Creep deformation of materials in light water reactors (LWRs) - Materials' Ageing and Degradation in Light Water Reactors - page 21

k

y

σσ

=+ σ 0

[3.15 ]

,

y

d

where 0 the friction hardening (stress felt by dislo-

cations while moving through the lattice), d the grain size and k y is known as
the Petch-unpinning coeffi cient that frees the dislocations locked by inter-
stitial solute atoms. This is true at low temperatures where grain boundary
sliding is not dominant.
On the contrary, under creep conditions the reverse is true. Materials with
fi ner grain size creep faster than coarse grained materials at higher tem-
peratures and at lower stresses. There are certain creep mechanisms that
operate faster in fi ner grained materials in comparison to coarse grained
materials. Hence, it is necessary to have knowledge of the grain size of a
material. The dependence of the steady-state creep rate on the grain size is
understood through the following equation:

σ y is the yield strength, σ

⎛
⎜

⎞ Q c

RT

−

−

exp

pn
σ ε Kd

c

⎛
⎝

[3.16 ]

σ

,

s 2

where K 2 is a constant, d is the grain size and p is the grain size exponent.
As is clear from this equation at a given stress and temperature, fi ner grain
sized materials are expected to creep faster than coarser grained materials.
However for dislocation-based mechanisms which are not grain size depen-
dent, the strain rate of deformation would be the same for both fi ne grained
and coarse grained materials.

3.3 Identifying the mechanisms of creep

It is possible to identify a particular micromechanism of creep through
knowledge of the stress exponent ( n ), the activation energy ( Q c ) and the
grain size exponent ( p ). Table 3.1 describes the different mechanisms of
creep and their relationship to the creep parameters n , Q c and p . In addition
to these three parameters, the relevant mechanism of creep can be identi-
fi ed through knowledge of the creep constant A given by K 2 in Equation
[3.16]. Each mechanism of creep possesses a distinct value of A .
The mechanisms of creep can be broadly classifi ed into two types:
diffusion-based processes and dislocation-based processes. Coble creep and
Nabarro-Herring (N-H) creep are mechanisms of deformation that fall
under the category of diffusion-based processes. Harper-Dorn (H-D), vis-
cous glide and dislocation climb are mechanisms of creep that fall under
the category of dislocation-based processes. Grain boundary sliding (GBS)
appears to proceed by a combination of diffusion- and dislocation-based

￿ ￿ ￿ ￿ ￿ ￿