Creep deformation of materials in light water reactors (LWRs) - Materials' Ageing and Degradation in Light Water Reactors - page 45

fact this low stress regime is associated with similar characteristics as the
climb-controlled creep with distinct subgrain formation and relatively large
primary creep region. On the other hand, dislocations may break away from
the solute atmospheres at high stresses, thus entering a climb-controlled
regime again as noted at higher stresses with higher n value. Following
Murty's work, this breakaway stress can be calculated from the equation 74

2

Wc
m

mo

[3.44 ]

σ

=

b

β 3

,

2 kTb T

where W m is the binding energy between solute atom and the dislocation, c o
is the solute concentration, and typically ranges between 2 and 4 depend-

ing on the shape of the solute atmosphere. Later, Langdon and co-workers 75
showed that this relation is valid for a number of solid solution alloys.
Assuming 0.23 eV as a reasonable value for W m , the critical stress for break-
away is estimated to be ~7.5 × 10 −4 E, which is in agreement with the experi-
mental results obtained from various class-A alloys. 65 At even higher stresses,
another regime may appear involving low temperature climb-controlled
creep with a stress exponent value of n + 2 (i.e. 7). This mechanism is asso-
ciated with the climb processes involving dominance of dislocation core dif-
fusion (Fig. 3.16b). However, this is often masked because the PLB regime
starts in the near vicinity.
As lower stresses are approached, one expects to note viscous creep with
n = 1 (Fig. 3.16b) either due to N-H or Coble creep mechanisms. Depending
on the test temperature, one of the regions such as with n = 3 for viscous
glide may completely disappear as noted in Fig. 3.16b. This could get further
complicated if an intervening GBS regime with n = 2 appears between vis-
cous creep and dislocation creep regimes.

β

3.5.2 Deformation mechanism maps

￿ ￿ ￿ ￿ ￿ ￿

The concept of deformation mechanism maps was proposed by Ashby. 76
Since different creep mechanisms operate or dominate in different stress,
temperature and grain size regimes, Ashby envisioned that a deformation
mechanism map would be an ideal representation of the materials consti-
tutive behavior. Over the years, this concept has been extended to describe
a variety of other physical phenomena such as sintering, 77 wear 78 and frac-
ture. 79 Figure 3.17 is a deformation mechanism map fi rst reported by Ashby
in 1972. The map was plotted as normalized stress (

/G ) against homologous
temperature ( T/T m ) for a constant grain size. The map was then constructed
by determining the stress or temperature boundaries where one mechanism
would dominate others. To this end, the creep constitutive relations of dif-
ferent mechanisms were compared and stress and temperature values where

σ