Bursting speed of rotating discs

Date
1957
Authors
Heckart, Harold
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Mathematics
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Abstract

This thesis is an extension of a paper by Weiss and Prager in which these authors have applied Tresca's yield condition and the associated flow rule to the determination of the bursting speed of a rotating annular disc, having constant initial thickness. In this thesis the results of the paper are extended directly to the problem of the axially-symmetric annular disc with an arbitrary initial thickness. It is found that Tresca's yield condition and the associated flow rule do not appear to be applicable to the problem of the solid disc;Von Mises' yield condition is next applied to the problem of the axially-symmetric disc with an arbitrary initial thickness. Under the assumption that the elastic strains are negligible in comparison with the plastic strains, the Von Mises' stress-strain rate law is used, rather than the more complex Prandtl-Reuss stress-strain Law; A set of simultaneous equations is obtained, whose solution is the set of stresses and strains corresponding to the considered angular velocity of the disc. Bursting speed of the disc is assumed to be that value of angular speed for which the strains may increase indefinitely without further increase in rotational speed. In general, this system of equations must be solved numerically, a process which may be carried out with the aid of a desk calculator;The bursting speed of a solid disc having a constant initial thickness is computed, using Von Mises' yield condition, and the results compared with the bursting speed of an annular disc obtained by the use of Tresca's yield condition. This comparison was made by way of some experimental results of Holms and Jenkins, and the agreement is found to be satisfactory.

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Disks, Rotating, Plasticity
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