Elastoplastic Analysis of a Rotating Solid Shaft Made of Linear Hardening Material

A rotating solid shaft made of hardening elastoplastic material is investigated. The problem formulation is based on the Prandtl–Reis equation and the assumption about the generalized plane strain state in the shaft. Plastic strains are determined using the maximum reduced stress condition, the flow...

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Bibliographic Details
Published in:Mechanics of solids 2021-09, Vol.56 (7), p.1243-1258
Main Authors: Prokudin, A. N., Burenin, A. A.
Format: Article
Language:English
Subjects:
Classical Mechanics
Elastoplasticity
Exact solutions
Physics
Physics and Astronomy
Plane strain
Rotating shafts
Rotation
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Summary:A rotating solid shaft made of hardening elastoplastic material is investigated. The problem formulation is based on the Prandtl–Reis equation and the assumption about the generalized plane strain state in the shaft. Plastic strains are determined using the maximum reduced stress condition, the flow rule associated with it, and the law of linear isotropic hardening. The analysis is restricted by the active loading of the shaft. It is shown that in the general case the four  plastic regions corresponding to different edges and faces of the yield surface may appear in the shaft. The exact solutions are found for each possible plastic region. The dependences of the critical rotation speed at which the entire shaft becomes plastic on the hardening parameter are established. The results are compared to the solutions for the Tresca and von Mises criteria.
ISSN:0025-6544
1934-7936
DOI:10.3103/S0025654421070207