Prediction of material behavior during biaxial stretching of superplastic 5083 aluminum alloy

  • Omid MajidiEmail author
  • Mohammad Jahazi
  • Nicolas Bombardier


In order to predict the flow behavior of a superplastic Al-Mg alloy sheet under near biaxial tension mode, finite element simulation was performed using commercial FE software (ABAQUS). To capture the time-dependent plastic behavior of the material, three constitutive models, i.e., the Voce model, a power law, and a newly introduced variable m value viscoplastic (VmV) model, were implemented in FE simulations. The models’ parameters were assessed from the three uniaxial stress-strain curves ranging from 10−3 to 10−1 s−1. To validate the simulation results, Nakazima hemispherical dome testing was performed under isothermal conditions using a constant strain rate of ~ 0.01 s−1 at 450 °C. After the tests, the thickness of the deformed parts was measured and the volume fractions of cavities at different locations were assessed using X-ray micro-tomography, and the impact of the strain path on the rate of cavitation was discussed. Based on the obtained results, when the material behavior was modeled using the VmV model, the accuracy of the prediction was about 2 and 5 times better than the ones from power law and Voce model, respectively. It was also observed that the volume fraction of the cavities exponentially increases with equivalent plastic strain and it depends on the strain path history.


Superplasticity Constitutive model AA5083 Nakazima test Cavitation Thickness variation 


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The authors would like to thank the NRC-ATC personnel for their valuable support.


The authors received financial support by the Natural Sciences and Engineering Research Council of Canada (NSERC), Innovation en Énergie Électrique (INOVÉE), and the Aluminium Association of Canada (AAC).


  1. 1.
    Hefti LD (2007) Commercial airplane applications of superplastically formed AA5083 aluminum sheet. J Mater Eng Perform 16:136–141CrossRefGoogle Scholar
  2. 2.
    Tang JS, Fuh YK, Lee S (2015) Superplastic forming process applied to aero-industrial strakelet: wrinkling, thickness, and microstructure analysis. Int J Adv Manuf Technol 77:1513–1523CrossRefGoogle Scholar
  3. 3.
    Friedman PA, Luckey SG (2004) On the expanded usage of superplastic forming of aluminium sheet for automotive applications. Mater Sci Forum 447:199–204CrossRefGoogle Scholar
  4. 4.
    Nieh TG, Wadsworth J, Sherby OD (2005) Superplasticity in metals and ceramics. Cambridge University Press, CambridgeGoogle Scholar
  5. 5.
    Chentouf SM, Belhadj T, Bombardier N, Brodusch N, Gauvin R, Jahazi M (2017) Influence of predeformation on microstructure evolution of superplastically formed Al 5083 alloy. Int J Adv Manuf Technol 88(9–12):2929–2937CrossRefGoogle Scholar
  6. 6.
    Dashwood R, Klaumunzer D, Jackson M, Fan ZY, Grimes R (2010) The development of superplastic magnesium alloy sheet. Key Eng Mater 433:273–279CrossRefGoogle Scholar
  7. 7.
    Kawasaki M, Figueiredo RB, Xu C, Langdon TG (2007) Developing superplastic ductilities in ultrafine-grained metals. Metall Mater Trans A 38:1891–1898CrossRefGoogle Scholar
  8. 8.
    Liu J, Zhang K (2015) Resistance heating superplastic forming and influence of current on deformation mechanism of TA15 titanium alloy. Int J Adv Manuf Technol 76:1673–1680CrossRefGoogle Scholar
  9. 9.
    Mis M, Hall R, Spence J, Emekwuru N, Kibble K, Stanford M, Banakhr F (2017) Construction of next-generation superplastic forming using additive manufacturing and numerical techniques. Proc Proc ImechE B J Eng Manuf 233:154–165. CrossRefGoogle Scholar
  10. 10.
    Krajewski PE, Morales AT (2004) Tribological issues during quick plastic forming. J Mater Eng Perform 13(6):700–709CrossRefGoogle Scholar
  11. 11.
    Farrell M, Drabek M, Qarni MJ (2017) A method for the systematic assessment of lubricant performance during superplastic sheet forming. Mater Werkst 48:976–982CrossRefGoogle Scholar
  12. 12.
    Krajewski PE, Schroth JG (2007) Overview of quick plastic forming technology. Mater Sci Forum 551:3–12CrossRefGoogle Scholar
  13. 13.
    Rashid MS, Kim C, Ryntz EF, Saunders FI, Verma R, Kim S (2001) Quick plastic forming of aluminum alloy sheet metal. US Patent No 6,253,588Google Scholar
  14. 14.
    Hales SJ, McNelley TR (1988) Microstructural evolution by continuous recrystallization in a superplastic Al-Mg alloy. Acta Metall 36(5):1229–1239CrossRefGoogle Scholar
  15. 15.
    McNelley TR, Oh-Ishi K, Zhilyaev AP, Swaminathan S, Krajewski PE, Taleff EM (2008) Characteristics of the transition from grain-boundary sliding to solute drag creep in superplastic AA5083. Metall Mater Trans A 39(1):50–64CrossRefGoogle Scholar
  16. 16.
    Soer WA, Chezan AR, De Hosson JTM (2006) Deformation and reconstruction mechanisms in coarse-grained superplastic Al–Mg alloys. Acta Mater 54(14):3827–3833CrossRefGoogle Scholar
  17. 17.
    Majidi O, Jahazi M, Bombardier N, Samuel E (2017) Variation of strain rate sensitivity index of a superplastic aluminum alloy in different testing methods. AIP Conf Proc 1896:020022–020027CrossRefGoogle Scholar
  18. 18.
    Khraisheh MK, Zbib HM, Hamilton CH, Bayoumi AE (1997) Constitutive modeling of superplastic deformation. Part I: theory and experiments. Int J Plast 13:143–164CrossRefzbMATHGoogle Scholar
  19. 19.
    Tanaka E, Murakami S, Ishikawa H (1997) Constitutive modeling of superplasticity taking account of grain and cavity growth. Trans Japan Soc Mech Eng Series A 63(609):962–967CrossRefGoogle Scholar
  20. 20.
    Abu-Farha FK, Khraisheh MK (2004) Constitutive modeling of deformation-induced anisotropy in superplastic materials. Mater Sci Forum 447:165–170CrossRefGoogle Scholar
  21. 21.
    Taleff EM, Hector LG, Verma R, Krajewski PE, Chang JK (2010) Material models for simulation of superplastic Mg alloy sheet forming. J Mater Eng Perform 19:488–494CrossRefGoogle Scholar
  22. 22.
    Lin J, Liu Y (2003) A set of unified constitutive equations for modelling microstructure evolution in hot deformation. J Mater Process Technol 143:281–285CrossRefGoogle Scholar
  23. 23.
    Majidi O, Jahazi M, Bombardier N (2018) A Viscoplastic model based on a variable strain rate sensitivity index for superplastic sheet metals. Int J Mater Form.
  24. 24.
    Nakazima K, Kikuma T, Hasuka K (1968) Study on the formability of steel sheets. Yawata Tech Rep 264:8517–8530Google Scholar
  25. 25.
    Salvo L, Cloetens P, Maire E, Zabler S, Blandin JJ, Buffière JY, Josserond C (2003) X-ray micro-tomography an attractive characterisation technique in materials science. Nucl Instrum Methods Phys Res Sect B 200:273–286CrossRefGoogle Scholar
  26. 26.
    Majidi O, Jahazi M, Bombardier N (2018) Characterization of mechanical properties and formability of a superplastic Al-Mg alloy. J Phys Conf Ser 1063:012165CrossRefGoogle Scholar
  27. 27.
    Voce E (1955) A practical strain-hardening function. Metallurgia 51(307):219–226Google Scholar
  28. 28.
    Zhang L, Min J, Carsley JE, Stoughton TB, Lin J (2017) Experimental and theoretical investigation on the role of friction in Nakazima testing. Int J Mech Sci 133:217–226CrossRefGoogle Scholar
  29. 29.
    Bae DH, Ghosh AK, Bradley JR (2003) Stress-state dependence of cavitation and flow behavior in superplastic aluminum alloys. Metall Mater Trans A 34(11):2449–2463CrossRefGoogle Scholar
  30. 30.
    Iwasaki H, Mori T, Tagata T, Matsuo M, Higashi K (1996) Cavitation in superplastic Al-Mg alloy. Mater Sci Forum 233-234:81–88. CrossRefGoogle Scholar
  31. 31.
    Campbell J (2011) Cavitation during superplastic forming. Materials 4(7):1271–1286CrossRefGoogle Scholar

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© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringÉcole de technologie supérieure (ÉTS)MontrealCanada
  2. 2.Department of Mechanical EngineeringMcGill UniversityMontrealCanada
  3. 3.Verbom Inc.ValcourtCanada

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