Creep deformation of materials in light water reactors (LWRs) - Materials' Ageing and Degradation in Light Water Reactors - page 19

where the subscripts E , a and p correspond to the elastic, anelastic and
plastic strains; the plastic strain ( ε p ) is given by Equation [3.9]. The anelas-

tic strain ( a ) is time dependent, completely recoverable strain in contrast

to the permanent plastic strain which is not recoverable and elastic strain
which is recoverable but instantaneous (time-independent). The anelastic
strain at the loading is given by

ε

1

⎧
⎧

⎫

v

=− ⎛
⎜

⎞
⎟

⎫ ⎬
⎪

v

[3.11]

σ σ

*

⎨
⎪
⎨
⎩

⎛
⎝

+ vt α ε

a

. α

μ μ

⎬
⎭

In the above equation, * (~2.5 × 10 22 ) are material constants in

Hart's equation of state and µ is the anelastic modulus.
In the following section we discuss the importance of the different param-
eters, namely stress temperature and microstructure. The strain rate of
deformation,

ν ~ 7 and α

can be expressed as

ε

f (, T , ),

[3.12 ]

ε σ

where σ is the applied stress and T is the test temperature.

3.2.1 Effect of stress and temperature

The steady-state strain rate of creep deformation, at a given temperature,
has been found to be directly dependent on the applied stress. The functional
dependence of strain rate on stress can be expressed by Norton's law 13

[3.13 ]

n

K ε σ

,

s

where K is a constant and n is the stress exponent. Similarly, for a constant
applied stress, the rate of creep deformation increases with increasing tem-
perature. The effect of temperature can be understood by including an extra
term indicated in the following equation

￿ ￿ ￿ ￿ ￿ ￿

⎛
⎜
⎛
⎝

⎞ Q c

RT

−

n

exp ε K

c

[3.14 ]

σ ,

s 1

where K 1 is another constant and Q c is the activation energy of creep defor-
mation. The activation energy term is included due to the fact that the creep
deformation is considered to be a fi rst order reaction rate process. The mag-
nitude of the activation energy is dependent upon the physical mechanism
governing the deformation process.