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Effect of the Anisotropic Yield Condition on the Predicted Distribution of Residual Stresses in a Thin Disk

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Abstract

The effect of the replacement of the exact yield condition by that averaged over the distribution of residual stresses in a thin hollow disk subjected to external pressure and subsequent unloading is investigated. The formulation of the boundary-value problem is specially simplified so that it is possible to obtain a mathematically exact semi-analytical solution, with the help of which it is easy to investigate the effect of averaging the yield condition on the stressed state including the distribution of residual stresses. The accepted exact yield condition is averaged using several generally accepted approaches. The comparative analysis of the distribution of residual stresses shows a significant deviation of the distribution resulting from solutions for the averaged yield conditions from the exact distribution of residual stresses.

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REFERENCES

  1. P. G. Miklyaev and Ya. B. Fridman, Anisotropy of Mechanical Properties of Metals (Metallurgiya, Moscow, 1986) [in Russian].

  2. R. Hill, The Mathematical Theory of Plasticity (Oxford University Press, New York, 1950).

    MATH  Google Scholar 

  3. W. T. Lankford, S. C. Snyder, and J. A. Bausher, Trans. Amer. Soc. Metals 42, 1197 (1950).

    Google Scholar 

  4. D. Banabic, Sheet Metal Forming Processes: Constitutive Modeling and Numerical Simulation (Springer, Heidelberg, 2010).

    Book  Google Scholar 

  5. V. V. Shevelev and S. P. Yakovlev, Anisotropy of Sheet Materials and Its Effect on the Hood (Mashinostroenie, Moscow, 1972) [in Russian].

  6. F. V. Grechnikov, Deformation of Anisotropic Materials (Reserves of Intensification) (Mashinostroenie, Moscow, 1998) [in Russian].

  7. P. H. Lequeu and J. J. Jonas, Metall. Trans. A 19 (1), 105 (1988).

    Article  Google Scholar 

  8. X. Wang, M. Guo, L. Cao, X. Peng, J. Zhang, and L. Zhuang, J. Wuhan Univ. Technol., Materials Sci. Edition 31 (3), 648 (2016).

    Google Scholar 

  9. H. Inoue and T. Takasugi, Materials Trans. 48 (8), 2014 (2007).

    Article  Google Scholar 

  10. V. N. Serebryany and N. N. Pozdnyakova, Russ. Metall., No. 1, 58 (2009).

    Article  ADS  Google Scholar 

  11. F. V. Grechnikov, Ya. A. Erisov, and V. M. Zaitsev, Izv. Samar. Nauch. Tsentra RAN 16 (4‒1), 154 (2014).

  12. R. H. Wagoner and M. Li, Int. J. Plast. 23, 345 (2007).

    Article  Google Scholar 

  13. M. B. Prime, Int. J. Solids and Struct. 118/119, 1339 (2017).

    Article  Google Scholar 

  14. S. Alexandrov, Elastic/Plastic Discs Under Plane Stress Conditions (Springer, Heidelberg, 2015).

    Book  MATH  Google Scholar 

  15. M. Watson, R. Dick, Y. H. Huang, A. Lockley, R. Cardoso, and A. Santos, J. Phys.: Conf. Ser. 734 (2), 022001 (2016).

    Google Scholar 

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Authors and Affiliations

  1. Samara Research Center, Russian Academy of Sciences, 443001, Samara, Russia

    F. V. Grechnikov

  2. Samara National Research University, 443086, Samara, Russia

    Ya. A. Erisov

  3. Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, 117526, Moscow, Russia

    S. E. Alexandrov

Authors
  1. F. V. Grechnikov
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  2. Ya. A. Erisov
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  3. S. E. Alexandrov
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Correspondence to Ya. A. Erisov.

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Translated by V. Bukhanov

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Grechnikov, F.V., Erisov, Y.A. & Alexandrov, S.E. Effect of the Anisotropic Yield Condition on the Predicted Distribution of Residual Stresses in a Thin Disk. Dokl. Phys. 64, 233–237 (2019). https://doi.org/10.1134/S1028335819050100

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  • DOI: https://doi.org/10.1134/S1028335819050100

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