Creep deformation of materials in light water reactors (LWRs) - Materials' Ageing and Degradation in Light Water Reactors - page 38

were annihilated at the subgrain boundaries. This annihilation process is
climb controlled.
There are a few other network and recovery based models that appear
attractive. These models consider the dislocation networks (Frank net-
works) present inside the subgrains to explain the hardening and recovery
during creep.

Microstructural features

Subgrain formation is widely believed to accompany deformation dur-
ing creep in the fi ve power-law regime. The formation of subgrains and
other dislocation networks is a natural consequence of plastic deforma-
tion during creep. During plastic deformation the total dislocation den-
sity increases. An increase in dislocation density is concurrent with the
increased work hardening particularly due to long range stresses acting
on the dislocations. In the presence of the long range stresses, the disloca-
tions tend to arrange themselves into low energy confi gurations. These low
energy confi gurations are basically walls of dislocations inside a grain. The
grain is thus divided into many smaller sections resulting in the formation
of subgrains constituting both low angle tilt and low angle twist boundar-
ies. Figure 3.13a shows the presence of distinct subgrains formed in a near
α -Ti alloy. 69

The subgrain size is an important microstructural feature of the fi ve
power-law creep regime. In fact, it has been empirically determined that the
subgrain size (

λ ) varies with applied stress σ according to: 4

1

λ

⎛
⎛

σ

⎞

−

[3.36 ] 20 =

⎝

.

b E

The dislocations within a subgrain usually form three-dimensional networks
known as Frank networks. These networks impede the movement of dislo-
cations and can cause strengthening known as network strengthening. All
the dislocations that are not associated with subgrain boundaries usually
form Frank networks.
Jogged screw dislocations have also been considered as important fea-
tures characteristic of deformation in the fi ve power-law regime. Figure
3.13b provides the deformation microstructure of Ti-48Al crept in the fi ve
power-law creep regime. 65 Long dislocations with a screw orientation can
be observed in Fig. 3.13b. Mills and co-workers 65 - 67 outlined the conditions
under which jogs signifi cantly larger than atomic height can be expected on
screw dislocations. These conditions are: (a) screws are compact such that
cross slip is relatively easy, (b) screw orientation is preferred due to strong
lattice friction, and (c) jog pair or kink pair expansion is sluggish due to

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