core Technology Development Program of the Korea Institute of Energy Technology Evaluation and Planning (KETEP), granted financial resource from the Ministry of Trade, Industry and Energy, Republic of Korea. (No. KETEP-2013 85400 40010)

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Sogang University, Seoul, 121-742, Korea

    Minsoo Kim, Felix Rickhey, Hyungyil Lee & Naksoo Kim

Authors
  1. Minsoo Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Felix Rickhey
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hyungyil Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Naksoo Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hyungyil Lee.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kim, M., Rickhey, F., Lee, H. et al. Numerical approach to the evaluation of forming limit curves for zircaloy-4 sheet. Journal of Materials Research 30, 3277–3287 (2015). https://doi.org/10.1557/jmr.2015.293

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1557/jmr.2015.293

Search

Navigation