Transcript Embrittlement

“Influence of atomic displacement rate on radiation-induced
ageing of power reactor components”
Ulyanovsk, 3 -7 October 2005
Displacement rates and primary knocked
atom spectra in WWER vessel steels
Pechenkin V.A., Konobeev Yu.V., Pyshin I.V. Petrov E.E.,
Khoromsky V.A (Institute of Physics and Power Engineering, Obninsk),
Kryuchkov V.P. (Concern “ROSENERGOATOM”, Moscow),
Voloschenko A.M., (Keldysh Institute of Applied Mathematics,
Moscow),
Tsofin V.I., Rozanov K.G. (OKB “Gidropress”, Podolsk)
INTRODUCTION
For the present, fast neutron fluence (E> 0.5 MeV in Russia and E>1 MeV in
USA and France) is used in Regulatory guides for forecasting the irradiation
embrittlement of WWER, PWR and BWR reactor pressurized vessels
Number of displacements per atom (dpa) should be considered as an
improved correlation parameter, that allows to take into account neutrons of
all energies
This parameter allows to compare results of irradiation in various neutron
spectra as well as by various particles: neutrons, ions and fast electrons
The calculation of dpa and PKA spectra is important for development of
irradiation embrittlement models and physically based regulatory guides
DOSE RATE
At an arbitrary location in the reactor the dose rate K (dpa/s)
is given by the following expression :

K    ( E ) d ( E ) dE
(1)
0
where (E) is the neutron energy spectrum, and d(E) is the
displacement neutron cross section
 d (E) 
Tmax

Td
d Fe ( E , T )
 (T )dT
dT
(2)
PKA - SPECTRUM
Inserting eqn. (2) in eqn. (1) and changing the order of
integration, one can find
K
Tmax

Td
dT  (T ) 
20 MeV

ET
d Fe ( E , T )
 (E) 
dE
dT
where the integral over E is the spectrum of primary
knocked atoms (PKA-spectrum).
CASCADE MODELS
If to neglect energy loss mechanisms such as electronic
excitation and ionization, the NRT displacement model NRT(T) is
given by the following simple expression: NRT(T) =10T, where T
is the PKA kinetic energy in units of keV.
By molecular dynamics (MD) simulations of cascades in alpha-Fe,
Doan (2000) has found (T)8.25 T 0.967 . This result can be
obtained from NRT(T)=10T, if to take the effective threshold
displacement energy for Fe equal to 48.5 eV instead of 40 eV in
the NRT-model.
Using another interatomic potential for the MD-simulation of
cascades in Fe, Stoller found that (T)/NRT(T) <1 at the effective
threshold displacement energy of 40 eV.
«EFFECTIVE DPA»
Below the number of displacements per atom calculated with
account of defects surviving in-cascade recombination is
called as «effective dpa»
Energy dependence of total point
defect survival fraction (per NRT)
obtained by R. Stoller in MD
cascade simulations.
The ratio =(T)/NRT(T) was
approximated as follows:
=0.5608T-0.3029+3.227  10-3 T
DETAILS OF CALCULATIONS
For calculation of dose rates at different locations in
WWER - 440 neutron and gamma spectra were
obtained using the 3D transport code KATRIN
developed by A.M. Voloschenko et al.
In WWER-1000 the approximate 3D distributions
have been received using the 3D synthesis of 2D (r,ϑ)
and (r,z) and 1D cylindrical (r ) solutions
PKA-spectra were calculated using the SPECTER
code developed by L. Greenwood
NEUTRON SPECTRA AT DIFFERENT
LOCATIONS IN WWER - 440
Nomlised neutron group fluxes
1
0.1
0.01
0.001
0.0001
outer vessel surface
inner vessel surface
surveillance specimen
1E-005
1E-011 1E-009 1E-007 1E-005
0.001
Neutron energy, MeV
0.1
1E+001
CALCULATED NEUTRON FLUXES, DOSE RATES
AND MEAN PKA ENERGIES
Neutron flux, point defect generation rate and mean PKA energy at different locations in
WWER-440 and WWER-1000
Type of
reactor
Cylindrical
coordinates
Neutron flux,
109 n/cm2s
Dose
rate,
10-12
dpaNRT/s
Heig
ht Z,
cm
Angle
,
radian
Radius
R,
cm
>0.5
MeV
>1
MeV
 NRT
Dose rate
calculated
using D,
eq.(1)
10-12
dpaNRT/s
Dose
rate,
10-12
dpaeff/s
Mean
energy of
PKA (keV)
WWER – 440
surveillance
specimens
145
0.519
160
4450
2540
4130
4080
1330
10.9
WWER – 440
inner surface
145
0.519
178
245
154
243
242
75.7
14.5
WWER – 440
outer surface
145
0.519
192
66.5
25.5
57.7
55.6
18.8
10.6
WWER –
1000
inner vessel surface
35.4
22.3
35.0
34.9
11.0
16.6
WWER –
1000
outer vessel surface
5.23
1.67
4.77
4.55
1.57
8.82
Ì D
EFFECT OF NEUTRON SPECTRA ON DPA AND
FLUENCES in WWER-440
R (cm)
Damage rates and neutron fluxes
10-11
dpa
s
for neutrons with
160
178
192
324 (78%)
19.7 (81%)
3.94 (68%)
44.5 (16.9%)
2.45
(12.4%)
0.665
(28.3%)
9.28 (1.7)
9.92 (1.25)
8.88 (2.36)
E> 0.5 MeV (contribution to the total rate)
1011
fluence
for neutrons with
s
E> 0.5 MeV (contribution to the total flux)
10-22
dpa
ratio of the total rate to
fluence
the flux of neutrons with E> 0.5 MeV (with
all energies)
EFFECTS OF GAMMA-QUANTA AND RPVS
COMPOSITION ON THE DOSE RATE
The contributions of gamma-quanta to dose rates dpaeff/s were
calculated for surveillance specimens (R = 160 cm), inner
(R = 178 cm) and outer (R = 192 cm) vessel surfaces in WWER-440.
For the calculation displacement cross sections for Fe have been
taken from the paper by K. Fukuya and I. Kimura (2003). The ratios of
gamma to neutron dpaeff/s equal 0.007, 0.035 and 0.004 respectively.
Although the total content of alloying elements (Cr, Ni, Mn, Mo,V) in
RPVS does not exceed several percents, additional calculations of
dose rates were performed with account of main alloying elements.
There are only small differences in the dose rates at the internal
vessel surface calculated for pure Fe and for base metal in WWER440 (2.4310-10 dpa/s и 2.4410-10 dpa/s) and in WWER-1000 (3.5010-11
dpa/s and 3.5110-11 dpa/s).
CONCLUSIONS

In WWER-440 displacement rates (dpa/s) at
surveillance specimen locations exceed ones at the
internal vessel surface by more than one order of value

The evaluated ratios of the displacement rate to the
neutron flux depend on the neutron spectra at specified
locations in WWER

PKA-spectra at different locations of WWERs differ
significantly. In WWER- 440 these spectra are harder at
the internal vessel surface as compared with the outer
vessel surface and surveillance specimen locations