Creep deformation of materials in light water reactors (LWRs) - Materials' Ageing and Degradation in Light Water Reactors - page 71

thickness. Steady-state creep dominates the service life of the clad and only
in very rare cases the material may enter tertiary creep range. The creep
rate of clad material under an irradiation environment is many times higher
(depending on the material chemistry and the fl ux) than that under out-of-
pile conditions. Further, the dimensional changes in clad tube (an aniso-
tropic material) happen in a preferential direction which gives rise to other
unwanted problems. The irradiation creep is not just the thermal creep
imposed with high defect density. In the former the interstitial and vacancy
loops that form during irradiation play a major role in the creep mechanism;
in the latter the creep rate increases with temperature. The irradiation creep
is weakly dependent on irradiation temperature ('athermal') and in-reactor
thermal creep controls the deformation above ~400°C.
Two mechanisms are proposed to explain the irradiation creep phenom-
enon: (a) stress-induced preferential absorption (SIPA), where extra planes
of atoms accumulate on crystal planes so as to produce creep strain in the
direction of the applied stress and (b) stress-induced preferential nucle-
ation (SIPN), which assumes that nucleation of loops is preferred on planes
with a high resolved normal stress. Both of these mechanisms assume that
the growth or formation of loops occur at a favorable orientation with
respect to applied stress and causes macroscopic strain. Neutron irradia-
tion produces large quantities of point defects - vacancies and self intersti-
tial atoms (SIAs). These defects migrate to different sinks like dislocations
and grain boundaries, in a preferential manner due to the anisotropy of
the zirconium crystal lattice, in order to reduce the energy of the system.
Because of the diffusional anisotropy, interstitial atoms tend to migrate to
dislocations lying on prism planes and to grain boundaries oriented paral-
lel to prism planes, while vacancies drift preferentially to dislocations lying
on basal planes and to boundaries parallel to basal planes. This gives rise
to elongation in one direction and contraction in the other. 136 The creep
rate is controlled by dislocation glide and this in turn can be controlled by
suitable alloying elements and by choosing an appropriate texture of zir-
conium matrix.
The total strain measured in an irradiation creep consists of the strain due
to thermal creep (

￿ ￿ ￿ ￿ ￿ ￿

ε th ), irradiation creep ( ε irr ) and irradiation growth ( ε g ) and

is assumed to be additive:

[3.66 ] εε ε

=+ ε + ε

g

th ir r

The creep rate ( () ) is given by the empirical relation

( )

QRT

[3.67 ]

ε

mn

f

( φ

φ e

−

fd A σ σ σ ρ

ρ ,