Modeling material behavior of AA5083 aluminum alloy sheet using biaxial tensile tests and its application in numerical simulation of deep drawing

  • Ved PrakashEmail author
  • D. Ravi Kumar
  • Alexander Horn
  • Hinnerk Hagenah
  • Marion Merklein


Improvement in accuracy of the predicted results from numerical simulation results into a reduction of cost and time involved in tool design and experimental trials. However, the predicted results from finite element simulations are significantly affected by the chosen yield criterion and work hardening law. The selection of yield criterion and work hardening law depends on the characterization methods used for defining the material behavior. In this work, the mechanical behavior of AA5083-O aluminum alloy sheet is modeled by performing biaxial tensile tests using cruciform specimen and hydraulic bulging experiments in addition to uniaxial tensile tests. Biaxial to uniaxial yield stress ratios are determined using the equal plastic work principle from the flow curves obtained from these tests. The obtained ratios are used to find the coefficients of Yld2000-2d and Hill48 yield criteria which is then used in the numerical simulations of cylindrical cup deep drawing. Numerical simulations are also carried out using uniaxial and biaxial flow curves fitted with different isotropic hardening laws. Thickness distributions and the load-displacement curves are predicted and validated by performing cylindrical cup deep drawing experiments.


Deep drawing Aluminum alloy Hydraulic bulge test Cruciform specimen Hardening laws Yield criteria Finite element simulation 



The authors would like to acknowledge the support received from UGC-DAAD project (F. No. 1-3/2016 (IC)) for the research carried out in this article. Ved Prakash would like to acknowledge the assistantship received from the Ministry of Human Resource Development (MHRD), Government of India for this research work.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. 1.
    Merklein M, Biasutti M (2013) Development of a biaxial tensile machine for characterization of sheet metals. J Mater Process Technol 213:939–946. CrossRefGoogle Scholar
  2. 2.
    Banabic D, Barlat F, Cazacu O, Kuwabara T (2010) Advances in anisotropy and formability. Int J Mater Form 3:165–189. CrossRefGoogle Scholar
  3. 3.
    Bruschi S, Altan T, Banabic D et al (2014) CIRP annals—manufacturing technology testing and modelling of material behaviour and formability in sheet metal forming. CIRP Ann Manuf Technol 63:727–749. CrossRefGoogle Scholar
  4. 4.
    Barlat F, Brem JC, Yoon JW et al (2003) Plane stress yield function for aluminum alloy sheets—part 1: theory. Int J Plast 19:1297–1319. CrossRefzbMATHGoogle Scholar
  5. 5.
    Deng Z, Hennig R (2017) Influence of material modeling on simulation accuracy of aluminum stampings. J Phys Conf Ser 896. Google Scholar
  6. 6.
    Banabic D, Hußnätter W (2009) Modeling the material behavior of magnesium alloy AZ31 using different yield criteria. Int J Adv Manuf Technol 44:969–976. CrossRefGoogle Scholar
  7. 7.
    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. CrossRefzbMATHGoogle Scholar
  8. 8.
    Keller S, Hotz HFW (2009) Yield curve determination using the bulge test combined with optical measurement. IDDRG 2009(42):319–330Google Scholar
  9. 9.
    Gutscher G, Wu HC, Ngaile G, Altan T (2004) Determination of flow stress for sheet metal forming using the viscous pressure bulge (VPB) test. J Mater Process Technol 146:1–7. CrossRefGoogle Scholar
  10. 10.
    Hill R (1950) C. A theory of the plastic bulging of a metal diaphragm by lateral pressure. London, Edinburgh, Dublin. Philos Mag J Sci 41:1133–1142. CrossRefzbMATHGoogle Scholar
  11. 11.
    Chakrabarty J, Alexander JM (1970) Hydrostatic bulging of circular diaphragms. J Strain Anal Eng Des 5:155–161. CrossRefGoogle Scholar
  12. 12.
    Shang HM, SHIM VPW (1984) A model study of the effect of the size of the die shoulder in hydroforming. J Mech Work Tech 10:307–323CrossRefGoogle Scholar
  13. 13.
    Atkinson M (1997) Accurate determination of biaxial stress—strain relationships from hydraulic bulging tests of sheet metals. Int J Mech Sci 39:761–769. CrossRefGoogle Scholar
  14. 14.
    Kruglov AA, Enikeev FU, Lutfullin RY (2002) Superplastic forming of a spherical shell out a welded envelope. Mater Sci Eng A. CrossRefGoogle Scholar
  15. 15.
    Gedikli H, Cora ÖN, Koç M (2011) Parametric Investigation of circular and elliptical bulge tests in warm hydroforming process for AA5754-O Sheet. Key Eng Mater 473:594–601. CrossRefGoogle Scholar
  16. 16.
    Alharthi H, Hazra S, Alghamdi A et al (2018) Determination of the yield loci of four sheet materials (AA6111-T4, AC600, DX54D+Z, and H220BD+Z) by using uniaxial tensile and hydraulic bulge tests. Int J Adv Manuf Technol 98:1307–1319. CrossRefGoogle Scholar
  17. 17.
    Mulder J, Vegter H, Aretz H et al (2015) Accurate determination of flow curves using the bulge test with optical measuring systems. J Mater Process Technol. CrossRefGoogle Scholar
  18. 18.
    Min J, Stoughton TB, Carsley JE et al (2017) Accurate characterization of biaxial stress-strain response of sheet metal from bulge testing. Int J Plast. CrossRefGoogle Scholar
  19. 19.
    Suttner S, Merklein M (2016) Experimental and numerical investigation of a strain rate controlled hydraulic bulge test of sheet metal. J Mater Process Technol 235:121–133. CrossRefGoogle Scholar
  20. 20.
    Altan T, Palaniswamy H, Bortot P, et al (2006) Determination of sheet material properties using biaxial bulge tests. 2nd Int Conf Accuracy Form Technol, pp 79–92Google Scholar
  21. 21.
    Yanaga D, Kuwabara T, Uema N, Asano M (2012) Material modeling of 6000 series aluminum alloy sheets with different density cube textures and effect on the accuracy of finite element simulation. Int J Solids Struct 49:3488–3495. CrossRefGoogle Scholar
  22. 22.
    Hill R (1948) A Theory of the yielding and plastic flow of anisotropic metals. Proc R Soc A Math Phys Eng Sci 193:281–297. MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    ISO 16808 (2014) ISO 16808:2014 Metallic materials—sheet and strip—determination of biaxial stress-strain curve by means of bulge test with optical measuring systems. 36Google Scholar
  24. 24.
    Lǎzǎrescu L, Nicodim I, Ciobanu I et al (2013) Determination of material parameters of sheet metals using the hydraulic bulge test. Acta Metall Slovaca 19:4–12. CrossRefGoogle Scholar
  25. 25.
    Sigvant M, Mattiasson 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 2:235–242. CrossRefGoogle Scholar
  26. 26.
    Nasser A, Yadav A, Pathak P, Altan T (2010) Determination of the flow stress of five AHSS sheet materials (DP 600, DP 780, DP 780-CR, DP 780-HY and TRIP 780) using the uniaxial tensile and the biaxial Viscous Pressure Bulge (VPB) tests. J Mater Process Technol 210:429–436. CrossRefGoogle Scholar
  27. 27.
    Swift HW (1952) Plastic instability under plane stress. J Mech Phys Solids 1:1–18. CrossRefGoogle Scholar
  28. 28.
    Hockett JE, Sherby OD (1975) Large strain deformation of polycrystalline metals at low homologous temperatures. J Mech Phys Solids 23:87–98. CrossRefGoogle Scholar
  29. 29.
    Panda SK, Kumar DR (2009) Study of formability of tailor-welded blanks in plane-strain stretch forming. Int J Adv Manuf Technol 44:675–685. CrossRefGoogle Scholar
  30. 30.
    Barlat F, Aretz H, Yoon JW et al (2005) Linear transfomation-based anisotropic yield functions. Int J Plast 21:1009–1039. CrossRefzbMATHGoogle Scholar
  31. 31.
    Lenzen M, Merklein M (2018) Improvement of Numerical modelling considering plane strain material characterization with an elliptic hydraulic bulge test. J Manuf Mater Process 2:6. CrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  • Ved Prakash
    • 1
    Email author
  • D. Ravi Kumar
    • 1
  • Alexander Horn
    • 2
  • Hinnerk Hagenah
    • 2
  • Marion Merklein
    • 2
  1. 1.Department of Mechanical EngineeringIndian Institute of Technology DelhiNew DelhiIndia
  2. 2.Lehrstuhl für FertigungstechnologieFriedrich-Alexander-UniversitätErlangenGermany

Personalised recommendations