The strain hardening rotating hollow shaft subject to a positive temperature gradient.

*(English)*Zbl 1140.74473Summary: Based on Tresca’s yield criterion and the flow rule associated with it, the distribution of stress, strain and displacement in a linearly strain hardening elastic-plastic hollow shaft subject to a positive radial temperature gradient and monotonously increasing angular speed is investigated. Presupposing circular symmetry and plane strain conditions, the problem is accessible to an analytical treatment. It is found that - depending on the temperature difference between the outer and the inner surface - qualitatively different types of solutions may occur, and that such a temperature difference on the one hand reduces the elastic limit angular speed but on the other hand may increase the fully plastic angular speed slightly. The residual stresses after stand-still and subsequent cooling are depicted, too.

##### MSC:

74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |

74F05 | Thermal effects in solid mechanics |

74C05 | Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials) |

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\textit{A. N. Eraslan} et al., Acta Mech. 194, No. 1--4, 191--211 (2007; Zbl 1140.74473)

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##### References:

[1] | Peterson G. P. and Wu D. (1993). A review of rotating and revolving heat pipes. Heat Technol. 11: 191–228 |

[2] | Gamer U. and Lance R. H. (1983). Stress distribution in a rotating elastic-plastic tube. Acta Mech. 50: 1–8 · Zbl 0525.73044 |

[3] | Mack W. (1991). Rotating elastic-plastic tube with free ends. Int. J. Solids Struct. 27: 1461–1476 · Zbl 0825.73353 |

[4] | Mack W. (1992). Entlastung und sekundäres Fließen in rotierenden elastisch-plastischen Hohlzylindern. ZAMM 72: 65–68 · Zbl 0825.73200 |

[5] | Eraslan A. N. (2004). Von Mises’ yield criterion and nonlinearly hardening rotating shafts. Acta Mech. 168: 129–144 · Zbl 1063.74016 |

[6] | Eraslan A. N. and Mack W. (2005). A computational procedure for estimating residual stresses and secondary plastic flow limits in nonlinearly strain hardening rotating shafts. Forschung im Ingenieurwesen 69: 65–75 |

[7] | Akis T. and Eraslan A. N. (2006). The stress response and onset of yield of rotating FGM hollow shafts. Acta Mech. 187: 169–187 · Zbl 1103.74016 |

[8] | Eraslan A. N. and Akis N. (2006). The stress response of partially plastic rotating FGM hollow shafts: analytical treatment for axially constrained ends. Mech. Based Des. Struct. Mach. 34: 241–260 · Zbl 1103.74016 |

[9] | Bree J. (1989). Plastic deformation of a closed tube due to interaction of pressure stresses and cyclic thermal stresses. Int. J. Mech. Sci. 31: 865–892 |

[10] | Jahanian S. and Sabbaghian M. (1990). Thermoelastoplastic and residual stresses in a hollow cylinder with temperature-dependent properties. J. Press. Vessel Techn. 112: 85–91 |

[11] | Wong H. and Simionescu O. (1996). An analytical solution of thermoplastic thick-walled tube subject to internal heating and variable pressure, taking into account corner flow and nonzero initial stress. Int. J. Engng. Sci. 34: 1259–1269 · Zbl 0901.73027 |

[12] | Orcan Y. and Eraslan A. N. (2001). Thermal stresses in elastic-plastic tubes with temperature-dependent mechanical and thermal properties. J. Thermal Stresses 24: 1097–1113 |

[13] | Eraslan A. N. and Argeso H. (2005). Computer solutions of plane strain axisymmetric thermomechanical problems. Turkish J. Engng. Environ. Sci. 29: 369–381 |

[14] | Chen W. F. and Han D. J. (1988). Plasticity for structural engineers. Springer, New York · Zbl 0666.73010 |

[15] | Carslaw H. S. and Jaeger J. C. (1959). Conduction of heat in solids, 2nd ed. Clarendon Press, Oxford · Zbl 0029.37801 |

[16] | Eraslan A. N. (2003). On the linearly hardening rotating solid shaft. Eur. J. Mech. A/Solids 22: 295–307 · Zbl 1038.74556 |

[17] | Gamer U., Mack W. and Varga I. (1997). Rotating elastic-plastic solid shaft with fixed ends. Int. J. Engng. Sci. 35: 253–267 · Zbl 0902.73050 |

[18] | Garbow B. S., Hillstrom K. E. and More J. J. (1981). Testing unconstrained optimization software. ACM Trans. Math. Softw. 7: 17–41 · Zbl 0454.65049 |

[19] | Lenard J. and Haddow J. B. (1972). Plastic collapse speeds for rotating cylinders. Int. J. Mech. Sci. 14: 285–292 |

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