Creep deformation of materials in light water reactors (LWRs) - Materials' Ageing and Degradation in Light Water Reactors - page 18

In comparison to the normal creep equation, the logarithmic creep behav-
ior is usually described by

( )

l

[3.8 ]

=+ ε +

εε α γ

,

0

where are constants. This equation indicates that over a long period

of time, the strain rate of deformation tends to become zero. Such an equa-
tion, as discussed in the previous section, would be useful for describing
exhaustion creep.
While Andrade's equation is an empirical correlation borne out of his
experimental observations, a number of researchers have derived similar
relations on the basis of physically based mechanisms. For example, the
Garofalo equation has been derived by considering sub-structural changes
during deformation and by modeling the whole phenomenon as a fi rst order
reaction. Webster et al . 8 and Amin et al . 9 have correlated the stress and tem-
perature dependence of

α and γ

ε s to the rate controlling mechanisms of
high temperature creep using fi rst order reaction rate concepts. They found
that the Garofalo equation can be derived by assuming that the transient
creep follows a fi rst order kinetic reaction rate theory with a rate constant
1

ε T , r and

K s that depends on stress and temperature. Here 1/ τ is the relaxa-

τ ε

is the relaxation
time for rearrangement of dislocations during transient creep controlled by
dislocation climb. The physical mechanisms, for example, dislocation climb,
that have been suggested to control or govern creep will be discussed in a
subsequent section.
During their analyses of the creep results on Zr-based alloys, Murty 10
found the following equation better describes the primary creep compared
to the Garofalo equation:

tion frequency which is similar to r in Equation [3.6] and τ

1

At AB ε

￿ ￿ ￿ ￿ ￿ ￿

i

ε

s

A

ε

d B

ε

[3.9 ]

= = = , A B ,

1

t

+ ε ε ε

s

ε r

t

s

where A is the ratio of the initial strain rate to steady-state value and B is
the inverse of the extent of the primary creep. A was found to be around
10 as reported earlier by Dorn and co-workers 4, 9 for many materials that
behave like pure metals and class-M alloys.
A distinctly different approach was used by incorporating anelastic 11 strain
in the description of the primary creep regime and especially in predicting
the transients in creep strain due to sudden stress changes. 12 Accordingly,
the total strain at any given time is given by

[3.10 ]

εε εε =+ ε +

Ea
ε +

p ,