Transcript Development of a New Embrittlement Correlation for the

MATGEN-IV
Cargese, Corsica
September 29, 2007
Multiscale Computer
Simulations and Predictive
Modeling of RPV Embrittlement
Naoki Soneda
Central Research Institute of Electric Power
Industry (CRIEPI), Japan
MATGEN-IV
Cargese, Corsica
September 29, 2007
Multiscale Modeling
of RPV Embrittlement
Naoki Soneda
Central Research Institute of Electric Power
Industry (CRIEPI), Japan
Irradiation Embrittlement of LWR RPV Steels
Fracture Toughness
Before irradiation
After irradiation
Decrease in USE
Increase in transition
temperature
Temperature
The accurate prediction of the transition temperature
shift is very important in ensuring the structural
integrity of reactor pressure vessels.
PWR RPV
2007/09/29
Goal:
Development of an accurate embrittlement correlation
method to predict the transition temperature shifts 3
Current Embrittlement Correlation Equation
– Prediction of Transition Temperature Shift –

US NRC


Regulatory Guide 1.99 Rev.2
JEAC4201-1991, Japan

 26  240  Si  61  Ni  301

RT NDT   16  1210  P  215  Cu  77 Cu  Ni  f 0.290.04 log f Base Metal
RT NDT




Cu  Ni  f 0.250.1log f
Weld Metal
Statistical analysis was performed to identify chemical elements
(Cu, Ni, Si and P) to be used in the equations.
Both the surveillance data of commercial reactors and test reactor
irradiation data were used.
The equations were developed based on the knowledge
in the 80’s.
2007/09/29
4
Activities in the 90’s and 00’s

New information and new findings



Surveillance data at higher fluences became available.
New understandings on the embrittlement mechanisms have been
obtained by state-of-the-art experiments and simulations.
New projects have started in the US

Development of mechanism guided correlation




US NRC, NUREG/CR-6551 (1998) & revised version (2000)
ASTM, ASTM Standard E 900–02 (2002)
US NRC, Regulatory Guide 1.99 Rev.3 (2007?)
Plant Life Management for 60-years operation is
necessary


2 plants will be 40 years old in 2010, and more than 10 plants are
now older than 30 years in Japan
Accurate prediction of embrittlement is very important for safe and
economical operation of the plants
2007/09/29
5
Surveillance Data

In the commercial light water reactors, some surveillance
capsules containing surveillance specimens are installed
at the vessel inner wall to irradiate the same RPV
material at a very similar irradiation condition to the
vessel.

Surveillance capsules are retrieved according to the
schedule of the surveillance program. The surveillance
specimens irradiated in the capsule are tested to
measure the transition temperature shift. This data is
called surveillance data.
2007/09/29
6
Activities in the 90’s and 00’s

New information and new findings



Surveillance data at higher fluences became available.
New understandings on the embrittlement mechanisms have been
obtained by state-of-the-art experiments and simulations.
New projects have started in the US

Development of mechanism guided correlation




US NRC, NUREG/CR-6551 (1998) & revised version (2000)
ASTM, ASTM Standard E 900–02 (2002)
US NRC, Regulatory Guide 1.99 Rev.3 (2007?)
Plant Life Management for 60-years operation is
necessary


2 plants will be 40 years old in 2010, and more than 10 plants are
now older than 30 years in Japan
Accurate prediction of embrittlement is very important for safe and
economic operation of the plants
2007/09/29
7
Analysis of the Recent Surveillance Data


Transition Temperature Shift
RTNDT   16  1210  P  215  Cu  77 Cu  Ni  f 0.290.04 log f
High Cu material
Irradiated at low flux
High Cu material
Low Cu material
Low Cu material
19
2
Irradiated to high 6x10 n/cm
(40years, PWR)
fluences
<3x1018n/cm2
(60years, BWR)
2007/09/29
Current prediction
Surveillance data
1x1020n/cm2
(60years, PWR)
Neutron Fluence (n/cm2, E>1MeV)
8
Embrittlement Mechanism
– General Consensus –

Formation of Cu-enriched clusters (CEC)






P
Cu
Dislocation
MD
Formation of matrix damage (MD)



in high Cu materials
CEC is associated with Ni, Mn and Si
2~3 nm in diameter
obstacle to dislocation motion
dose rate effect exists
G.B.
CEC
point defect clusters such as dislocation loops or vacancy
clusters, or point defect – solute atom complexes.
main contributor to the embrittlement in low Cu materials
Phosphorus segregation on grain boundary


P segregation weakens grain boundaries.
not very important for relatively low P materials
2007/09/29
9
Are the formation of SMD(MD)
and CRP(CEC) independent?
ASTM E 900-02
Total
No effect of chemical
composition?
Is the linear sum
approximation appropriate?
Is an exponential
function appropriate?
 20,370  0.5076
18
  f
SMD  6.70  10  exp
 Tc  460

CRP  B  1  2.106Ni
Is it product-form
dependent?
Is there any
other effect such
as dose rate and
other elements?
2007/09/29
1.173

T
RTNDT  SMD  CRP
SMD
CRP
f1/2
Dose it saturate at
high fluences?
1 1
 log f   18.24 
 F Cu      tanh

1.052


2 2
Is the threshold
value appropriate
234, welds
0, Cu  0.072 wt%
128, forgings


0.577
B
,
F Cu   Cu - 0.072 , Cu  0.072 wt%
208, CE plates
Cu , Cu  Cu
max
 max
156, otherplates
0.25wt.%, for welds with Linde 80 or Linde 0091flux;
Cu max  
0.305wt.%, for other welds
10
Issues to be studied

Do CEC and MD cause embrittlement?
 What
is the nature of MD?
 What
is the nature of CEC?

Are CEC and MD formed independently?

Does the contribution of CEC saturate?

What is the effect of temperature?

What is the effect of dose rate?
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11
Approach

Mechanical property tests of neutron irradiated
RPV steels

Nano-structural characterization

Multi-scale computer simulation
2007/09/29
12
Ratio to Fe
Normalized
counts
of gamma rays
規格化された強度
Nano-structural Characterization
Unirrad.
As-irrad.
500°C
1.4
thermally
熱時効材
aged
1.2
1.0
0.8
50nm
未照射材
unirradiated
Irradiated
照射材
0.6
0
10
20
30
40
50
Transmission Electron Microscope
(TEM)
P (x10 m c)
電子の運動量
Electron
momentum
-3
L
0
Cu-enriched clusters formed
by neutron irradiation
LEAP
(Local Electrode Atom Probe)
~40 nm
Positron Annihilation
(Coincidence Doppler Broadening)
~300 nm
2007/09/29
3-Dimensional Atom Probe
13
Multi-scale Computer Simulation
Molecular Dynamics
Dislplacement cascade
~10-11sec
~10-8m
Molecular Dynamics
Dislocation
Kinetic Monte Carlo
Microstructural evolution
during irradiation 9
~10 sec
~10-7m
Radiation damage
Dislocation Dynamics
Dislocation behavior
during deformation
~100sec
~10-4m
Point defect production
Dislocation
loop
Interaction between
dislocation and damage
Dislocation Dynamics
Prediction of mechanical
property
~100m
Molecular Dynamics
Vacancies
Cu atoms
Stress (MPa)
Irradiated
Unirradiated
Detailed analysis of
microstructure
2007/09/29
Strain (%)
14
Issues to be studied

Do CEC and MD cause embrittlement?
 What
is the nature of MD?
 What
is the nature of CEC?

Are CEC and MD formed independently?

Does the contribution of CEC saturate?

What is the effect of temperature?

What is the effect of dose rate?
2007/09/29
15
Damage accumulation in bcc-Fe
– Kinetic Monte Carlo (KMC) simulation –
KMC tracks all the events.
Input Data
Defect
production
10-9-10-8m
～10-11s
Diffusion
Clustering
10-9-10-7m
10-12-10-8s
Cluster diffusion
～10-5m
Formation and
growth of loops
Dissociation
10-6-10-3m
Microstructure evolution
2007/09/29
• Database of displacement
cascades for a wide range of
PKA energies
• Diffusion kinetics such as
diffusivities and diffusion
modes (1D, 3D…) of point
defects and clusters
• Thermal stabilities (binding
energies) of point defect
clusters
Most of the data can be
obtained from molecular
dynamics simulations. 16
Primary Knock-on Atom (PKA) Energy Spectrum
• Displacement cascade simulation
results are necessary for different
PKA energies to simulate the
PKA energy spectrum.
• Molecular dynamics simulations
have done for the PKA energies
of 100eV, 200eV, 500eV, 1keV,
2keV, 5keV, 10keV, 20keV and
50keV.
L.R. Greenwood, JNM 216 (1994) 29.
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17
Displacement Cascade Simulation


Molecular Dynamics
Inter-atomic potential



Constant volume at a temperature of 600K




Ackland Potential
ZBL pair potential is used for the short distance interaction
Thermal bath at the periphery of the computation box
Periodic boundary condition
Automatic time step control
Number of atoms：
12,000 atoms for 100eV PKA cascade
~4,000,000 atoms for 50keV PKA cascade
2007/09/29
18
MD Simulation of Displacement Cascade
PKA energy: 50keV
SIA
Vacancy
Volume : (28.6nm)3
2,000,000 atoms
Wide variety of defect production is observed in high energy cascades
of 50keV, which is not be observed in lower energy cascades.
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19
Small SIA & Small Vacancy Cluster
@3.2ps
Isolated subcascade formation
2007/09/29
Case 45
@10.0ps
Black dots : vacancies
White circles : SIAs
20
Large SIA & Small Vacancy Cluster
@0.1ps
Overlapped subcascade formation
(similar size subcascades)
2007/09/29
Case 09
@11.0ps
Black dots : vacancies
White circles : SIAs
21
Large SIA & Large Vacancy Cluster (1)
@3.2ps
Overlapped subcascade formation
(large & small subcascades)
2007/09/29
Case 28
@10.2ps
Black dots : vacancies
White circles : SIAs
22
Large SIA & Large Vacancy Cluster (2)
@1.9ps
Case 39
@12.1ps
70 SIAs
93 SIAs
234 vacancies
One large cascade is formed, and then …
2007/09/29
Black dots : vacancies
White circles : SIAs
23
Large SIA & large vacancy cluster (3)
@40.0ps
[001]
Cascade collapse occurred in a-Fe
[110]
Large SIA loop
b = a0/2 <111>
[001]
Case 39
2007/09/29
Black dots : vacancies
White circles : SIAs
[010]
Large vacancy loop
b = a0 <100>
24
Channelling
Case 31
<112> direction
Periodic boundary condition
2007/09/29
Black dots : vacancies
White circles : SIAs
Direction
50keV
20keV
011
2
0
133
1
0
233
2
0
111
0
1
112
1
1
337
1
0
113
1
0
114
1
0
115
0
1
116
1
2
001
7
0
• All the events occur on (110) plane.
• PKA is always the channeling
particle in 20keV cascades.
25
Dispersed defect production
Direction
50keV
20keV
011
1
0
111
1
0
113
2
0
001
1
0
• Similar direction to channeling, but
associated with many interactions
• Did not occur in 20keV cascades
Periodic boundary condition
Case 42
2007/09/29
Black dots : vacancies
White circles : SIAs
Gray : replaced atoms
26
Summary of Cascade Database
100eV, 200eV, 500eV, 1keV, 2keV, 5keV, 10keV, 20keV, 50keV
20keV
(50runs)
2
10% 8%%
80%
50keV
(100runs)
53%
5
15% %
17%
10%
Small clusters
Large SIA & V clusters
Periodic boundary condition
Channeling
2007/09/29
Periodic boundary conditionLarge
Dispersed defect formation
SIA clusters
27
Diffusivity
 Em 
D  D0  exp  

 kT 


Diffusion simulation of a point defect by MD
Calculate Do and Em by MD
U
x
2007/09/29
28
Diffusion Kinetics
– Molecular Dynamics –
Diffusivity
1D motion of
SIA clusters
 E 
D  D0  exp   m 
 kT 
 Ea 

kT


   0  exp  
Migration energy, Em
Rotation frequency
2007/09/29
29
N. Soneda, T. Diaz de la Rubia, Phil. Mag. A, 81 (2001), 331.
MD Simulation of SIA Cluster (I3)
1.6ns @ 500K
(lattice unit)
2007/09/29
1D motion
1.6ns @ 1000K
1D motion + rotation
30
– I1 ~ I20 –
Diffusivity (cm2/s)
Diffusivity (cm2/s)
Diffusivities of SIA Clusters
1/T (K-1)
1/T (K-1)
• 1D motion is a common feature for the SIA cluster migration
• Migration energies of large SIA clusters are as low as 0.06eV, which
means that SIA clusters are highly mobile.
2007/09/29
31
Migration Energies of SIA Clusters
E m  0.06 
2007/09/29
0.11
n 1. 6
32
Rotation Frequency of Small Clusters
Activation energy of rotation for the I3 cluster is high.
2007/09/29
33
Binding Energies of Point Defect Clusters
Eb n   E f n  1  E f 1  E f n 
2007/09/29
N. Soneda, T. Diaz de la Rubia, Phil. Mag. A, 78 (1998), 995.
34
Repeat until target dose or time is reached
Algorithm of KMC Simulation
Set all the possible events
Diffusion
Dissociation
Disp. cascade
Calculate event frequency
P=
i
i
i
Choose one event
Update time
Do event
Bigmac (LLNL)
2007/09/29
SNP
Em
Eb+Em
dose rate
R = Random()*P
t = -log(R) / P
Calculate interaction between
the neighboring particles
(clustering, annihilation, etc.)
KineMon (CRIEPI / Univ. Tokyo)
35
Accumulation of Point Defect Clusters in
Neutron Irradiated bcc-Fe
350K
600K
10
23
Number density (m -3)
SIA
SIA
SIA
SIA
cluster (>37)
cluster (>100)
loop (Nicol et al., 2000)
loop (Victoria et al., 2000)
-8
10
Dose rate: 10 dpa/s
Temperature: 600K
n-spectrum: Fission
Grain size: 10 m
22
No stable vacancy cluster
10
21
10
-4
10
-3
10
-2
10
Dose (dpa)
2007/09/29
36
-1
Microstructural evolution at different dose rates
25
10
Temperature: 600K
n-spectrum: Fission
Grain size: 10m
Number density (m -3)
10
Vacancy
24
10
-4-4
10
10 dpa/s
dpa/s
10
23
10
10-6-6dpa/s
dpa/s
10
25
(Smoothed data)
Temperature: 600K
n-spectrum: Fission
Grain size: 10m
Number density (m -3)
10
22
SIA
24
SIA cluster > 37
-6
10-6
dpa/s
10
dpa/s
10-4-4dpa/s
dpa/s
10
10
10
23
22
No stable
vacancy
cluster is
No stable
vacancy
cluster
-8
-10
-8dpa/s
at 10
dpa/s10
and
10 dpa/s
formed
below
10
21
10
-5
10
-4
10
-3
Dose (dpa)
10
-2
10
-1
10
-10dpa/s
10-10
10
dpa/s
-8
10-8dpa/s
dpa/s
10
21
10
-5
10
-4
10
-3
10
-2
10
Dose (dpa)
• Stable SIA clusters are always produced, but the stability of vacancy clusters
depends on the dose rate.
• Threshold dose rate exists between 10-6dpa/s and 10-8dpa/s, below which no
dose rate effect is observed in defect cluster formation.
2007/09/29
37
-1
Experimental observation of SIA loops
– TEM observation –
0.12Cu/0.58Ni
4x1019n/cm2
B=[011]、 3g (g=21-1)
0.68Cu/0.59Ni
6x1019n/cm2
50nm
Mean size:
2.6 nm
Number density: 1.8x1022 m-3
B=[133]、 3g (g=-110)
50nm
Mean size:
2.3 nm
Number density: 1.9x1022 m-3
• Dislocation loops are observed in the RPV materials irradiated in
commercial reactors.
• Number densities of the loops are relatively low.
2007/09/29
38
Dislocation – Loop interaction
•
•
•
•
•
•
Box size : 37×16×35nm (~1.7million atoms)
Potential : EAM potential (Ackland et.al.)
Burgers vector:
Edge dislocation
[111]
SIA loop
[111]
SIA loop size : ~2nm
Applied shear stress : 50MPa ~ 650MPa
Temperature : 300K
t
b=[111]
011
b=[111]
t
111
211
2007/09/29
39
Dislocation Loop – Edge Dislocation Interaction
Molecular Dynamics Simulation
I
IV
t = 50MPa
t = 650MPa
Repulsion
Superjog (II)
t = 150MPa
t = 250MPa
II
Superjog (I)
2007/09/29
t = 300,350,500MPa
III
Pinning
II’
Superjog (I’)
40
Type II Interaction
1
2
3
150MPa
Dislocation reacts
with SIA loop
4
Dislocation is pinned.
No bowing-out of the
dislocation is observed
at this
applied stress.
2007/09/29
5
Superjog formation
6
Vacancies are left behind.
41
Details of Loop – Dislocation Interaction
b=1/2[-1 1 1]
Formation of Bridge Dislocation
b= [0 0 1]
(=1/2[-1 1 1]+1/2[1 –1 1])
b=1/2[1 -1 1]
Trailing Bridge Dislocation
b=1/2[-1 -1 1]
b= [0 0 1]
Leading Bridge Dislocation
b=1/2[1 1 1]
Pinning occurs at this stage.
2007/09/29
42
Contribution of vacancy-type defects to
embrittlement
EPRI/CRIEPI Joint Program
Recovery of S during PIA
Recovery of Hardness during PIA
25
20
Low Cu, BWR Irradiation
0.002
0.0015
10
S
VHN
15
EP2, BWR4A
EP2, BWR4D
5
0.001
0
0.0005
-5
-10
-100
EP2 BWR4A
EP2 BWR4C
0
A/R
100
Low Cu, BWR Irradiation
200
300
400
Annealing Temperature (oC)
500
600
0
-100
0
A/R
100
200
300
400
500
600
Temperature (oC)
S is a measure of total amount
of open volume.

Recoveries of Hv and S occur at different temperatures indicating
that the vacancy type defect is not responsible for the Hv.
2007/09/29
43
Summary of matrix damage
Candidates
Answer
Dislocation loop of interstitial type
Yes
Vacancy cluster
No
Point defect – solute atom complex See the followings
2007/09/29
44
Issues to be studied

Do CEC and MD cause embrittlement?
 What
is the nature of MD?
 What
is the nature of CEC?

Are CEC and MD formed independently?

Does the contribution of CEC saturate?

What is the effect of temperature?

What is the effect of dose rate?
2007/09/29
45
0.3x0.3x10mm
3D Atom Probe
Electro-polish
Optical Microscope
500m
TEM
Detector
Fast = light
50nm
Z
Y
Time of flight
X
Needle tip
Element
Detection position
Slow = heavy
3D position
Pulse voltage
2007/09/29
46
~40nm
Formation of Cu-enriched Clusters
~200nm
• High Cu (0.25wt.%) RPV steel irradiated in a
test reactor was examined.
• Cu-enriched clusters are formed with very high
density, and they are associated with Ni, Mn,
Si and, sometimes, P.
• The primary mechanism in high Cu content
materials is the precipitation of Cu atoms
beyond the solubility limit.
• What is the formation process?
• What happens in medium – low Cu materials?
2007/09/29
Cu
Si
47
Small
40
HL
熱時効温度：350℃
HM
Cu Ni Mn Si
HH
0.3 0.6 1.4 0.2
HHC HL
C
–
HM
0.3 1.0 1.4 0.2 –
HH
0.3 1.8 1.4 0.2 –
HHC 0.3 1.8 1.4 0.2 0.1
30
Large
Cluster Size
100%
高Cu材
80%
Com p os ition
Increase in Vickers Hardness (Hv)
ビッカース硬さ上昇量 (ΔHv)
Thermal ageing of Fe-Cu-Ni-Mn-Si alloys
20
aged at 350oC
10
60%
Si
Cu
Ni
F eN i58
Mn
Fe
40%
20%
0%
0
1
0
2000
4000
6000
8000
10
10000
Ageing
time (hour)
熱時効時間 (Hour)
19
28
37
46
55
64
73
82
91 100 109 118
Clu ster n u m b er
LEAP measurement
Distribution of Cu atoms
49 x 65 x 270 nm3
17.5M atoms

Clusters consist of Cu, Ni, Mn and Si. Amount of Si is very small.
2007/09/29
48
Computer simulation of the thermal ageing
– Kinetic Lattice Monte Carlo (KLMC) simulation –


Consider all the atoms in the crystal
Diffusion by vacancy mechanism + regular solution approximation
for complex alloys
w  v exp  Ea kT 
Ea  E 2  e0
z
E    ij
i
j 1
Energy change by vacancy jump
Migration energy
Jump probability
Activation energy
Pair interaction energy
Total energy of the crystal
Ordering parameter
 ij  Vij    ii   jj  2
Solubility
Vij  kT ln 1  Cij   ln Cij   z 1  2Cij 
e0  Evm  Eibv
Vacancy migration energy & vacancy binding energy
ai  wi
2007/09/29
z
w
j 1
j
Choose one of the possible sites
49
Determination of KLMC parameters

b
i v
Binding energies between
a vacancy and a solute
atom in pure iron are
obtained from first
principles calculations
using the VASP code.
Energy
Binding
Vacancy
– Solute
（eV)(eV)
Vacancy
- solute Atom
atom binding
energy
e0  E  E
m
v
0.7
Sc
0.6
0.5
0.4
Zn
0.3
Cu
0.2
Ni
Mn
0.1
Ti
Co
Cr
0.0
V
Fe
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3
Vacancy
solute atom
volume
(Å ) (A3)
Vacancy
– -Solute
Atombinding
Binding
Volume
2007/09/29
50
Process of precipitation : KLMC result
673K
573K
~40nm
2007/09/29
51
Effect of Ni on cluster formation
8760hrs = 3.15x107sec
Cu : 0.3, Mn 1.4, Si 0.9 (at.%)
Nd ~ 6.8x1023 m-3
1.8at.% Ni
(a) 1.6x107sec
(b) 3.2x107sec
(c) 7.9x107sec
(d) 7.9x108sec
(b) 3.2x107sec
(c) 7.9x107sec
(d) 7.9x108sec
1.0at.% Ni
(a) 1.6x107sec
Ni enhances the nucleation of clusters.
2007/09/29
Cu
Ni
Mn
Si
:
:
:
:
0.3
1.0 or 1.8
1.4
0.9 (at.%)
52
Comparison between
simulations and experiments
Simulation
Experiment
0.25
2.00
Cu: 0.3at.%
LEAP
Volume fraction (at.%)
(at.%)
fraction
Volume
体積分率
(at.%)
1.75
Ni: 0.6at.%
Ni: 1.0at.%
Ni: 1.8at.%
1.50
1.25
1.00
0.75
0.50
0.20
SANS
0.3Cu, 1.8Ni
RSC
(310)
0.15
0.10
(60)
0.05
0.25
0.00
1.E+06
1.E+07
1.E+08
時効時間
(sec)
Ageing
time
(sec)

1.E+09
0.00
0.E+00
(17)
1.E+07
2.E+07
3.E+07
4.E+07
Ageing time (sec)
Direct and quantitative comparison of the microstructural changes with
experiments can be made.
2007/09/29
53
Calculation Conditions




Potential : Ackland potential
Edge dislocation :
b=a/2[111]
Cu precipitate size : 1.5～5nm
Box size :
50×24×56nm(～6.0x106 atoms) for small Cu
 50×36×56nm(～8.5x106 atoms) for large Cu



Applied shear stress : 350MPa
Temperature : 300K
Cu precipitate
τ
Edge dislocation
b=a/2[111]
011
y
2007/09/29
z
211
τ
x 111
54
Hardening due to Cu precipitates
distance
Maximum
Maximum bow-out
bowing distance
(nm) (nm)
– Molecular Dynamics –
4nm Cu ppt
350MPa shear stress
2007/09/29
35
30
25
20
bow-out
distance
15
10
5
0
0
1
2
3
4
5
Cu precipitate size (nm)
6
Diameter of Cu ppt (nm)
55
Interaction Process (Small Precipitate)
011
111
2007/09/29
Simple Shear
56
Interaction Process (Large Precipitate)
111
211
(011)
Atom stacking below/on/above the slip plane changes from bcc to
fcc-like structure.
2007/09/29
57
Dislocation Motion at Break-out
Pure edge
Pure screw
Original slip plane
Motion of screw dislocation
Top view
Super jog formation
2007/09/29
58
What is the difference between the thermal
ageing and irradiation?
Neutron irradiation
Thermal ageing
100%
100%
unknown
Al
V
H
O
As
Mo
80%
Com p os ition
Composition
60%
C
P
Si
Cu
Ni
FeNi58
Cr
Mn
40%
20%
60%
Si
Cu
Ni
FeN i58
Mn
Fe
40%
20%
Fe
0%
Cluster #
Cluster number


504
493
482
471
460
449
438
427
416
405
394
383
372
361
350
339
328
317
306
295
284
273
262
0%
251
Composition
Composition
80%
1
10
19
28
37
46
55
64
73
82
91 100 109 118
Clu ster n u m b er
Cluster number
Si content is much larger in the irradiated material than in the thermally
aged materials.
Low Si content in thermally aged materials is also seen by simulations aged
for much longer time.
2007/09/29
59
70
60
35 x 41 x 491 nm3
13.7M atoms
Cu
P
2.24 x 1023 m-3
4.16 x 10-3
3.07 nm
Nd
Vf
dG
50
Counts
Counts
0.12Cu
4x1019n/cm2
40
30
20
10
0
0.0
0.4
0.8
1.2
1.6
2.0
2.4
2.8
3.2
3.6
4.0
4.4
4.8
5.2
5.6
6.0
Cluster
diameter
(nm)
Cluster
diameter (nm)
AP2
unknown
MoN
100%
Sn
Si
V Cu
H
O Ni
As
Ni
Mo
Composition (at.%)
(at.%)
Composition
Co
Al
80%
60%
C
P
Si
40%
RG Guinier D
(nm)
(nm)
V-weighted average 1.40
3.62
Simple average
1.19
3.07
20%
Fe
61.9
60.3
Mn
5.6
5.7
Composition (at.%)
FeNi58
Ni
Cu
6.8
3.3
4.3
7.2
3.3
3.9
Cu
Ni
Si
6.7
7.1
P
1.0
1.1
FeNi58
Cr
Mn
Fe
0%
1
11 21
31 41 51
2007/09/29
61 71 81
91 101 111 121 131 141 151 161 171 181 191 201 211 221 231 241 251 261 271 281 291 301 311 321 331 341 351 361
Cluster ID
Cluster ID
Mn
60
Fe
DP2
0.07Cu
6x1019n/cm2
nm3
33 x 38 x 284
8.1M atoms
1.21 x 1023 m-3
2.87 x 10-3
3.40 nm
Nd
Vf
dG
20
Counts
Counts
Cu
P
Si
25
15
10
5
0
0.0
DP2
0.4
0.8
1.2
1.6
2.0
2.4
2.8
3.2
3.6
4.0
4.4
4.8
5.2
diameter (nm) (nm)
GuinierCluster
diameter
5.6
6.0
unknown
MoN
Sn
Co
100%
V
Composition (at.%)
Composition (at.%)
Si
Al
H
Cu
O
80%
As
Ni
P Ni
Si
Cu Mn
Mo
C
60%
Ni
40%
20%
V-weighted average
Simple average
RG Guinier D
(nm)
(nm)
1.48
3.83
1.32
3.40
Fe
61.7
59.8
Mn
5.3
5.5
Composition (at.%)
FeNi58
Ni
Cu
7.5
3.1
1.9
7.7
3.2
1.8
FeNi58
Si
8.7
8.9
P
0.7
0.7
Cr
Mn
Fe
0%
1
5
9
2007/09/29
13
17
21
25
29
33
37
41
45
49
53
57
61
65
69
Cluster ID
73
Cluster ID
77
81
85
89
93
97 101 105 109 113 117 121 125 129 133
61
Fe
25
0.03Cu
19n/cm2
6x10
Cu
Counts
Counts
20
41 x 49 x 264 nm3
11.2M atoms
P
Si
Nd 5.61 x 1022 m-3
Vf 1.13 x 10-3
dG 3.14 nm
15
10
5
0
0.0
CP2
0.4
0.8
1.2
1.6
2.0
2.4
2.8
3.2
3.6
4.0
4.4
4.8
Clusterdiameter
diameter (nm)
Cluster
(nm)
Composition (at.%)
Composition (at.%)
100%
5.2
5.6
6.0
Si
unknown
Cu
Cd
Sn
Co
Al
V
H
O
As
Mo
C
P
Si
Cu
Ni
FeNi58
Cr
Mn
Fe
Ni
Ni
Mn
80%
60%
40%
20%
RG
Guinier D
Composition (at.%)
(nm)
(nm)
Fe
Mn
FeNi58
Ni
Cu
Si
P
V-weighted average 1.48
Simple average
1.22
3.80
3.14
62.5
60.9
5.7
6.2
8.3
8.2
3.4
3.4
0.3
0.3
11.8
11.6
1.1
1.0
Fe
0%
1
6
11
2007/09/29
16
21
26
31
36
41
46
51
56
61
66
71
76
Cluster ID
Cluster ID
81
86
91
96 101 106 111 116 121 126 131 136 141
62
8
0.04Cu
3x1019n/cm2
6
5
Counts
Counts
Cu
P
Si
Nd 2.31 x 1022 m-3
Vf 4.51 x 10-4
dG 3.10 nm
7
43 x 52 x 194 nm3
9.6M atoms
4
3
2
1
0
0.0
0.4
0.8
1.2
1.6
2.0
2.4
2.8
3.2
3.6
4.0
4.4
4.8
5.2
5.6
6.0
Cluster
diameter (nm)
Cluster
diameter
(nm)
GF1
Composition (at.%)
Composition (at.%)
100%
unknown
Si
Cu
Co
Al
Ni
V
H
Ni
O
Mn
As
Cd
Sn
80%
60%
Mo
C
40%
20%
V-weighted average
Simple average
RG
(nm)
1.46
1.20
Guinier D
(nm)
3.78
3.10
Fe
60.8
59.2
Mn
6.2
6.7
Composition (at.%)
FeNi58
Ni
Cu
9.1
3.7
0.3
8.8
3.9
0.3
P
Si
Si
11.5
11.6
P
0.7
0.7
Cu
Ni
Fe
FeNi58
Cr
Mn
Fe
0%
1
3
5
2007/09/29
7
9
11 13 15 17 19
21 23 25 27 29 31 33 35
37 39 41 43 45 47 49 51 53
Cluster ID
Cluster ID
55 57 59 61 63 65 67 69
71 73
63
Are the Ni-Si-Mn clusters responsible for
embrittlement (hardening)?
280
DW0
DW2
等時焼鈍時間：30分
Holding time: 30min
400oC
450oC
500oC
600oC
240
Hv
ビッカース硬さ （Hv (1.0)）
260
220
200
180
0
50 100 150 200 250 300 350 400 450 500 550 600 650
温度 （℃） (oC)
Temperature
As irrad.
• Recovery of hardness
occurs at 500℃.
• Clusters becomes very
diffuse at the same
temperature.
2007/09/29
50x60x158 nm3
10.0M atoms
35x45x300 nm3
10.4M atoms
31x39x238 nm3
6.6M atoms
3
31x42x299 nm3 24x33x272
64 nm
8.6M atoms
5.1M atoms
Spacial Distribution Function, SDF(r)
Mean concentration of the element of interest as a function of the distance
from an atom of the element.

1
SDF r  
nr 
2
4r r
N
 n r 
k 1
k
r
r
SDF
SDF
nr 
1

N

r： <5nm
r：0.1nm
Uniform distribution
r
2007/09/29
clustering
r
65
Analysis of clustering using SDF
Cu_aRDF
Ni_aRDF
FeNi58_aRDF
Mn_aRDF
Si_aRDF
P_aRDF
C_aRDF
0.8
0.6
0.4
0.2
0
0.8
1
2
3
4
0.4
0.2
5
1
1
Cu_aRDF
Ni_aRDF
FeNi58_aRDF
Mn_aRDF
Si_aRDF
P_aRDF
C_aRDF
SDF (atoms/nm3)
SDF (atoms/nm3)
500℃
0.6
0.4
0.2
0
0
1
2
3
4
2007/09/29
radius /(nm)
nm
Distance
3
4
5
5
0.6
0.4
0.2
0
1
2
3
4
5
550℃
DW2-60_01219
Cu_aRDF
Ni_aRDF
FeNi58_aRDF
Mn_aRDF
Si_aRDF
P_aRDF
C_aRDF
0.8
0.6

0.4
0.2
0
Cu_aRDF
Ni_aRDF
FeNi58_aRDF
Mn_aRDF
Si_aRDF
P_aRDF
C_aRDF
radius /(nm)
nm
Distance
radius /(nm)
nm
Distance
DW2-50_01265
0.8
2
450℃
DW2-45_01236
0.8
0
0
radius /(nm)
nm
Distance
1
1
0.6
0
0
Cu_aRDF
Ni_aRDF
FeNi58_aRDF
Mn_aRDF
Si_aRDF
P_aRDF
C_aRDF
400℃
DW2-40_01261
SDF (atoms/nm3)
1
SDF (atoms/nm3)
SDF (atoms/nm3)
1
As Irrad.
DW2_00693

0
1
2
3
Distance
radius /(nm)
nm
4
5
Slope becomes very
weak at 500oC in
good correspondence
with the diffuse
clustering.
Ni-Si-Mn clusters
cause hardening.
66
Answer to “What is the nature of CEC?”

CEC is a Cu-Ni-Si-Mn cluster. The Cu content in the
cluster is affected very much by the bulk Cu content,
while Ni, Si and Mn contents are not affected by their
bulk contents and it can be a Ni-Si-Mn cluster without Cu
at very low Cu material. Thus it will be more appropriate
to call such clusters as “Solute-atom Clusters (SC)”.

The number density of SC becomes larger when Cu
content is high.

SC causes hardening, and thus embrittlement.

Further question: Why do Ni, Si and Mn form clusters
even though their solubility is very high in Fe-matrix? (cf:
Cu form clusters because of its low solubility.)

One possible answer: It is the irradiation induced segregation of
Ni, Si and Mn atoms on point defect clusters. (heterogeneous
nucleation)
Interaction between SC (CEC) and MD
2007/09/29
67
Issues to be studied

Do CEC and MD cause embrittlement?
 What
is the nature of MD?
 What
is the nature of CEC?

Are CEC and MD formed independently?

Does the contribution of CEC saturate?

What is the effect of temperature?

What is the effect of dose rate?
2007/09/29
68
Are SC (CEC) and MD formed independently?

Cu atoms beyond the solubility limit form precipitates in
high Cu materials.

This mechanism is independent of the MD formation.

Formation of Ni-Si-Mn clusters may be caused by
solute-atom segregation to point-defect clusters

What is the interaction between Cu and point defect
clusters?
2007/09/29
69
Precipitation of Cu on dislocations in Fe
LEAP analysis of
irradiated RPV steel
Clustering of Cu atoms
2007/09/29
on dislocations is evident.
KLMC
KLMC results of thermal ageing of Fe-Cu
crystal at 823K using the lattice sites
including two edge dislocations.
70
Interaction between Cu atoms and point
defect clusters

Computer simulations show strong binding between the Cu
atoms and point defect clusters of both vacancy and SIA.
vacancy
SIA
Cu atom
Cu atom
100 Vac &
100 Cu
20 SIA &
20 Cu
KLMC, with Metropolis algorithm, + MD results of the lowest
energy configuration of point defect – Cu atom clusters.
2007/09/29
71
Cu-vacancy clusters
Vacancy
Cu atom
100 Vac. & 10 Cu atoms
100 Vac. & 100 Cu atoms
• Cu atoms and
vacancies form
stable clusters.
• Central vacancy
cluster + Cu shell
10 Vac. & 10 Cu atoms
2007/09/29
10 Vac. & 100 Cu atoms
72
Cu-SIA clusters
Fe atom
Cu atom
Lattice site
4 SIAs & 1 Cu atoms
4 SIAs & 16 Cu atoms
2007/09/29
4 SIAs & 8 Cu atoms
A row of four Cu
atoms is a stable
configuration.
20 SIAs & 20 Cu atoms
73
Mechanism Cu-SIA cluster formation
Fe atom
Cu atom
Lattice site
Binding energy of
the Cu precipitate
and the SIA loop
~1.7eV
2007/09/29
74
Issues to be studied

Do CEC and MD cause embrittlement?
 What
is the nature of MD?
 What
is the nature of CEC?

Are CEC and MD formed independently?

Does the contribution of CEC saturate?

What is the effect of temperature?

What is the effect of dose rate?
2007/09/29
75
Issues to be studied

Do CEC and MD cause embrittlement?
 What
is the nature of MD?
 What
is the nature of CEC?

Are CEC and MD formed independently?

Does the contribution of CEC saturate?

What is the effect of temperature?

What is the effect of dose rate?
2007/09/29
76
Temperature effect on MD
Kinetic Monte Carlo Simulation
Experimental correlation
ASTM E 900-02
13
1.2 10
(T : 100 ~ 350oC)
R.B. Jones, T.J. Williams, Effects of
Radiation on Materials: 17th
International Symposium, ASTM STP
1270, American Society for Testing and
Mateirals, 1996, 569.
2007/09/29
1/2
d
-3
= A(2.9 - 4.6x10 T)(t)
1/2
12
6.0 10
12
1/2
4.0 10
1/2
FT  1.869  4.57 10 T
N
d
3
/ (t)
1/2
0.5
12
8.0 10
N
SMD  A  FT   t 
(m
Jones & Williams
dpa )
(T in
oF)
13
1.0 10
-3/2
 20,370  0.5076
  f
SMD  A  exp
 Tc  460
Vacancy cluster
SIA cluster
12
2.0 10
N
d
1/2
-3
= B(2.6 - 4.6x10 T)(t)
1/2
0
0.0 10
480
500
227℃
520
540
T (K)
560
580
600
620
307℃
77
Issues to be studied

Do CEC and MD cause embrittlement?
 What
is the nature of MD?
 What
is the nature of CEC?

Are CEC and MD formed independently?

Does the contribution of CEC saturate?

What is the effect of temperature?

What is the effect of dose rate?
2007/09/29
78
Dose Rate Effect in Low Cu Material
Transition temperature shift (oC)
Comparison of French surveillance
data and test reactor irradiation data
Comparison of test reactor data
irradiated at different fluxes
Fluence (x1019n/cm2)
in yield stress (MPa)
Increase硬化量（MPa）
60
50
40
高照射量
30
低照射量
20
10
CRIEPI/UCSB Joint Program
05
P. Petrequin, ASMES:1996. Report Number
6 EUR 16455 EN 1996.
中性子照射量
Fluence
低(~10 18 n/cm 2)
Low
High
高(~10 19 n/cm 2)
6
7 8 9
2
3
4
5
11
10
6
7 8 9
12
10
Dose rate (n/cm22 -s)
中性子照射速度（n/cm
-s）
No clear dose rate effect is observed in low Cu materials.
2007/09/29
79
Dose Rate Effect in High Cu Material
Low Dose Region 0.001
0.010
0.100
High Dose Region
High Cu
Low Cu
0.001
0.010
0.100
T.J. Williams, P.R. Burch,
C.A. English, and P.H.N.
Ray, 3rd Int. Symp. on
Environmental
Degradation of Materials
in Nuclear Power
Systems – Water
Reactors (1988), 121.
G.R. Odette, E.V. Mader, G.E. Lucas,
W.J. Phythian, C.A. English, ASTM STP
1175 (1994), 373.
Dose rate effect is evident in high Cu materials
2007/09/29
80
Detailed Comparison of Surveillance Data and
Test Reactor Irradiation Data of High Cu Material
0.24 wt.%Cu
80
SP1
70
Delta Tr30 (oC)
60
50
SPT2
Dose Rate (n/cm2-s)
~1x109
~2x1010
7x1011
40
SPT1
30
Surveillance (A)
20
Surveillance (W)
MTR
10
0
0.0E+00
5.0E+17
1.0E+18
1.5E+18
2.0E+18
2.5E+18
3.0E+18
Fluence (n/cm2)
Very clear dose rate effect is observed in the material
irradiated at very low dose rates.
2007/09/29
81
SP1
80
SP1
60
Cu
P
Counts
Counts
41 x 48 x 149 nm3
6.3M atoms
4.32 x 1023 m-3
4.39 x 10-3
2.58 nm
Nd
Vf
dG
70
50
Cu content
Bulk: 0.18at.%
Matrix: 0.11at.%
40
30
20
10
0
0.0
0.4
0.8
1.2
SP1
1.6
2.0
2.4
2.8
3.2
3.6
4.0
4.4
4.8
5.2
5.6
Guinier
Clusterdiamter
diameter (nm)(nm)
6.0
Si
100%
unknown
Cu
MoN
Sn
Composition (at.%)
(at.%)
Composition
80%
Co
Al
V
H
60%
Ni
Ni
O
As
Mo
Mn
C
40%
Guinier
(nm)
Fe
Size-weighted average
3.0
62.4
6.5
6.5
3.2
11.0
3.3
0.3
Ni
Simple average
2.6
61.6
6.5
5.9
3.2
11.2
3.7
0.2
Cr
Method
20%
Mn
FeNi58
Ni
Cu
Si
P
P
Si
(at.%)
Cu
FeNi58
Mn
Fe
0%
1
13
25
2007/09/29
37
49
61
73
85
97 109 121 133 145 157 169 181 193 205 217 229 241 253 265 277 289 301 313 325 337 349 361 373 385 397 409
Cluster ID
Cluster ID
82
Fe
TG1-L1
30
SPT1
Nd
Vf
dG
25
Cu
P
TG1-L1 01865:
24.1x28.6x175nm3
Count
Counts
20
2.7M atoms
2.94 x 1023 m-3
1.25 x 10-3
1.96 nm
15
10
5
0
0.0
0.4
0.8
1.2
1.6
TG1-L1
2.0
2.4
2.8
3.2
3.6
4.0
4.4
4.8
5.2
5.6
Guinier
diameter
Cluster
diameter (nm)(nm)
Si
100%
unknown
Cu
MoN
Composition (at.%)
(at.%)
Composition
Sn
80%
Co
Ni
Ni
H
Al
V
60%
O
As
Mn
Mo
C
40%
Guinier
(nm)
Fe
Size-weighted average
2.1
58.4
6.6
5.8
2.7
11.1
3.5
0.2
Simple average
2.0
56.8
6.8
6.0
2.7
11.7
3.7
0.2
Method
20%
Mn
FeNi58
Ni
Cu
Si
P
Si
(at.%)
Cu
Ni
Fe
FeNi58
Cr
Mn
0%
1
2007/09/29
P
6
11
16
21
26
31
36
41
46
51
56
61
Cluster ID
Cluster
ID
66
71
76
81
86
91
96
101 106 111
Fe
83
6.0
TG1-L2
30
SPT2
Nd
Vf
dG
25
Cu
P
TG1-L2 01849:
27.7x32.1x259nm3,
Count
Counts
20
5.1M atoms
6.37 x 1023 m-3
2.94 x 10-3
2.01 nm
15
10
5
0
0.0
TG1-L2
0.4
0.8
1.2
1.6
2.0
2.4
2.8
3.2
3.6
4.0
4.4
Guinier
diameter
Cluster
diameter (nm)(nm)
100%
4.8
5.2
5.6
Si
unknown
MoN
Sn
Cu
Co
Composition (at.%)
(at.%)
Composition
Al
Ni
O Ni
V
80%
H
As
Mo
60%
C
Mn
P
Si
40%
Guinier
(nm)
Fe
Size-weighted average
2.2
57.1
5.6
6.6
2.9
11.1
4.2
0.2
Simple average
2.0
55.0
5.8
6.9
3.1
11.7
4.3
0.3
Method
20%
Mn
FeNi58
Ni
Cu
Si
P
(at.%)
Cu
Ni
FeNi58
Cr
Mn
Fe
Fe
0%
1
2007/09/29
5
9
13
17
21
25
29
33
37
41
45
49
53
57
61
Cluster ID
Cluster ID
65
69
73
77
81
85
89
93
97 101 105 109 113 117
84
6.0
Estimation of the Number of Vacancy Jumps

Diffusion of vacancies leads to the diffusion of solute atoms
such as copper. We have two types of vacancies in the
irradiated metals:



Effect of dose rate on the number of vacancy jumps can be a
measure of the dose rate effect on the solute diffusion (and
clustering).


Irradiation-induced vacancy
Thermal vacancy
In KMC, we can count the number of vacancy jumps.
The number of thermal vacancy jumps can be estimated as:
 E
6
nth  t  2  D0  exp  

 kT
v
m
2007/09/29
3
  
 Sk
  2    exp 
 k
  a0 
v

E

f

exp




 kT



85
Dose rate effect on the number of vacancy jumps
- KMC study Irradiation time (s)
Number of vacancy jumps (x10 8)
10
50
10
10
9
10
8
10
7
10
6
10
5
10
4
10
3
10
2
Dose: 0.01 dpa
n-spectrum: fission
Temperature: 600K
40
Total vacancy jumps
30
20
Irradiation-induced vacancy jumps
10
Thermal vacancy jumps
0
10
-12
BWR
10
-11
10
-10
PWR
10
-9
10
-8
10
-7
10
-6
10
-5
10
-4
Dose rate (dpa/s)
At low dose rates, it is likely that the diffusion due to thermal vacancy may
contribute
to solute atom clustering.
86
2007/09/29
Dose rate effect at high dose region
10
25
Temperature: 600K
n-spectrum: Fission
Grain size: 10m
100
24
10
10-4-4dpa/s
dpa/s
80
10
23
-6-6
10
10 dpa/s
dpa/s
10
22
No stable
vacancy
cluster is
No stable
vacancy
cluster
-8
-8 10 -10dpa/s
at 10
dpa/s10
and
formed
below
dpa/s
10
21
10
-5
10
-4
10
-3
10
-2
10
-1
10
25
60
50
40
30

20
0
(Smoothed data)
Temperature: 600K
n-spectrum: Fission
Grain size: 10m
10
70
10
Dose (dpa)
Number density (m -3)
V (Osetsky, Bacon, Mohles, 2003)
I (b[-111])
I (b[1-11])
I (b[11-1])
I (b[111])
90
Critical angle (deg.)
Number density (m -3)
10
Obstacle strength of SIA loops (MD)
Vacancy
0
SIA
1
2
3
4
5
6
Diameter (nm)
24
SIA cluster > 37
-6
10-6
dpa/s
10
dpa/s
-4
-4
10 dpa/s
dpa/s
10
10
10
10
23
Dislocation Dynamics
Simulations
22
-10dpa/s
10-10
10
dpa/s
dpa/s
10 dpa/s
-8
10-8
21
10
-5
2007/09/29
10
-4
10
-3
Dose (dpa)
10
-2
10
-1
87
DD simulations of flux effect in Fe
3.5E+08
3.0E+08
Stress (Mpa)
2.5E+08
2.0E+08
1.5E+08
1.0E+08
1e-9dpa/s
1e-7dpa/s
1e-5dpa/s
5.0E+07
0.0E+00
0
0.0005
0.001
0.0015
0.002
0.0025
Strain
2007/09/29
88
Summary of Understanding on Embrittlement
Mechanism

Hardening due to the formation of solute atom clusters
(SCs) and dislocation loops (MD) is the primary
mechanism of embrittlement.

Formation of SC depends on the formation of MD.

Irradiation induced solute clustering model

Formation of MD is temperature dependent.

Dose rate effect exists in high Cu materials especially at
very low dose rates.
2007/09/29
89
Development of Embrittlement Correlation
Method

Two step modeling



Step 1: modeling of microstructural changes
Step 2: modeling of mechanical property change
Approach


2007/09/29
To formulate the microstructural changes by rate
equations.
To optimize the coefficients of the equations using
surveillance data.
90
Modeling of Microstructural Changes
ind
enh
C SC
C SC
C SC


t
t
t

Irradiation induced SC


Irradiation enhanced SC


mat
avail
0
  4  C Cu
 1  DCu   2  C MD   9  C Cu
 DCu  1   8  C Ni

2
C SC
C MD
2
  5  Ft 2   6   7  C Ni    
t
t
Effect of Tirrad
SC depends on MD
Effect of Ni
mat
enh
C Cu
C Sc
 v SC 
 v SC  C SC Cu available to form clusters decreases.
t
t
mat

avail
v SC   2  C Cu
 DCu
avail
Cu
C
0
  mat
sol
C

C
Cu
 Cu

2
 tr
avail
vSC  1  CCu
 DCu
C
C
C
C
mat
Cu
mat
Cu
CCu : amount of Cu in the matrix
avail : amount of Cu beyond the
CCu
sol
Cu
sol
Cu
solubility in the matrix
thermal
irrad
thermal
DCu  DCu
 DCu
 DCu
 1   2
2007/09/29
Thermal vacancy plays a role.
91
Correlation between microstructure and
mechanical property
100
80
T41J
60
40
20
0
0
0.02
0.04
0.06
0.08
Vf 1/2
2007/09/29
Transition temperature shift is almost proportional to Vf1/2
of solute atom clusters.
92
Modeling of Mechanical Property Change
Model of cluster size

  
mat
TSC  17  V f  17  16  f CCu
, C SC  g C Ni0  ht   C SC

mat
f CCu
, CSC

0
mat
CCu
 CCu
 12 
 13
CSC
   1    C 
gC
0
Ni
14

2
0 15
Ni
ht   10  1  11  DSC   t
DSC  DCu
TMD  18  CMD
T 
2007/09/29
TSC 2  TMD 2
Cu effect
Ni effect
SC contribution does not
saturate at least under test
reactor irradiation
1~18 :one set of coefficients is determined.
Total shift is NOT a simple sum of the two
contributions.
93
Comparison between the measured value
and the prediction
Method
140
120
予測値（℃） (oC)
Prediction
100
80
Std. Dev.
Mean Error
JEAC4201
11.9
-1.3
RG1.99ｒ2
15.4
-1.9
EWO
10.4
2.8
E900-02
11.7
2.3
CRIEPI
9.4
0.7
CRIEPI adj
5.4
0.1
60
40
補正なし
w/o
adjustment
w 補正あり
adjustment
プラント補正なし
1:1
プラント補正あり
-2σ
+2σ
20
0
-20
T
Offset
0
20
40
60
80
100
120
140
t
-20
2007/09/29
Measured
value (oC)
監視試験測定値（℃）
94
Summary

The mechanisms of neutron irradiation embrittlement of
RPVs are studies using multi-scale computer simulations
and experiments.

A new embrittlement correlation method to predict
transition temperature shifts is developed, in which the
understandings of the mechanisms were formulated using
the rate equations.

The above approach will be adopted in the revision of
JEAC4201 this year.
2007/09/29
95