Creep deformation of materials in light water reactors (LWRs) - Materials' Ageing and Degradation in Light Water Reactors - page 25

generally associated with Newtonian viscous creep. The creep experiments
carried out at 0.99 T m provided stress exponent and activation energy values
( n = 1 and Q = Q L ) considered unique to N-H creep. However the grain
size-independent behavior of the material combined with experimental
strain rates around 1400 times larger than theoretical N-H creep predictions
were suggestive of a new mechanism of creep. When the results obtained by
Harper and Dorn were compared with theoretical N-H creep predictions,
a large discrepancy was noted. In addition, by using markers Harper and
Dorn 22 found that the strains in the center of the grain are equal to the
macroscopic strains noted in the creep experiments. The steady-state strain
rate of deformation of this creep mechanism, now known as Harper-Dorn
(H-D) creep mechanism, is given by

bD σ kT σ

L

[3.21 ] ε

A

=

HD

.

Studies over the years, on a host of other materials have led to a belief that
H-D creep is seen only in large grained materials (studies carried out by
Harper and Dorn were on Al with a grain size of 3.3 mm) and at very low
stresses and high temperatures. The primary characteristics of high temper-
ature H-D creep are summarized below: 5

￿ The stress exponent is equal to one.

￿ The creep rate is independent of grain size and similar creep rates are

observed both in polycrystals and single crystals.
The activation energy for creep is equal to that for lattice diffusion. ￿

￿ The creep curves show a distinct primary stage which is followed by a

steady-state stage.
There is a random and reasonably uniform distribution of dislocations in

￿

specimens crept to the steady state.
The dislocation density is low, of the order of 5 × 10

￿ ￿ ￿ ￿ ￿ ￿

￿

7 m −2 , and is indepen-

dent of stress.
Very similar results are obtained in pure metals and solid solution alloys

￿

revealing that solute concentration has no effect on the creep behavior
at these conditions.

While the initial studies were confi ned to very high temperatures (>0.95
T M ), recent studies show that H-D creep can be rate controlling at inter-
mediate temperatures as well. Creep studies in alpha titanium, 23 beta
cobalt, 24 alpha iron 25 and alpha zirconium 26 have shown the presence of a
H-D regime at homologous temperatures of around 0.35 to 0.6 for applied
stresses around 9 × 10 −5 G (G is shear modulus) and grain sizes of around
500 µ m.