Environmental Engineering Reference
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where p , n and m are constants and
φ
is the neutron fl ux, n/m 2 /s or dpa/s
σ
is the applied stress, MPa
t is the time, s
Q is the activation energy, cal/mole
Q / R is the activation temperature, K
R is the universal gas constant, 1.98 cal/K/mole
T is the temperature, K
f is a texture parameter
G is the grain size
ρ
is a parameter related to the dislocation density and degree of CW
A is a metallurgical factor for a specifi c alloy.
Recent extensive reviews of creep data have been given by Holt (2008) and
Adamson et al . (2009, noted below as AGP, 2009).
Using large amounts of data, it was determined (AGP, 2009) that in the
temperature range 275-390ºC (548-663K), with fl ux in the range 0.50-50 ×
10 13 n/cm 2 /s, E > 1 MeV and independent of the direction of creep, material
composition and material condition, the fl ux dependency, p , is 0.85. Purely
irradiation creep mechanisms would predict p = 1, but the inevitable con-
tributions of thermal creep tend to reduce the value below unity. For the
very low neutron fl uxes that occur at fuel bundle extremities, lower values
of p would be expected. For the value of m, giving the fl uence dependency,
Soniak et al . (2002) obtained 'm' near 0.5.
Continued analyses conclude that the stress dependency of in-reactor
creep is linear, n = 1, in the most relevant stress range of <10-200 MPa.
This applies for temperatures in the range of 275-390°C (548-663K), inde-
pendent of the direction of creep, fl ux, material composition and material
condition. Mechanistic analyses, described briefl y above, predict a range of
n-values from 1 to higher than 2. SIPA and elastodiffusion predict a linear
stress dependency, but the favoured climb and glide mechanisms predict
higher values of n .
The temperature dependence of in-reactor creep also has components
based on thermal and irradiation processes. It is generally assumed that
pure irradiation creep has only a small temperature dependence (often the
process is called 'athermal'), but thermal processes play an increasingly
large role at temperatures above about 300°C (573K). At temperatures
above about 350°C (623K) thermally produced vacancies and annealing of
small vacancy clusters compete with irradiation-produced PDs, and thermal
processes dominate in-reactor creep by 400°C (673K). In all cases increas-
ing the temperature increases the creep rate. Analysis of a large amount of
normalized data by Garzarolli (in AGP, 2009) indicates that temperature
dependency in the most interesting range of 270-400°C varies and depends
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