Multiscale Computer Simulations and Predictive Modeling of RPV Embrittlement

1
Multiscale Computer Simulations and Predictive
Modeling of RPV Embrittlement
MATGEN-IV Cargese, Corsica September 29, 2007

• Naoki Soneda
• Central Research Institute of Electric Power
  Industry (CRIEPI), Japan

2
Multiscale Modeling of RPV Embrittlement
MATGEN-IV Cargese, Corsica September 29, 2007

• Naoki Soneda
• Central Research Institute of Electric Power
  Industry (CRIEPI), Japan

3
Irradiation Embrittlement of LWR RPV Steels
The accurate prediction of the transition
temperature shift is very important in ensuring
the structural integrity of reactor pressure
vessels.
Goal Development of an accurate embrittlement
correlation method to predict the transition
temperature shifts
PWR RPV
4
Current Embrittlement Correlation Equation
Prediction of Transition Temperature Shift

• US NRC
• Regulatory Guide 1.99 Rev.2
• JEAC4201-1991, Japan
• 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 80s.

Base Metal
Weld Metal
5
Activities in the 90s and 00s

• 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 90002 (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

6
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.

7
Activities in the 90s and 00s

• 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 90002 (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

8
Analysis of the Recent Surveillance Data
Current prediction Surveillance data
High Cu material
High Cu material Irradiated at low flux
Transition Temperature Shift
Low Cu material
Low Cu material Irradiated to high fluences
6x1019n/cm2 (40years, PWR)
1x1020n/cm2 (60years, PWR)
lt3x1018n/cm2 (60years, BWR)
Neutron Fluence (n/cm2, Egt1MeV)
9
Embrittlement Mechanism General Consensus

• Formation of Cu-enriched clusters (CEC)
• in high Cu materials
• CEC is associated with Ni, Mn and Si
• 23 nm in diameter
• obstacle to dislocation motion
• dose rate effect exists
• Formation of matrix damage (MD)
• 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

10
ASTM E 900-02
Is an exponential function appropriate?
Dose it saturate at high fluences?
Is there any other effect such as dose rate and
other elements?
11
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?

12
Approach

• Mechanical property tests of neutron irradiated
  RPV steels
• Nano-structural characterization
• Multi-scale computer simulation

13
Nano-structural Characterization
50nm
Transmission Electron Microscope (TEM)
LEAP (Local Electrode Atom Probe)
Positron Annihilation (Coincidence Doppler
Broadening)
Cu-enriched clusters formed by neutron irradiation
3-Dimensional Atom Probe
14
Multi-scale Computer Simulation
Molecular Dynamics Dislplacement cascade
Molecular Dynamics
Dislocation
10-11sec 10-8m
Kinetic Monte Carlo Microstructural evolution
during irradiation
109sec 10-7m
Dislocation Dynamics Dislocation behavior during
deformation
Dislocation loop
Radiation damage
Interaction between dislocation and damage
100sec 10-4m
Point defect production
Dislocation Dynamics Prediction of mechanical
property
Molecular Dynamics
100m
Vacancies
Irradiated
Unirradiated
Stress (MPa)
Cu atoms
Detailed analysis of microstructure
Strain ()
15
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?

16
Damage accumulation in bcc-Fe Kinetic Monte
Carlo (KMC) simulation
KMC tracks all the events.
Input Data

• 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.
17
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.
18
Displacement Cascade Simulation

• Molecular Dynamics
• Inter-atomic potential
• Ackland Potential
• ZBL pair potential is used for the short distance
  interaction
• Constant volume at a temperature of 600K
• 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

19
MD Simulation of Displacement Cascade
Volume (28.6nm)3 2,000,000 atoms
Vacancy
SIA
PKA energy 50keV
Wide variety of defect production is observed in
high energy cascades of 50keV, which is not be
observed in lower energy cascades.
20
Small SIA Small Vacancy Cluster
Case 45
_at_3.2ps
_at_10.0ps
Isolated subcascade formation
Black dots vacancies White circles SIAs
21
Large SIA Small Vacancy Cluster
Case 09
_at_0.1ps
_at_11.0ps
Overlapped subcascade formation (similar size
subcascades)
Black dots vacancies White circles SIAs
22
Large SIA Large Vacancy Cluster (1)
Case 28
_at_3.2ps
_at_10.2ps
Overlapped subcascade formation (large small
subcascades)
Black dots vacancies White circles SIAs
23
Large SIA Large Vacancy Cluster (2)
Case 39
_at_1.9ps
_at_12.1ps
70 SIAs
93 SIAs
234 vacancies
One large cascade is formed, and then
Black dots vacancies White circles SIAs
24
Large SIA large vacancy cluster (3)
_at_40.0ps
001
Cascade collapse occurred in a-Fe
110
Large SIA loop b a0/2 lt111gt
001
010
Case 39
Black dots vacancies White circles SIAs
Large vacancy loop b a0 lt100gt
25
Channelling
Case 31
lt112gt direction
Periodic boundary condition

• All the events occur on (110) plane.
• PKA is always the channeling particle in 20keV
  cascades.

Black dots vacancies White circles SIAs
26
Dispersed defect production

• Similar direction to channeling, but associated
  with many interactions
• Did not occur in 20keV cascades

Periodic boundary condition
Black dots vacancies White circles SIAs Gray
replaced atoms
Case 42
27
Summary of Cascade Database
100eV, 200eV, 500eV, 1keV, 2keV, 5keV, 10keV,
20keV, 50keV
20keV (50runs)
50keV (100runs)
Small clusters
Large SIA V clusters
Channeling
Large SIA clusters
Dispersed defect formation
28
Diffusivity

• Diffusion simulation of a point defect by MD
• Calculate Do and Em by MD

U
x
29
Diffusion Kinetics Molecular Dynamics
Diffusivity
1D motion of SIA clusters
Migration energy, Em
Rotation frequency
N. Soneda, T. Diaz de la Rubia, Phil. Mag. A, 81
(2001), 331.
30
MD Simulation of SIA Cluster (I3)
1.6ns _at_ 500K
1.6ns _at_ 1000K
1D motion rotation
1D motion
(lattice unit)
31
Diffusivities of SIA Clusters I1 I20
Diffusivity (cm2/s)
Diffusivity (cm2/s)
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.

32
Migration Energies of SIA Clusters
33
Rotation Frequency of Small Clusters
Activation energy of rotation for the I3 cluster
is high.
34
Binding Energies of Point Defect Clusters
N. Soneda, T. Diaz de la Rubia, Phil. Mag. A, 78
(1998), 995.
35
Algorithm of KMC Simulation
Diffusion Em Dissociation EbEm Disp.
cascade dose rate
Set all the possible events
Calculate event frequency
Choose one event
R Random()P
Repeat until target dose or time is reached
Update time
t -log(R) / P
Calculate interaction between the neighboring
particles (clustering, annihilation, etc.)
Do event
Bigmac (LLNL)
KineMon (CRIEPI / Univ. Tokyo)
36
Accumulation of Point Defect Clusters in Neutron
Irradiated bcc-Fe
350K
600K
37
Microstructural evolution at different dose rates
Vacancy
SIA
10-4dpa/s
10-6dpa/s
10-4dpa/s
10-6dpa/s
No stable vacancy cluster is formed below
10-8dpa/s
10-10dpa/s
10-8dpa/s

• 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.

38
Experimental observation of SIA loops TEM
observation
0.12Cu/0.58Ni4x1019n/cm2
0.68Cu/0.59Ni6x1019n/cm2
B011? 3g (g21-1)
B133? 3g (g-110)
Mean size 2.6 nm Number density 1.8x1022 m-3
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.

39
Dislocation Loop interaction

• Box size 371635nm (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
b111
011
t
b111
111
211
40
Dislocation Loop Edge Dislocation
Interaction Molecular Dynamics Simulation
I
IV
t 650MPa
t 50MPa
Repulsion
Superjog (II)
t 150MPa
t 250MPa
t 300,350,500MPa
II
III
II
Pinning
Superjog (I)
Superjog (I)
41
Type II Interaction
1
2
3
150MPa
Dislocation reacts with SIA loop
4
5
6
Dislocation is pinned. No bowing-out of the
dislocation is observed at this applied stress.
Superjog formation
Vacancies are left behind.
42
Details of Loop Dislocation Interaction
b1/2-1 1 1
Formation of Bridge Dislocation b 0 0 1
(1/2-1 1 11/21 1 1)
b1/21 -1 1
Trailing Bridge Dislocation b1/2-1 -1 1
b 0 0 1
Leading Bridge Dislocation b1/21 1 1
Pinning occurs at this stage.
43
Contribution of vacancy-type defects to
embrittlement
EPRI/CRIEPI Joint Program
Recovery of DS during PIA
Recovery of Hardness during PIA
Low Cu, BWR Irradiation
Low Cu, BWR Irradiation
DS is a measure of total amount of open volume.

• Recoveries of DHv and DS occur at different
  temperatures indicating that the vacancy type
  defect is not responsible for the DHv.

44
Summary of matrix damage
45
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?

46
3D Atom Probe
0.3x0.3x10mm
Electro-polish
Optical Microscope
500mm
Detector
Y
Fast light
Time of flight
Z
X
Needle tip
Element
Detection position
Slow heavy
3D position
Pulse voltage
47
Formation of Cu-enriched Clusters
40nm

• 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.

200nm

• What is the formation process?
• What happens in medium low Cu materials?

Cu Si
48
Thermal ageing of Fe-Cu-Ni-Mn-Si alloys
Cu Ni Mn Si C HL 0.3 0.6 1.4 0.2 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
Increase in Vickers Hardness (DHv)
aged at 350oC
LEAP measurement
Ageing time (hour)
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.

49
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

Energy change by vacancy jump
Jump probability
Migration energy
Activation energy
Pair interaction energy
Total energy of the crystal
Ordering parameter
Solubility
Vacancy migration energy vacancy binding energy
Choose one of the possible sites
50
Determination of KLMC parameters

• Binding energies between a vacancy and a solute
  atom in pure iron are obtained from first
  principles calculations using the VASP code.

Vacancy Solute Atom Binding Energy (eV)
Vacancy Solute Atom Binding Volume (A3)
51
Process of precipitation KLMC result
673K
573K
40nm
52
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
(d) 7.9x108sec
(b) 3.2x107sec
(a) 1.6x107sec
(c) 7.9x107sec
1.0at. Ni
(a) 1.6x107sec
(b) 3.2x107sec
(c) 7.9x107sec
(d) 7.9x108sec
Ni enhances the nucleation of clusters.
(at.)
53
Comparison between simulations and experiments
Simulation
Experiment
0.3Cu, 1.8Ni
Volume fraction (at.)
Ageing time (sec)

• Direct and quantitative comparison of the
  microstructural changes with experiments can be
  made.

54
Calculation Conditions

• Potential Ackland potential
• Edge dislocation ba/2111
• Cu precipitate size 1.55nm
• Box size
• 502456nm(6.0x106 atoms) for small Cu
• 503656nm(8.5x106 atoms) for large Cu
• Applied shear stress 350MPa
• Temperature 300K

Cu precipitate
t
Edge dislocation
ba/2111
011
y
t
111
x
z
211
55
Hardening due to Cu precipitates Molecular
Dynamics
bow-out distance
Maximum bow-out distance (nm)
4nm Cu ppt 350MPa shear stress
Diameter of Cu ppt (nm)
56
Interaction Process (Small Precipitate)
011
Simple Shear
111
57
Interaction Process (Large Precipitate)
111
211
(011)
Atom stacking below/on/above the slip plane
changes from bcc to fcc-like structure.
58
Dislocation Motion at Break-out
Pure edge
Pure screw
Original slip plane
Motion of screw dislocation
Top view
Super jog formation
59
What is the difference between the thermal ageing
and irradiation?
Neutron irradiation
Thermal ageing
Composition
Composition
Cluster number
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.

60
0.12Cu4x1019n/cm2
Nd 2.24 x 1023 m-3 Vf 4.16 x 10-3 dG 3.07 nm
35 x 41 x 491 nm3 13.7M atoms
Cu P
Si
Cu
Ni Ni
Composition (at.)
Mn
Fe
Cluster ID
61
0.07Cu6x1019n/cm2
Nd 1.21 x 1023 m-3 Vf 2.87 x 10-3 dG 3.40 nm
Cu P Si
33 x 38 x 284 nm3 8.1M atoms
Si
Cu
Ni Ni
Mn
Composition (at.)
Fe
Cluster ID
62
0.03Cu6x1019n/cm2
Nd 5.61 x 1022 m-3 Vf 1.13 x 10-3 dG 3.14 nm
Cu P Si
41 x 49 x 264 nm3 11.2M atoms
Si
Cu
Ni Ni
Mn
Composition (at.)
Fe
Cluster ID
63
0.04Cu3x1019n/cm2
Nd 2.31 x 1022 m-3 Vf 4.51 x 10-4 dG 3.10 nm
Cu P Si
43 x 52 x 194 nm3 9.6M atoms
Si
Cu
Ni Ni
Mn
Composition (at.)
Fe
Cluster ID
64
Are the Ni-Si-Mn clusters responsible for
embrittlement (hardening)?
400oC
450oC
500oC
600oC
Holding time 30min
DHv
Temperature (oC)
As irrad.

• Recovery of hardness occurs at 500?.
• Clusters becomes very diffuse at the same
  temperature.

35x45x300 nm3 10.4M atoms
50x60x158 nm3 10.0M atoms
31x39x238 nm3 6.6M atoms
31x42x299 nm3 8.6M atoms
24x33x272 nm3 5.1M atoms
65
Spacial Distribution Function, SDF(r)
Mean concentration of the element of interest as
a function of the distance from an atom of the
element.

• r lt5nm
• Dr0.1nm

SDF
SDF
Uniform distribution
clustering
r
r
66
Analysis of clustering using SDF
450?
400?
As Irrad.
SDF (atoms/nm3)
SDF (atoms/nm3)
SDF (atoms/nm3)
Distance (nm)
Distance (nm)
Distance (nm)
500?
550?

• Slope becomes very weak at 500oC in good
  correspondence with the diffuse clustering.
• Ni-Si-Mn clusters cause hardening.

SDF (atoms/nm3)
SDF (atoms/nm3)
Distance (nm)
Distance (nm)
67
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
68
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?

69
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?

70
Precipitation of Cu on dislocations in Fe
LEAP analysis of irradiated RPV steel
KLMC
KLMC results of thermal ageing of Fe-Cu crystal
at 823K using the lattice sites including two
edge dislocations.
Clustering of Cu atoms on dislocations is evident.
71
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.

SIA
vacancy
Cu atom
Cu atom
20 SIA 20 Cu
100 Vac 100 Cu
KLMC, with Metropolis algorithm, MD results of
the lowest energy configuration of point defect
Cu atom clusters.
72
Cu-vacancy clusters
Vacancy
Cu atom

• Cu atoms and vacancies form stable clusters.
• Central vacancy cluster Cu shell

100 Vac. 10 Cu atoms
100 Vac. 100 Cu atoms
10 Vac. 10 Cu atoms
10 Vac. 100 Cu atoms
73
Cu-SIA clusters
Fe atom
Cu atom
Lattice site
A row of four Cu atoms is a stable configuration.
4 SIAs 1 Cu atoms
4 SIAs 8 Cu atoms
4 SIAs 16 Cu atoms
20 SIAs 20 Cu atoms
74
Mechanism Cu-SIA cluster formation
Fe atom
Cu atom
Lattice site
Binding energy of the Cu precipitate and the SIA
loop 1.7eV
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?

76
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?

77
Temperature effect on MD
Kinetic Monte Carlo Simulation
Experimental correlation
ASTM E 900-02
(T in oF)
Jones Williams
(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.
227?
307?
78
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?

79
Dose Rate Effect in Low Cu Material
Comparison of French surveillance data and test
reactor irradiation data
Comparison of test reactor data irradiated at
different fluxes
Fluence
Low
High
Transition temperature shift (oC)
Increase in yield stress (MPa)
CRIEPI/UCSB Joint Program
Fluence (x1019n/cm2)
P. Petrequin, ASMES1996. Report Number 6 EUR
16455 EN 1996.
Dose rate (n/cm2-s)
No clear dose rate effect is observed in low Cu
materials.
80
Dose Rate Effect in High Cu Material
Low Dose Region
High Dose Region
High Cu
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.
Low Cu
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
81
Detailed Comparison of Surveillance Data and Test
Reactor Irradiation Data of High Cu Material
0.24 wt.Cu
Dose Rate (n/cm2-s) 1x109 2x1010 7x1011
Very clear dose rate effect is observed in the
material irradiated at very low dose rates.
82
SP1
Nd 4.32 x 1023 m-3 Vf 4.39 x 10-3 dG 2.58 nm
Cu P
41 x 48 x 149 nm3 6.3M atoms
Cu content Bulk 0.18at. Matrix 0.11at.
Si
Cu
Ni Ni
Mn
Composition (at.)
Fe
Cluster ID
83
SPT1
Nd 2.94 x 1023 m-3 Vf 1.25 x 10-3 dG 1.96 nm
Cu P
Count
TG1-L1 01865 24.1x28.6x175nm3 2.7M atoms
Guinier diameter (nm)
Si
Cu
Ni Ni
Composition (at.)
Mn
Fe
Cluster ID
84
SPT2
Nd 6.37 x 1023 m-3 Vf 2.94 x 10-3 dG 2.01 nm
Cu P
Count
TG1-L2 01849 27.7x32.1x259nm3, 5.1M atoms
Si
Guinier diameter (nm)
Cu
Ni Ni
Mn
Composition (at.)
Fe
Cluster ID
85
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
• Irradiation-induced vacancy
• Thermal vacancy
• 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).
• In KMC, we can count the number of vacancy jumps.
• The number of thermal vacancy jumps can be
  estimated as

86
Dose rate effect on the number of vacancy jumps-
KMC study -
BWR
PWR
At low dose rates, it is likely that the
diffusion due to thermal vacancy may contribute
to solute atom clustering.
87
Dose rate effect at high dose region
Obstacle strength of SIA loops (MD)
Dislocation Dynamics Simulations
88
DD simulations of flux effect in Fe
89
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.

90
Development of Embrittlement Correlation Method

• Two step modeling
• Step 1 modeling of microstructural changes
• Step 2 modeling of mechanical property change
• Approach
• To formulate the microstructural changes by rate
  equations.
• To optimize the coefficients of the equations
  using surveillance data.

91
Modeling of Microstructural Changes
Irradiation induced SC
Irradiation enhanced SC
Effect of Tirrad
Effect of Ni
SC depends on MD
Cu available to form clusters decreases.
amount of Cu in the matrix
amount of Cu beyond the solubility in the
matrix
Thermal vacancy plays a role.
92
Correlation between microstructure and mechanical
property

• Transition temperature shift is almost
  proportional to Vf1/2 of solute atom clusters.

93
Modeling of Mechanical Property Change
Model of cluster size
Cu effect
Ni effect
SC contribution does not saturate at least under
test reactor irradiation
x1 x18 one set of coefficients is determined.
Total shift is NOT a simple sum of the two
contributions.
94
Comparison between the measured value and the
prediction
Prediction (oC)
w/o adjustment
w adjustment
Measured value (oC)
95
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.