Creep deformation of materials in light water reactors (LWRs) - Materials' Ageing and Degradation in Light Water Reactors - page 41

creep is equal to that for grain boundary diffusion in the case of Coble creep
and equal to lattice diffusion activation energy with N-H creep. Usually the
activation energy of deformation is constant if a single thermally activated
process is rate controlling. The Arrhenius plot - log of strain rate of defor-
mation against reciprocal of temperature (in K) - is a straight line in such
a case. However in certain cases more than one mechanism of creep, each
with different activation energies, could be rate controlling. The Arrhenius
plot in such a case is curved in the temperature range where the activity
of the mechanisms is comparable. There are two cases which should be
considered.
In case 1, the mechanisms of creep are independent of each other and
hence occur simultaneously or in parallel. Each mechanism contributes a
strain i and the strain rates of deformation are additive. The total strain rate

of deformation in such a scenario is given by

ε

∑

ε ε

i

[3.38 ]

.

i

For example, for the case of two mechanisms occurring simultaneously, the
temperature dependence of strain rate is given by

exp ⎛
⎝

⎞

exp ⎛
⎝

⎞
⎟

Q
RT

Q
RT

2

1

()

[3.39 ]

⎛
⎝

⎛
⎝

⎠ +

− ε ε exp ε ε −

01

. ε

02

ep

The Arrhenius plot for such a scenario is shown in Fig. 3.15a, and if Q 1 >
Q 2 , mechanism 1 makes the dominant contribution to the creep rate at high
temperatures and mechanism 2 becomes dominant at low temperatures. In
the temperature range where the activity of both mechanisms is compara-
ble, the Arrhenius plot is curved. At any given temperature, the faster mech-
anism is expected to control the rate of deformation.
In case 2, the mechanisms of creep occur sequentially and are known as
series or sequential mechanisms. One mechanism cannot operate unless
the other has taken place and vice versa . Here instead of the deformation
strains, the time periods over which each mechanism has occurred are addi-
tive. Thus the total strain rate of deformation, assuming each mechanism
contributes to the total strain, is given by

￿ ￿ ￿ ￿ ￿ ￿

1 1

∑

=

[3.40 ]

.

ε ε

i

i

For the case of two mechanisms occurring sequentially, the temperature
dependence of the creep-rate is given by