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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.

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multiscale computer simulations and predictive modeling of rpv embrittlement

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

multiscale modeling of rpv embrittlement

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
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

current embrittlement correlation equation prediction of transition temperature shift
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 80’s.

Base Metal

Weld Metal

activities in the 90 s and 00 s
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
surveillance data
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.
activities in the 90 s and 00 s7
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
analysis of the recent surveillance data
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)

<3x1018n/cm2

(60years, BWR)

Neutron Fluence (n/cm2, E>1MeV)

embrittlement mechanism general consensus
Embrittlement Mechanism– General Consensus –
  • Formation of Cu-enriched clusters (CEC)
    • 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
  • 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
astm e 900 02

Are the formation of SMD(MD) and CRP(CEC) independent?

Total

SMD

DT

Is the linear sum approximation appropriate?

CRP

No effect of chemical composition?

f1/2

Is it product-form dependent?

Is the threshold value appropriate

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?

issues to be studied
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?
approach
Approach
  • Mechanical property tests of neutron irradiated RPV steels
  • Nano-structural characterization
  • Multi-scale computer simulation
nano structural characterization

~40 nm

~300 nm

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

multi scale computer simulation
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 (%)

issues to be studied15
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?
damage accumulation in bcc fe kinetic monte carlo kmc simulation

Defect production

Diffusion

10-9-10-8m

~10-11s

Clustering

10-9-10-7m

10-12-10-8s

Cluster diffusion

Dissociation

~10-5m

Formation and growth of loops

10-6-10-3m

Microstructure evolution

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.

primary knock on atom pka energy spectrum
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.

displacement cascade simulation
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

md simulation of displacement cascade
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.

small sia small vacancy cluster
Small SIA & Small Vacancy Cluster

Case 45

@3.2ps

@10.0ps

Isolated subcascade formation

Black dots : vacancies

White circles : SIAs

large sia small vacancy cluster
Large SIA & Small Vacancy Cluster

Case 09

@0.1ps

@11.0ps

Overlapped subcascade formation

(similar size subcascades)

Black dots : vacancies

White circles : SIAs

large sia large vacancy cluster 1
Large SIA & Large Vacancy Cluster (1)

Case 28

@3.2ps

@10.2ps

Overlapped subcascade formation

(large & small subcascades)

Black dots : vacancies

White circles : SIAs

large sia large vacancy cluster 2
Large SIA & Large Vacancy Cluster (2)

Case 39

@1.9ps

@12.1ps

70 SIAs

93 SIAs

234 vacancies

One large cascade is formed, and then …

Black dots : vacancies

White circles : SIAs

large sia large vacancy cluster 3
Large SIA & large vacancy cluster (3)

@40.0ps

[001]

Cascade collapse occurred in a-Fe

[110]

Large SIA loop

b = a0/2<111>

[001]

[010]

Case 39

Black dots : vacancies

White circles : SIAs

Large vacancy loop

b = a0 <100>

channelling
Channelling

Case 31

<112> 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

dispersed defect production
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

summary of cascade database

53%

15%

5

%

17%

10%

2%

80%

10%

8%

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

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

U

x

diffusion kinetics molecular dynamics
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.

slide30

MD Simulation of SIA Cluster (I3)

1.6ns @ 500K

1.6ns @ 1000K

1D motion

1D motion + rotation

(lattice unit)

slide31

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.
slide33

Rotation Frequency of Small Clusters

Activation energy of rotation for the I3 cluster is high.

binding energies of point defect clusters
Binding Energies of Point Defect Clusters

N. Soneda, T. Diaz de la Rubia, Phil. Mag. A, 78 (1998), 995.

algorithm of kmc simulation

P = SNi Pi

i

Algorithm of KMC Simulation

Diffusion Em

Dissociation Eb+Em

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

KineMon (CRIEPI / Univ. Tokyo)

Bigmac (LLNL)

microstructural evolution at different dose rates
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.
experimental observation of sia loops tem observation

50nm

50nm

Experimental observation of SIA loops– TEM observation –

0.12Cu/0.58Ni4x1019n/cm2

0.68Cu/0.59Ni6x1019n/cm2

B=[133]、 3g (g=-110)

B=[011]、 3g (g=21-1)

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.
slide39

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

t

b=[111]

111

211

slide40

Dislocation Loop – Edge Dislocation Interaction

Molecular Dynamics Simulation

I

IV

t = 50MPa

t = 650MPa

Repulsion

Superjog (II)

t = 150MPa

t = 250MPa

t = 300,350,500MPa

II

III

II’

Superjog (I)

Pinning

Superjog (I’)

slide41

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.

slide42

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.

contribution of vacancy type defects to embrittlement
Contribution of vacancy-type defects to embrittlement

EPRI/CRIEPI Joint Program

Recovery of DS during PIA

Recovery of Hardness during PIA

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

Low Cu, BWR Irradiation

Low Cu, BWR Irradiation

DS is a measure of total amount of open volume.

issues to be studied45
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?
3d atom probe

TEM

50nm

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

formation of cu enriched clusters

~40nm

Formation of Cu-enriched Clusters
  • 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

thermal ageing of fe cu ni mn si alloys
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.
computer simulation of the thermal ageing kinetic lattice monte carlo klmc simulation
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

determination of klmc parameters
Determination of KLMC parameters
  • Binding energies between a vacancy and a solute atom in pure iron are obtained from first principles calculationsusing the VASP code.

Vacancy – Solute Atom Binding Energy (eV)

Vacancy – Solute Atom Binding Volume (A3)

effect of ni on cluster formation

Cu

Ni

Mn

Si

:

:

:

:

0.3

1.0 or 1.8

1.4

0.9

Effect of Ni on cluster formation

Cu : 0.3, Mn 1.4, Si 0.9 (at.%)

8760hrs = 3.15x107sec

1.8at.% Ni

Nd ~ 6.8x1023 m-3

(d) 7.9x108sec

(b) 3.2x107sec

(a) 1.6x107sec

(c) 7.9x107sec

1.0at.% Ni

(b) 3.2x107sec

(a) 1.6x107sec

(c) 7.9x107sec

(d) 7.9x108sec

Ni enhances the nucleation of clusters.

(at.%)

comparison between simulations and experiments
Comparison between simulations and experiments

Simulation

Experiment

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

0.3Cu, 1.8Ni

Volume fraction (at.%)

Ageing time (sec)

calculation conditions
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

τ

111

x

z

211

hardening due to cu precipitates molecular dynamics
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)

slide57

Interaction Process (Large Precipitate)

111

211

(011)

Atom stacking below/on/above the slip plane changes from bcc to fcc-like structure.

slide58

Dislocation Motion at Break-out

Pure edge

Pure screw

Original slip plane

Motion of screw dislocation

Top view

Super jog formation

what is the difference between the thermal ageing and irradiation
What is the difference between the thermal ageing and irradiation?

Neutron irradiation

Thermal ageing

  • 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.

Composition

Composition

Cluster number

Cluster number

0 12cu 4x10 19 n cm 2

Counts

Cluster diameter (nm)

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

0 07cu 6x10 19 n cm 2

Counts

Guinier diameter (nm)

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

0 03cu 6x10 19 n cm 2

Counts

Cluster diameter (nm)

Nd 5.61 x 1022 m-3

Vf 1.13 x 10-3

dG 3.14 nm

0.03Cu6x1019n/cm2

Cu

P

Si

41 x 49 x 264 nm3

11.2M atoms

Si

Cu

Ni

Ni

Mn

Composition (at.%)

Fe

Cluster ID

0 04cu 3x10 19 n cm 2

Counts

Cluster diameter (nm)

Nd 2.31 x 1022 m-3

Vf 4.51 x 10-4

dG 3.10 nm

0.04Cu3x1019n/cm2

Cu

P

Si

43 x 52 x 194 nm3

9.6M atoms

Si

Cu

Ni

Ni

Mn

Composition (at.%)

Fe

Cluster ID

are the ni si mn clusters responsible for embrittlement hardening
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.

50x60x158 nm3

10.0M atoms

35x45x300 nm3

10.4M atoms

31x39x238 nm3

6.6M atoms

31x42x299 nm3

8.6M atoms

24x33x272 nm3

5.1M atoms

spacial distribution function sdf r
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: <5nm
  • Dr:0.1nm

SDF

SDF

Uniform distribution

clustering

r

r

analysis of clustering using sdf
Analysis of clustering using SDF

450℃

400℃

As Irrad.

  • 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)

SDF (atoms/nm3)

Distance (nm)

Distance (nm)

Distance (nm)

500℃

550℃

SDF (atoms/nm3)

SDF (atoms/nm3)

Distance (nm)

Distance (nm)

answer to what is the nature of cec
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

issues to be studied68
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?
are sc cec and md formed independently
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?
precipitation of cu on dislocations in fe
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.

interaction between cu atoms and point defect clusters
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.

cu vacancy clusters
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

cu sia clusters
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

mechanism cu sia cluster formation
Mechanism Cu-SIA cluster formation

Fe atom

Cu atom

Lattice site

Binding energy of the Cu precipitate and the SIA loop ~1.7eV

issues to be studied75
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?
issues to be studied76
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?
temperature effect on md
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℃

issues to be studied78
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?
dose rate effect in low cu material
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, ASMES:1996. Report Number 6 EUR 16455 EN 1996.

Dose rate (n/cm2-s)

No clear dose rate effect is observed in low Cu materials.

dose rate effect in high cu material
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

detailed comparison of surveillance data and test reactor irradiation data of high cu material
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.

slide82
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

slide83
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

slide84
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

estimation of the number of vacancy jumps
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:
dose rate effect on the number of vacancy jumps kmc study
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.

dose rate effect at high dose region
Dose rate effect at high dose region

Obstacle strength of SIA loops (MD)

Dislocation Dynamics

Simulations

summary of understanding on embrittlement mechanism
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.
development of embrittlement correlation method
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.
modeling of microstructural changes
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.

correlation between microstructure and mechanical property
Correlation between microstructure and mechanical property

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

modeling of mechanical property change
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.

comparison between the measured value and the prediction

プラント補正なし

プラント補正あり

Comparison between the measured value and the prediction

Prediction (oC)

w/o adjustment

w adjustment

Measured value (oC)

summary
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.