Skip to main content
SpringerLink
Log in

Prediction for forming limit of Al2024T3 sheet based on damage theory using finite element method

  • Published:
Acta Mechanica Solida Sinica Aims and scope Submit manuscript

Abstract

This paper presents the application of anisotropic damage theory to the study of forming limit diagram of Al2024T3 aluminum alloy sheet. In the prediction of limiting strains of the aluminum sheet structure, a finite element cell model has been constructed. The cell model consists of two phases, the aluminum alloy matrix and the intermetallic cluster. The material behavior of the aluminum alloy matrix is described with a fully coupled elasto-plastic damage constitutive equation. The intermetallic cluster is assumed to be elastic and brittle. By varying the stretching ratio, the limiting strains of the sheet under biaxial stretching have been predicted by using the necking criterion proposed. The prediction is in good agreement with the experimental findings. Moreover, the finite element cell model can provide information for understanding the microscopic damage mechanism of the aluminum alloy. Over-estimation of the limit strains may result if the effect of material damage is ignored in the sheet metal forming study.

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

Similar content being viewed by others

References

  1. Marciniak, Z. and Kuczynski, K., Limit strains in the processes of stretch-forming sheet metal, Inter J Mech Sci, Vol.9, 1967, 609–620.

    Article  Google Scholar 

  2. Azrin, M. and Backofen, W.A., The deformation and failure of a biaxially stretched sheet, Metallurgical Trans, Vol.1, 1970, 2857–2865.

    Google Scholar 

  3. Venter, R., Johnson, W. and de Malherbe, M.C., The limit strains of inhomogeneous sheet metal in biaxial tension, Inter J Mech Sci, Vol.13, 1971, 299–308.

    Article  Google Scholar 

  4. Sowerby, R. and Duncan, J.L., Failure in sheet metal in biaxial tension, Inter J Mech Sci, Vol.13, 1971, 217–229.

    Article  Google Scholar 

  5. Parmar, A. and Mellor, P.B., Predictions of limit strains in sheet metal using a more general yield criterion, Inter J Mech Sci, Vol.20, 1978, 385–391.

    Article  Google Scholar 

  6. Needleman, A. and Triantafyllidis, N., Void growth and local necking in biaxially stretched sheets, Tran ASME, J Engng Mater Tech, Vol.100, 1978, 164–9.

    Article  Google Scholar 

  7. Gurson, A.L., Continuum theory of ductile rupture by void nucleation and growth: Part I — Yield criteria and flow rules for porous ductile media, Trans ASME, J Engng Mater Tech, Vol.99, 1977, 2–15.

    Article  Google Scholar 

  8. Padwal, S.B. and Chaturvedi, R.C., Prediction of forming limits using Hosford’s modified yield criterion, Inter J Mech Sci, Vol.34, 1992, 541–547.

    Article  Google Scholar 

  9. Hosford, W.F., Comments on anisotropic yield criteria, Inter J Mech Sci, Vol.27, 1985, 423–427.

    Article  Google Scholar 

  10. van Minh, H., Sowerby, R. and Duncan, J.L., Probabilistic model of limit strains in sheet metal, Inter J Mech Sci, Vol.17, 1975, 339–349.

    Article  Google Scholar 

  11. Yamaguchi, K. and Mellor, P.B., Thickness and grain size dependence of limit strains in sheet metal stretching, Inter J Mech Sciz, Vol.18, 1976, 85–90.

    Article  Google Scholar 

  12. Date, P.P. and Padmanabhan, K.A., On the prediction of the forming-limit diagram of sheet metals, Inter J Mech Sci, Vol.34, 1992, 363–374.

    Article  Google Scholar 

  13. Chow, C.L. and Wang, J., An anisotropic theory of elasticity for continuum damage mechanics, Inter J Fract, Vol.33, 1987, 3–16.

    Article  Google Scholar 

  14. Chow, C.L. and Wang, J., An anisotropic theory of continuum damage mechanics for ductile fracture, Engng Fract Mech, Vol.27, 1987, 547–558.

    Article  Google Scholar 

  15. Chow, C.L. and Wang, J., An anisotropic continuum damage theory and its application to ductile crack initiation, Damage Mech Compos ASME AD, Vol.12, 1987, 1–10.

    Google Scholar 

  16. Chow, C.L. and Wang, J., Ductile fracture characterization with an anisotropic continuum damage theory, Engng Fract Mech, Vol.30, 1988, 547–563.

    Article  Google Scholar 

  17. Lee, W.B., Tai, W.H. and Tang, C.Y., Damage evolution and forming limit prediction of an Al2024-T3 aluminum alloy, J Mate Process Tech, Vol.63, 1997, 100–104.

    Article  Google Scholar 

  18. Tang, C.Y., Shen, W. and Lee, T.C., A damage-base criterion for fracture preditiion in metal forming processes: a case study in Al 2024T3 sheet, J Mater Process Tech, Vol.89, 1999, 79–83.

    Article  Google Scholar 

  19. Tang, C.Y., Chow, C.L., Shen, W. and Tai, W.H., Development of a damage-based criterion for ductile fracture prediction in sheet metal forming, J Mater Process Tech, Vol.91, 1999, 270–277.

    Article  Google Scholar 

  20. Tang, C.Y. and Tai, W.H., Material damage and forming limits of textured sheet metals, J Mater Process Tech, Vol.99, 2000, 135–140.

    Article  Google Scholar 

  21. Tang, C.Y., Modelling of craze damage in polymeric materials: a case study in polystyrene and high impact polystyrene. Ph.D. Thesis, The Hong Kong Polytechnic University, 1995.

  22. Tang, C.Y., Shen, W., Fung, L.C. and Lee, T.C., Second-order continuity tensor and stiffness degradation of aluminum alloy 2024T3 under large strain at room temperature, Inter J Mech Sci, Vol.42, 2000, 87–105.

    Article  Google Scholar 

  23. Tang, C.Y., Lee, T.C. and Rao, B., An experimental study of shear damage using in-situ single shear test, Inter J Damage Mech, Vol.11, 2002, 335–353.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, China

    C. Y. Tang, Jianping Fan & C. P. Tsui

  2. School of Civil Engineering and Mechanics, Huazhong University of Science and Technology, Wuhan, 430074, China

    Jianping Fan

Authors
  1. C. Y. Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jianping Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. C. P. Tsui
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jianping Fan.

Additional information

Project supported by the Research Committee of The Hong Kong Polytechnic University (No.G-YX34).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tang, C.Y., Fan, J. & Tsui, C.P. Prediction for forming limit of Al2024T3 sheet based on damage theory using finite element method. Acta Mech. Solida Sin. 19, 174–180 (2006). https://doi.org/10.1007/s10338-006-0621-9

Download citation

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10338-006-0621-9

Key words

Search

Navigation