Creep deformation of materials in light water reactors (LWRs) - Materials' Ageing and Degradation in Light Water Reactors - page 37

This is known as 'natural creep law' and Weertman showed that L/h in
Equation [3.31] varied as σ 1.5 so that

45

[3.33 ]

AD L

ε

σ

.

This equation with n = 4.5 and D = D L agreed closely with the experimental
results on pure aluminum. Subsequently, this has been generalized with n
close to 5 and is referred to as the fi ve power-law creep.
At high stresses, Equation [3.30] predicts an exponential stress
dependence:

⎛
⎜

⎞
⎟

⎛
⎜

⎞
⎟

V V kT L

h

σ σ

Vk / T

sinh exp so that

σ

Ab

⎛
⎝

⎞
⎠ ≈

⎛
⎝

De

ε ρ ρ

/

kT

L

1

[3.34 ]

2 Vk kT VkT /

σ σ σ

and A De ε σ

= AD e

∼

L

,

L

as is commonly noted in the PLB regime. Both the power-law and exponen-
tial stress regimes can be combined into a single equation as proposed by
Garofalo 6

( )

n ,

ε AD L

[3.35 ]

σ

which describes both the power-law creep regime at low stresses and expo-
nential stress dependence at high stresses.
Another model that considered the non-conservative motion of disloca-
tions was proposed by Barrett and Nix. 64 This model came to be known as
the 'jogged screw dislocation' model. The rate controlling mechanism is the
motion of screw dislocations containing edge jogs. The edge jogs impede
the motion of the screw dislocations and the non-conservative motion of
the edge jogs becomes the rate controlling mechanism. This model is sim-
ilar to the Weertman model in the sense that the rate of climb of the edge
jogs is dependent on the concentration gradient established by the climb-
ing jogs. In the original model Barrett and Nix assumed the jogs to be of
atomic height, but recently Viswanathan et al . 65 have shown that these jogs
could be several times larger than atomic dimensions. The modifi ed jogged
screw model proposed by Viswanathan et al. has been used to satisfactorily
explain the creep behavior of titanium aluminides 65 and some titanium and
zirconium alloys. 66 , 67
Ivanov and Yanushkevich 68 were the fi rst to identify subgrain boundaries
as important rate controlling features. The subgrain walls were suggested
as obstacles to the motion of dislocations emitted within the subgrain.
Subsequent plastic deformation could occur only when the dislocations

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