Creep deformation of materials in light water reactors (LWRs) - Materials' Ageing and Degradation in Light Water Reactors - page 24

D
dkT

Ω σ

L

[3.17 ]

ε B

=

H

2

D
dkT

B δσ Ω

BB
δ

[3.18 ]

ε

c

=

3

.

π

In Equation [3.17], B H is the N-H constant and has a value of about 12-15,
D L is the lattice diffusivity, is the atomic volume and k is the Boltzmann

constant. In Equation [3.18], B c is the Coble constant and has a value of 150,
D B is the grain boundary diffusivity, and

Ω

B is the grain boundary thickness.
From the above relationships it is understood that the creep strain rate var-
ies linearly with stress and is inversely proportional to the grain size. Usually
with decreasing grain size, it is observed that Coble creep dominates N-H
creep and vice versa . But when both the mechanisms operate in parallel the
strain rate can be expressed by

δ

B Ω

σ

ε D

[3.19 ]

=

ef

2

f ,

dkT

where D eff is the effective diffusion coeffi cient and is given by

D L ⎛
⎝

⎞

D δ π

BB

DD 1

[3.20 ]

⎛
⎝

+

.

ef L

d D

L

From Equations [3.19] and [3.20], it is clear that the grain boundary diffu-
sion will contribute more to the creep rate for larger D B / D L ratios and for
smaller grain sizes. In the derivation of the N-H and Coble creep equations,
the following assumptions were made:

￿ ￿ ￿ ￿ ￿ ￿

i. The grain boundaries are perfect sources and sinks of vacancies, and
ii. The initial dislocation density of the crystal is low.

This implies that the only sources and sinks for vacancies are the grain
boundaries. Since their discovery, both N-H and Coble creep have been
found to occur in a variety of materials and experimental results have
agreed well with the proposed theory. 21 - 26

Harper-Dorn creep

Through their classic experiments on high purity aluminum (99.95%),
Harper and Dorn 22 came across a rate controlling mechanism that was
seemingly independent of the grain size but still displayed characteristics