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Elastic‐Plastic Stresses in Rotating Discs by von Mises and Tresca
Author(s) -
Rees D.W.A.
Publication year - 1999
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/(sici)1521-4001(199904)79:4<281::aid-zamm281>3.0.co;2-v
Subject(s) - von mises yield criterion , mechanics , stress (linguistics) , annulus (botany) , yield (engineering) , residual stress , plasticity , yield surface , radial stress , materials science , mathematics , structural engineering , finite element method , physics , composite material , constitutive equation , engineering , velocity vector , linguistics , philosophy
The von Mises and Tresca yield criteria are combined with an equilibrium equation to provide the elastic‐plastic stress distribution within the discs rotating at high speed. The Tresca criterion provides a closed solution that is traditionally associated with this problem. This paper examines and compares this with an alternative solution from the von Mises criterion. The latter requires that a suitable numerical solution to a govening differential equation is matched to the boundary conditions. For this a Runge‐Kutta and a predictor‐corrector method are combined to ensure a state of yield and continuity in stress at the interface between the inner core of perfectly plastic material and the outer elastic annulus. A comparison between the two solutions in a hollow disc shows that Tresca advances the elastic‐plastic interface further than von Mises for a given speed. Thus, the Tresca prediction to the fully plastic speed is lower. The distributions of radial and hoop stress corresponding to the two criteria show only subtle differences within the elastic‐plastic speed range for this disc. By contrast, in a solid disc there is a marked difference in the radial stress predictions. This alters the distribution of residual stress and the apparent benefit that can be gained from compressive residual stress when pre‐stressed discs are raised to their operating elastic speeds.