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Mathematical Techniques Applying to the Thermal Fatigue Behaviour of High Temperature Alloys

Published online by Cambridge University Press:  07 June 2016

P. W. H. Howe
P. W. H. Howe*
Affiliation:
National Gas Turbine Establishment
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Summary

During thermal fatigue testing of a specimen with a thin edge, or during rapid temperature changes in the gas flow past turbine blades, the thin edges are deformed plastically in compression during heating and subsequently creep in tension as the bulk of the specimen or blade heats up. The plastic deformation is determined from temperature distributions, which are calculated by Biot’s variational method. The creep deformation is determined as a function of time by a differential equation, which expresses the balance between increasing elastic stress and reduction of stress due to creep relaxation, and which is solved (i) by digital computer, (ii) by transformation to a Riccati equation soluble in terms of Bessel functions, or (iii) by transformation to a second-order differential equation with a periodic coefficient. Using the thermal stresses obtained from the solution of the differential equation, the theoretical thermal fatigue endurance is determined from cyclic (mechanical) stress endurance data. Agreement between theoretical and experimental thermal fatigue endurances is obtained, over ranges of temperature, strain and strain rate, or, equivalently, over ranges of temperature, edge radius and heat transfer coefficient. This agreement supports the use of the theoretical methods in wider contexts. The accuracy of the temperature distributions is better than the accuracy of other factors entering into the correlation between theoretical and experimental endurances. Improvement in the interpretation of experimental results requires consideration of the alteration of the stress cycles during the course of thermal fatigue testing. This requirement is catered for partially by the various solutions of the differential equation for thermal stress.

Type
Research Article
Information
Aeronautical Quarterly , Volume 13 , Issue 4 , November 1962 , pp. 368 - 396
Copyright
Copyright © Royal Aeronautical Society. 1962

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