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A quadratic yield function with multi-involved-yield surfaces describing anisotropic behaviors of sheet metals under tension/compression

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Abstract

A quadratic yield function which can describe the anisotropic behaviors of sheet metals with tension/compression symmetry and asymmetry is proposed. Five mechanical properties are adopted to determine the coefficients of each part of the yield function. For particular cases, the proposed yield function can be simplified to Mises or Hill’s quadratic yield function. The anisotropic mechanical properties are expressed by defining an angle between the current normalized principal stress space and the reference direction with the assumption of orthotropic anisotropy. The accuracy of the proposed yield function in describing the anisotropy under tension and compression is demonstrated.

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References

  1. M. Zhan, K. Guo, H. Yang, Advances and trends in plastic forming technologies for welded tubes, Chin. J. Aeronaut. 29 (2) (2016) 305–315.

    Article  Google Scholar 

  2. B. Meng, M. Wan, X. Wu, et al., Inner wrinkling control in hydrodynamic deep drawing of an irregular surface part using drawbeads, Chin. J. Aeronaut. 27 (3) (2014) 697–707.

    Article  Google Scholar 

  3. X. Li, N. Son, G. Guo, et al., Prediction of forming limit curve (FLC) for Al–Li alloy 2198-T3 sheet using different yield functions, Chin. J. Aeronaut. 26 (5) (2013) 1317–1323.

    Article  Google Scholar 

  4. R. Hill, A theory of the yielding and plastic flow of anisotropic metals, Proc. R. Soc. Lond A 193 (1948) 281–297.

    Article  MathSciNet  Google Scholar 

  5. T. Park, K. Chung, Non-associated flow rule with symmetric stiffness modulus for isotropic-kinematic hardening and its application for earing in circular cup drawing, Int. J. Solids Struct. 49 (2012) 3582–3593.

    Article  Google Scholar 

  6. H. Wang, M. Wan, Y. Yan, X. Wu, Effect of the solving method of parameters on the description ability of the yield criterion about the anisotropic behavior, J. Mech. Eng. 49 (2013) 45–53.

    Article  Google Scholar 

  7. R. Hill, Theoretical plasticity of textured aggregates, Math. Proc. Camb. Phil. Soc. 85 (1979) 179–191.

    Article  MathSciNet  Google Scholar 

  8. R. Hill, Constitutive modelling of orthotropic plasticity in sheet metals, J. Mech. Phys. Solids 38 (1990) 405–417.

    Article  MathSciNet  Google Scholar 

  9. R. Hill, A user-friendly theory of orthotropic plasticity in sheet metals, Int. J. Mech. Sci. 35 (1993) 19–25.

    Article  Google Scholar 

  10. F. Barlat, J. Lia, Plastic behavior and stretchability of sheet metals. 1. A yield function for orthotropic sheets under plane-stress conditions, Int. J. Plast. 5 (1989) 5166.

    Article  Google Scholar 

  11. F. Barlat, D.J. Lege, J.C. Brem, A six-component yield function for anisotropic materials, Int. J. Plast. 7 (1991) 693–712.

    Article  Google Scholar 

  12. F. Barlat, R.C. Becker, Y. Hayashida, Y. Maeda, M. Yanagawa, K. Chung, J.C. Brem, D.J. Lege, K. Matsui, S.J. Murtha, S. Hattori, Yielding description of solution strengthened aluminum alloys, Int. J. Plast. 13 (1997) 385–401.

    Article  Google Scholar 

  13. F. Barlat, Y. Maeda, K. Chung, M. Yanagawa, J.C. Brem, Y. Hayashida, D.J. Lege, K. Matsui, S.J. Murtha, S. Hattori, R.C. Becker, S. Makosey, Yield function development for aluminum alloy sheets, J. Mech. Phys. Solids 45 (11–12) (1997) 1727–1763.

    Article  Google Scholar 

  14. D. Banabic, Sheet Metal Forming Processes Constitutive Modeling and Numerical Simulation, Springer-verlag, Berlin Heidelberg, Dordrecht London New York, 2010.

    Book  Google Scholar 

  15. F. Barlat, J.C. Brem, J.W. Yoon, K. Chung, R.E. Dick, D.J. Lege, F. Pourboghrat, S.-H. Choi, E. Chu, Plane stress yield function for aluminum alloy sheets—Part 1: theory, Int. J. Plast. 19 (2003) 1297–1319.

    Article  Google Scholar 

  16. H. Wang, M. Wan, Forming limit of sheet metals based on mixed hardening model, Sci. China Ser. E Technolog. Sci. 52 (5) (2009) 1202–1211.

    Article  Google Scholar 

  17. H. Wang, Y. Ya, M. Wan, X. Wu, Experimental investigation and constitutive modeling for the hardening behavior of 5754O aluminum alloy sheet under two-stage loading, Int. J. Solids Struct. 49 (26) (2012) 3693–3710.

    Article  Google Scholar 

  18. H. Wang, M. Wan, X. Wu, Y. Yan, The equivalent plastic strain-dependent Yld2000-2d yield function and the experimental verification, Comput. Mater. Sci. 47 (1) (2009) 12–22.

    Article  Google Scholar 

  19. H. Wang, M. Wa, Y. Yan, Effect of the flow stress–strain relation on the forming limit of 5754O aluminum alloy, Trans. Nonferrous Metals Soc. China 22 (10) (2012) 2370–2378.

    Article  Google Scholar 

  20. F. Barlat, H. Aretz, J.W. Yoon, M.E. Karabin, J.C. Brem, R.E. Dick, Linear transformation based anisotropic yield function, Int. J. Plast. 21 (2005) 1009–1039.

    Article  Google Scholar 

  21. J.W. Yoon, F. Barlat, R.E. Dick, M.E. Karabin, Prediction of six or eight ears in a drawn cup based on a new anisotropic yield function, Int. J. Plast. 22 (2006) 174–193.

    Article  Google Scholar 

  22. F. Kabirian, A.S. Khan, Anisotropic yield criteria in σ-τ stress space for materials with yield asymmetry, Int. J. Solids Struct. 67–68 (2015) 116–126.

    Article  Google Scholar 

  23. Y. Koh, D. Kim, D.Y. Seoka, J. Bak, S.W. Kim, Y.S. Lee, K. Chung, Characterization of mechanical property of magnesium AZ31 alloy sheets for warm temperature forming, Int. J. Mech. Sci. 93 (2015) 204–217.

    Article  Google Scholar 

  24. N. Chandola, R.A. Lebensohn, O. Cazacu, Combined effects of anisotropy and tension–compression asymmetry on the torsional response of AZ31 Mg, Int. J. Solids Struct. 58 (2015) 190–200.

    Article  Google Scholar 

  25. G. Tari, M.J. Worswick, Elevated temperature constitutive behavior and simulation of warmforming of AZ31BD, J. Mater. Process. Technol. 221 (2015) 40–55.

    Article  Google Scholar 

  26. D.G. Taria, M.J. Worswicka, U. Alia, M.A. Gharghourib, Mechanical response of AZ31B magnesium alloy: experimental characterization and material modeling considering proportional loading at room temperature, Int. J. Plast. 55 (2014) 247–267.

    Article  Google Scholar 

  27. W. Muhammad, M. Mohammadi, J. Kang, R.K. Mishra, K. Inal, An elasto-plastic constitutive model for evolving asymmetric/anisotropic hardening behavior of AZ31B and ZEK100 magnesium alloy sheets considering monotonic and reverse loading paths, Int. J. Plast. 70 (2015) 30–59.

    Article  Google Scholar 

  28. A.S. Khan, S. Yu, Deformation induced anisotropic responses of Ti-6Al-4V alloy. Part I: experiments, Int. J. Plast. 38 (2012) 1–13.

    Article  Google Scholar 

  29. A.S. Khan, E. Pandey, T. Gnaupel-Herold, R.K. Mishra, Mechanical response and texture evolution of AZ31 alloy at large strains for different strain rates and temperatures, Int. J. Plast. 27 (2011) 688–706.

    Article  Google Scholar 

  30. C. Liu, Y. Huang, M.G. Stout, On the asymmetric yield surface of plastically orthotropic materials: a phenomenological study, Acta Mater. 45 (1997) 2397–2406.

    Article  Google Scholar 

  31. O. Cazacu, F. Barlat, A criterion for description of anisotropy and yield differential effects in pressure-insensitive metals, Int. J. Plast. 20 (2004) 2027–2045.

    Article  Google Scholar 

  32. O. Cazacu, B. Plunkett, F. Barlat, Orthotropic yield criterion for hexagonal close packed metals, Int. J. Plast. 22 (2006) 1171–1194.

    Article  Google Scholar 

  33. B. Plunkett, O. Cazacu, F. Barlat, Orthotropic yield criterion for description of anisotropy in tension and compression of sheet metals, Int. J. Plast. 24 (2008) 847–866.

    Article  Google Scholar 

  34. A.S. Khan, S. Yu, H. Liu, Deformation induced anisotropic responses of Ti–6Al–4V alloy. Part II: a strain rate and temperature dependent anisotropic yield function, Int. J. Plast. 38 (2012) 14–26.

    Article  Google Scholar 

  35. J.W. Yoon, Y. Lou, J. Yoon, M.V. Glazoff, Asymmetric yield function based on the stress invariants for pressure sensitive metals, Int. J. Plast. 56 (2014) 184–202.

    Article  Google Scholar 

  36. H. Wu, Anisotropic plasticity for sheet metals using the concept of combined isotropic-kinematic hardening, Int. J. Plast. 18 (2002) 1661–1682.

    Article  Google Scholar 

  37. H. Wu, H. Hong, Y. Shiao, Anisotropic plasticity with application to sheet metals, Int. J. Mech. Sci. 41 (1999) 703–724.

    Article  Google Scholar 

  38. C. Sansour, I. Karsaj, J. Soric, A formulation of anisotropic continuum elastoplasticity at finite strains. Part I: modelling, Int. J. Plast. 22 (2006) 2346–2365.

    Article  Google Scholar 

  39. R.K. Verma, T. Kuwabara, K. Chung, A. Haldar, Experimental evaluation and constitutive modeling of non-proportional deformation for asymmetric steels, Int. J. Plast. 27 (2011) 82–101.

    Article  Google Scholar 

  40. W. Hu, A novel quadratic yield model to describe the feature of multi-yield-surface of rolled sheet metals, Int. J. Plast. 23 (2007) 2004–2028.

    Article  Google Scholar 

  41. H. Vegter, A.H. Boogaard, A plane stress yield function for anisotropic sheet material by interpolation of biaxial stress states, Int. J. Plast. 22 (2006) 557–580.

    Article  Google Scholar 

  42. A.S. Khan, S. Huang, Continuum Theory of Plasticity, Wiley, 1995.

  43. H. Aretz, A non-quadratic plane stress yield function for orthotropic sheet metals, J. Mater. Process. Technol. 168 (2005) 1–9.

    Article  Google Scholar 

  44. F. Yoshida, H. Hamasaki, T. Uemori, A user-friendly 3D yield function to describe anisotropy of steel sheets, Int. J. Plast. 45 (2013) 119–139.

    Article  Google Scholar 

  45. T. Kuwabara, S. Ikeda, T. Kuroda, Measurement and analysis of differential work-hardening in cold-rolled steel sheet under biaxial tension, J. Mater. Process Technol. 80–81 (1998) 517–523.

    Article  Google Scholar 

  46. T. Kuwabara, Advances in experiments on metal sheets and tubes in support of constitutive modeling and forming simulations, Int. J. Plast. 23 (2007) 385–419.

    Article  Google Scholar 

  47. T. Kuwabara, F. Sugawara, Multiaxial tube expansion test method for measurement of sheet metal deformation behavior under biaxial tension for a large strain range, Int. J. Plast. 45 (2013) 103–118.

    Article  Google Scholar 

  48. X. Wu, Investigation of the Plastic Deformation Behavior of Anisotropic Sheet Metals Under Different Loading Paths, Doctoral Dissertation, Beihang University, Beijing, China, 2004.

    Google Scholar 

  49. X.Y. Lou, M. Li, R.K. Boger, S.R. Agnew, R.H. Wagoner, Hardening evolution of AZ31B Mg sheet, Int. J. Plast. 23 (2007) 44–86.

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Mechanical and Materials Engineering, North China University of Technology, Beijing, 100144, China

    Haibo Wang, Yu Yan, Zhengyang Chen, Qiang Li & Dong He

  2. School of Mechanical Engineering and Automation, Beihang University, Beijing, 100191, China

    Min Wan

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  1. Haibo Wang
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  2. Yu Yan
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  3. Min Wan
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  5. Qiang Li
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Correspondence to Haibo Wang.

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Wang, H., Yan, Y., Wan, M. et al. A quadratic yield function with multi-involved-yield surfaces describing anisotropic behaviors of sheet metals under tension/compression. Acta Mech. Solida Sin. 30, 618–629 (2017). https://doi.org/10.1016/j.camss.2017.10.004

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  • DOI: https://doi.org/10.1016/j.camss.2017.10.004

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