Advertisement

International Journal of Material Forming

, Volume 4, Issue 4, pp 357–369 | Cite as

Investigation of anisotropy problems in sheet metal forming using finite element method

  • Tomasz Trzepieciński
  • Hirpa L. GelgeleEmail author
Original Research

Abstract

This paper discusses the results of the numerical study of rectangular cup drawing of steel sheets using finite element methods. To be able to verify the results of the numerical solutions, an experimental study was done where the material behavior under deformation was analyzed. A 3D parametric finite element (FE) model was built using the commercial FE-package ABAQUS/Standard. ABAQUS allows analyzing physical models of real processes putting special emphasis on geometrical non-linearities caused by large deformations, material non-linearities and complex friction conditions. Friction properties of the deep drawing quality steel sheet were determined by using the pin-on-disc tribometer. The results show that the friction coefficient depends on the measured angle from the rolling direction and corresponds to the surface topography. A quadratic Hill anisotropic yield criterion was compared with von Mises yield criterion having isotropic hardening. The sensitivity of constitutive laws to the initial data characterizing material behavior is also presented. It is found out that plastic anisotropy of the matrix in ductile sheet metal has influence on deformation behavior of the material. When the material and friction anisotropy are taken into account in the finite element analysis, this approach gives better approximate numerical results for real processes.

Keywords

Anistropy Finite element analysis Sheet metal drawing Material modeling 

Notes

Acknowledgement

The authors gratefully acknowledge the financial support provided by Island, Liechtenstein and Norway to this project under the Scholarship and Training Fund co-financed by European Economic Area and Norwegian Financial Mechanism.

References

  1. 1.
    Daxin E, Takaji M, Zhiguo L (2005) Stress analysis of rectangular cup drawing. J Mat Proc Technol 205:469–475Google Scholar
  2. 2.
    Daxin E, Yuping P, Takaji M (2004) Analysis of flange corner deformation in the process of fine copper cup drawing sheet rectangular. J Plast Eng 11:39–42Google Scholar
  3. 3.
    Wen T, Daxin E (2004) Application of FEM on the study of material flowing deformation rule in the process of rectangular cup drawing. Mod Manuf Eng 4:40–42Google Scholar
  4. 4.
    Elbitar T, Gemeal A (2008) Finite Element Analysis of Deep drawing and hole flanging processing of an oil filter cover. Int J Mater Form Suppl 1:125–128CrossRefGoogle Scholar
  5. 5.
    Brunet M, Morestin F, Walter-Leberre H (2005) Failure analysis of anisotropic sheet-metals using non-local plastic damage model. J Mat Proc Technol 170:457–470CrossRefGoogle Scholar
  6. 6.
    Khelifa M, Oudjene M (2008) Numerical damage prediction in deep- drawing of sheet metals. J Mat Proc Technol 200:71–76CrossRefGoogle Scholar
  7. 7.
    Garcia C, Celentano D, Flores F, Ponthot J-P, Olivia O (2006) Numerical modeling and experimental validation of steel deep drawing processes part II: applications. J Mat Proc Technol 172:461–471CrossRefGoogle Scholar
  8. 8.
    Duchene L, Habraken AM (2005) Analysis of the sensitivity of FEM predictions to numerical parameters in deep drawing simulations. Eur J Mech A, Solids 24:614–629zbMATHCrossRefGoogle Scholar
  9. 9.
    Saxsena RK, Dixit PM (2009) Finite element simulation of earing defect in deep drawing. Int J Adv Manuf Technol 45:219–233CrossRefGoogle Scholar
  10. 10.
    Zienkiewicz OC, Taylor RL (2000) Finite element method, vol. 1–2. Butterworth-Heinemann, OxfordGoogle Scholar
  11. 11.
    Hu P, Liu YQ, Wang JC (2001) Numerical study of the flange earring of deep-darwing sheets with stronger anisotropy. Int J Mech Sci 43:279–296zbMATHCrossRefGoogle Scholar
  12. 12.
    Gronostajski Z (2000) The constitutive equations for FEM analysis. J Mat Proc Technol 106:40–44CrossRefGoogle Scholar
  13. 13.
    Padmanabhan R, Oliveira MC, Alves JL, Menezes LF (2007) Influence of process parameters on the deep drawing of stainless steel. Finite Elem Anal Des 43:1062–1067CrossRefGoogle Scholar
  14. 14.
    Banabic D, Bunge H-J, Pohlandt K, Tekkaya AE (2000) Formability of Metallic Materials: plastic anisotropy, formability testing, forming limits. Springer-Verlag, Berlin HeidelbergGoogle Scholar
  15. 15.
    Van Houutte P (1992) Anisotropic plasticity. In: Hartley P, Pillingar I, Sturgess C (eds) Numerical modeling of material deformation process: research, development and applications. Springer-Verlag, LondonGoogle Scholar
  16. 16.
    Hill R (1948) A theory of the yielding and plastic flow of anisotropic metals. Proc R Soc Lond Ser A 193:281–297zbMATHCrossRefGoogle Scholar
  17. 17.
    Hill R (1979) Theoretical plasticity of textured aggregates. Math Proc Cambridge Philos Soc 85:179–191MathSciNetzbMATHCrossRefGoogle Scholar
  18. 18.
    Hosford WF (1972) A generalized isotropic yield function. Trans ASME J App Mech E39:607–609CrossRefGoogle Scholar
  19. 19.
    Hill R (1993) A user-friendly theory of orthotropic plasticity in sheet metals. Int J Mech Sci 35:19–25zbMATHCrossRefGoogle Scholar
  20. 20.
    Barlat F, Lian J (1989) Plastic behavior and stretchability of sheet metals. Part I: a yield function for orthotropic sheets under plane stress conditions. Int J Plast 5:51–66CrossRefGoogle Scholar
  21. 21.
    Barlat F, Lege DJ, Brem JC (1991) A six-component yield function for anisotropic materials. Int J Plast 7:693–712CrossRefGoogle Scholar
  22. 22.
    Karafllis AP, Boyce MC (1993) A general anisotropic yield criterion using bounds and a transformation weighting tensor. J Mech Phys Solids 41:1859–1886CrossRefGoogle Scholar
  23. 23.
    Haddag B, Balan T, Abed-Meraim F (2007) Investigation of advanced strain-path dependent material models for sheet metal forming simulations. Int J Plast 23:951–979zbMATHCrossRefGoogle Scholar
  24. 24.
    Bouvier S, Alves JL, Oliveira MC, Menezes LF (2005) Modeling of anisotropic work-hardening behavior of metallic materials subjected to strain-path changes. Comp Mat Sci 32:301–315CrossRefGoogle Scholar
  25. 25.
    Tikhovskiy I, Raabe D, Roters F (2008) Simulation of earing of a 17% Cr stainless steel considering texture gradients. Mat Sci Eng A 488:482–490CrossRefGoogle Scholar
  26. 26.
    De Magalhaes Correia JP, Ferron G, Moreira LP (2003) Analytical and numerical investigation of wrinkling for deep-drawn anisotropic metal sheets. Int J Mech Sci 45:1167–1180zbMATHCrossRefGoogle Scholar
  27. 27.
    Zhiying C, Xianghuai D (2009) The GTN damage model based on Hill’48 anisotropic yield criterion and its application in sheet metal forming. Comp Mat Sci 44:1013–1021CrossRefGoogle Scholar
  28. 28.
    Liu YQ, Wang JC, Hu P (2002) The numerical analysis of anisotropic sheet metals in deep- drawing processes. J Mat Proc Technol 120:45–52CrossRefGoogle Scholar
  29. 29.
    Hjiaj M, Feng Z-Q, de Saxc G, Mróz Z (2004) On the modeling of complex anisotropic frictional contact laws. Int J Eng Sci 42:1013–1034zbMATHCrossRefGoogle Scholar
  30. 30.
    Khan AS, Huang S (1995) Continuum theory of plasticity. Wiley, New YorkzbMATHGoogle Scholar
  31. 31.
    Chakrabarty J (1987) Theory of plasticity. McGraw-Hill Inc., New YorkGoogle Scholar
  32. 32.
    Yi S, Bohlen J, Heinemann F, Letzig D (2010) Mechanical anisotropy and deep drawing behavior of AZ31 and ZE10 magnesium alloy sheets. Acta Mater 58:592–605CrossRefGoogle Scholar
  33. 33.
    von-Mises R (1913) Mechanik der festen Kö¨rper im plastisch deformablen Zustand, Nachr. Ges. Wiss. Göttingen, 582Google Scholar
  34. 34.
    Stachowicz F, Trzepieciński T (2003) Opory tarcia podczas kształtowania blach karoseryjnych. Mat. Konf. SAKON, Przecław, 297–302Google Scholar
  35. 35.
    Zhang X, Long S, Ma Z, Pan Y, Zhou Y (2007) Cup-drawing formation of steel sheet with nickel coating by finite element method. Trans Nonferrous Met Soc China 17:37–40Google Scholar
  36. 36.
    Hibbit Karlsson & Sorensen Inc. (2007) ABAQUS Theory and User’s Manuals, v. 6.7. HKS inc. Dassault Syst`emes, RI, USAGoogle Scholar
  37. 37.
    Habraken AM, Duchêne L (2004) Anisotropic elasto-plastic finite element analysis using a stress-strain interpolation method based on a polycrystalline model. Int J Plast 20:1525–1560zbMATHCrossRefGoogle Scholar
  38. 38.
    Xu WL, Ma CH, Li CH, Feng WJ (2004) Sensitive factors in springback simulation for sheet metal forming. J Mat Proc Technol 151:217–222CrossRefGoogle Scholar
  39. 39.
    Serri J, Martiny M, Ferron G (2005) A numerical analysis of the formability of unstable austenitic steels. J Mat Proc Technol 165:1241–1247CrossRefGoogle Scholar
  40. 40.
    Ragai I, Lazim D, Nemes JA (2005) Anisotropy and springback in draw-bending of stainless steel 410: experimental and numerical study. J Mat Proc Technol 166:116–127CrossRefGoogle Scholar
  41. 41.
    da Rocha AB, Santos AD, Teixeira P, Butuc MC (2009) Analysis of plastic flow localization under strain paths changes and its coupling with finite element simulation in sheet metal forming. J Mat Proc Technol 209:5097–5109CrossRefGoogle Scholar
  42. 42.
    Trzepieciński T, Stachowicz F (2005) Modelowanie numeryczne procesu kształtowania wytłoczek prostokątnych. Rudy Metale 50:582–585Google Scholar
  43. 43.
    Stachowicz F, Spišák E (1999) Sposoby oceny zdolności blach cienkich do kształtowania plastycznego na zimno, Oficyna Wydawn. Politechniki Rzeszowskiej, RzeszówGoogle Scholar

Copyright information

© Springer-Verlag France 2010

Authors and Affiliations

  1. 1.Department of Material Formation and ProcessingRzeszow University of TechnologyRzeszówPoland
  2. 2.Department of Mechanical and Structural Engineering and Materials TechnologyUniversity of StavangerStavangerNorway

Personalised recommendations