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radiation hardening in these steels (1020, A516 and A588) is opposite to
that noted in Armco-Fe of small grain sizes. A plausible explanation for
this observation lies in the fact that the source hardening and the slope
of the Hall-Petch plot are very small in these steels. Once these materials
are exposed to fast neutrons, the hardening will essentially be due to fric-
tion hardening with negligible contribution from source hardening thereby
resulting in grain size independent yield strength (i.e. horizontal line in
Hall-Petch plot). Exposure to the additional low energy neutrons along
with fast neutrons is expected to result in a slight increase in friction harden-
ing, thereby resulting in a Hall-Petch line parallel to that noted for fast fl u-
ence exposure alone. Hence, exposure to the total neutron energy spectrum
in these steels will lead to an additional grain size independent hardening
as observed in the bar chart in Fig. 1.21. Thus, identifying the yield stress
as a sum of friction and source terms lends explanation and support to the
experimental observations in both pure iron and steels.
1.3.2 Toughness loss
As described in the foregoing sections on fracture, the energy absorbed
before failure is an indication of the toughness of a material. Exposure of
the material to neutron fl uxes reduces the toughness value and increases the
transition temperature (
RT
NDT
), below which the material fails in a brittle
manner (absorbing very low energy) (Fig. 1.5); this is commonly referred
to as radiation embrittlement. The extent to which the
RT
NDT
is raised from
the initial value is an indication of the degradation. A simple model devel-
oped using the concentrations of copper and nickel, and the value of fl ux
and fl uence could yield a fair prediction for the shift in
RT
NDT
.
31
The most
severely affected region in a RPV is the belt region where fast neutron bom-
bardment is at a maximum. Presence of copper and phosphorous are found
to promote the embrittlement effect while that of nickel acting alone is
unclear,
32
although in combination with copper, the effect of embrittlement
due to nickel is increased. The role of other elements like Mo, Mn, As, Cr
and Sn is not completely understood. The change in DBTT may be evalu-
ated using Cottrell brittle fracture theory and is given in terms of friction
and source hardening terms:
(
)
(
2
)
12
+
Φ
dd
Φ
σ
yi
σσ
[1.23 ]
Δ
DBTT
ΔΔ
α
Gb
φ
t
G
b
Φ
σ
Δ
=
=
=
σ
Δ
i
i
(
)
(
Δ
i
αφα
t
α
G
b
Φ
.
)
1
dd
+
Thus, one needs to know the infl uence of neutron irradiation and test
temperature on both the friction and source hardening terms to evaluate
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