Summary
Subject of the investigation is the deformation of a perfectly plastic cylinder with uniform temperature inside its cylindrical core and zero surface temperature. The calculation is based on Tresca's yield condition and the flow rule associated to it. For small radii of the hot core, a plastic region appears at the center expands towards the surface of the cylinder with increasing core temperature. The other possibility is that, depending on the core radius, two plastic regions form one after the other or simultaneously, in the core and at the surface and join in the fully plastic state. The image points of the cylinder lie on different edges and sides of the Tresca-prism in stress space.
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References
Wiedemann, E., Kellenberger, W.: Konstruktion elektrischer Maschinen. Berlin Heidelberg, New York: Springer 1967.
Vogt, K., et al.: Elektrische Maschinen. Berlin: VEB Technik n. d.
Carslaw, H. S., Jaeger, J. C.: Conduction of heat in solids, 2nd ed. London: Oxford 1959.
Burak, Y., Galapats, B. P., Kolodii, B. I.: Elastoplastic equilibrium for an infinite cylinder during induction heating (in Russian). Prikl. Mekh.4, 29–39 (1968).
Perzyna, P., Sawczuk, A.: Problems of thermoplasticity. Nuclear Engineering and Design24, 1–55 (1973).
Skalski, K.: Quasi-stationary state of thermal stresses in a thick walled tube (in Polish). Engineering Transactions22, 601–629 (1975).
Belousov, V. Y.: Residual stresses for a long two-layer cylinder with nonsteady cooling (in Russian). Problemy Prochnosti7, 98–101 (1983).
Gamer, U., Sayir, M.: Elastic-plastic stress distribution in a rotating solid shaft. ZAMP35, 601–617 (1984).
Mack, W.: Rotating elastic-plastic tube with free ends. Int. J. Solids Structures27, 1461–1476 (1991).
Gamer, U.: Elastic-plastic deformation of a centrally heated disk. J. Thermal Stresses8, 41–51 (1985).
Gamer, U.: On the elastic-plastic deformation of a sphere subjected to a spherically symmetrical temperature field. J. Thermal Stresses13, 159–173 (1988).
Orçan, Y.: On the analysis of stress and deformation in elastic-plastic shrink fits and the centrally heated cylinder. Ph. D. Thesis, Middle East Technical University, Ankara 1990.
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Orçan, Y., Gamer, U. Elastic-plastic deformation of a centrally heated cylinder. Acta Mechanica 90, 61–80 (1991). https://doi.org/10.1007/BF01177400
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DOI: https://doi.org/10.1007/BF01177400