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767
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<TITLE>
mathematical techniques applying to the thermal fatigue behaviour
of high temperature alloys .
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<TEXT>
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
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 .
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