Irreversible deformation of a rotating disc under plasticity and creep

A.S. Begun a,b∗ , L.V. Kovtanyuk a∗∗

a Institute of Automation and Control Processes Far Eastern Branch, Russian Academy of Sciences, Vladivostok, 690041 Russia

b Vladivostok State University of Economics and Service, Vladivostok, 690014 Russia

E-mail: ∗asustinova@mail.ru, ∗∗lk@iacp.dvo.ru

Received January 18, 2021

 

ORIGINAL ARTICLE

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DOI: 10.26907/2541-7746.2021.2.167-180

For citation: Begun A.S., Kovtanyuk L.V. Irreversible deformation of a rotating disc under plasticity and creep. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2021, vol. 163, no. 2, pp. 167–180. doi: 10.26907/2541-7746.2021.2.167-180. (In Russian)

 

Abstract

This paper is devoted to the study of deformation of a disk rotating with variable velocity (acceleration, deceleration, rotation at a constant rate) under consecutive accumulation of irreversible creep and plastic flow strains. The deformation processes of a hollow disk and a disk with an inclusion are studied. Under the assumption of a plane stress state within the framework of the flow theory, solutions of differential equations are obtained for calculating the fields of stresses, deformations, displacements, and velocities using finite difference schemes. In the case of an axisymmetric problem, the solution is obtained using the finite element method. The laws of viscoplastic flow area development are investigated. In a sufficiently thick disk, the radius of the elastoplastic boundary changes significantly along the thickness of the disk. The obtained solution is compared with the case of ideal elastoplasticity. Taking into account the viscosity leads to a deceleration of the flow. It is shown that the presence of angular acceleration during fast overclocking significantly affects the distribution of stress intensities.

Keywords: elasticity, creep, rotating disk, viscoplastic flow

References

  1. Dem’yanushko I.V., Briger I.A. Raschet na prochnost’ vrashchayushchikhsya diskov [Strength Analysis of Rotating Disks]. Moscow, Mashinostroenie, 1978. 247 p. (In Russian)
  2. Levin A.V. Rabochie lopatki i diski parovykh turbin [Moving Blades and Disks of Steam Turbines]. Moscow, Gosenergoizdat, 1963. 624 p. (In Russian)
  3. Aleksandrova N. Application of Mises yield criterion to rotating solid disk problem. Int. J. Eng. Sci., 2012, vol. 51, pp. 333–337. doi: 10.1016/j.ijengsci.2011.10.006.
  4. Bayat M., Sahari B.B., Saleem M., Ali A., Wong S.V. Bending analysis of a functionally graded rotating disk based on the first order shear deformation theory. Appl. Math. Modell., 2009, vol. 33, no. 11, pp. 4215–4230. doi: 10.1016/j.apm.2009.03.001.
  5. Dai T., Dai H.-L. Thermo-elastic analysis of a functionally graded rotating hollow circular disk with variable thickness and angular speed. Appl. Math. Modell., 2016, vol. 40, nos. 17– 18, pp. 7689–7707. doi: 10.1016/j.apm.2016.03.025.
  6. Gamer U. Elastic-plastic deformation of the rotating solid disk. Ing.-Arch., 1984, vol. 54, pp. 345–354. doi: 10.1007/BF00532817.
  7. Gupta V.K., Chandrawat H.N., Singh S.B., Ray S. Creep behavior of a rotating functionally graded composite disc operating under thermal gradient. Metall. Mater. Trans. A, 2004, vol. 35, no. 4, pp. 1381–1391. doi: 10.1007/s11661-004-0313-3.
  8. Gupta S.K., Sonia T.P. Creep transition in a thin rotating disc of variable density. Def. Sci. J., 2000, vol. 50, no. 2, pp. 147–153.
  9. Nyashin Y., Shishlyaev V. Analytic creep durability of rotating uniform disks. Int. J. Rotating Mach., 1998, vol. 4, no. 4, pp. 249–256. doi: 10.1155/S1023621X98000219.
  10. Rees D.W.A. Elastic-plastic stresses in rotating discs by von Mises and Tresca. ZAMM – J. Appl. Math. Mech., 1999, vol. 79, no. 4, pp. 281–288. doi: 10.1002/(SICI)1521-4001(199904)79:4¡281::AID-ZAMM281¿3.0.CO;2-V.
  11. Wahl A.M. A comparison of flow criteria applied to elevated temperature creep of rotating disks with consideration of the transient condition. Creep in Structures. Proc. IUTAM Symp. (International Union of Theoretical and Applied Mechanics). Hoff N.J. (Ed.). Berlin, Heidelberg, Springer, 1962, pp. 195–214. doi: 10.1007/978-3-642-86014-0 11.
  12. Zheng Y., Bahaloo H., Mousanezhad D., Vaziri A., Nayeb-Hashemi H. Displacement and stress fields in a functionally graded fiber-reinforced rotating disk with nonuniform thickness and variable angular velocity. J. Eng. Mater. Technol., 2017, vol. 139, no. 3, art. 031010, pp. 1–10. doi: 10.1115/1.4036242.
  13. Begun A.S., Kovtanyuk L.V. Calculation of stresses, strains, and displacements in a rotating disk under creep conditions. Vestn. Chuv. Gos. Pedagog. Univ. im. I.Ya. Yakovleva. Ser. Mekh. Predel’nogo Sostoyaniya, 2019, no. 1, pp. 84–93. (In Russian)
  14. Begun A.S., Kovtanyuk L.V. Deformation of a viscoelastic disk rotating with acceleration. Vestn. Chuv. Gos. Pedagog. Univ. im. I.Ya. Yakovleva. Ser. Mekh. Predel’nogo Sostoyaniya, 2020, no. 3, pp. 143–151. (In Russian)

 

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