Multiscale Computer Simulations and Predictive Modeling of rpv embrittlement Naoki Soneda



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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

  • Naoki Soneda

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



Irradiation Embrittlement of LWR RPV Steels



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.



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

  • 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’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



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



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

  • Mechanical property tests of neutron irradiated RPV steels

  • Nano-structural characterization

  • Multi-scale computer simulation



Nano-structural Characterization



Multi-scale Computer Simulation



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 –



Primary Knock-on Atom (PKA) Energy Spectrum



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



Small SIA & Small Vacancy Cluster



Large SIA & Small Vacancy Cluster



Large SIA & Large Vacancy Cluster (1)



Large SIA & Large Vacancy Cluster (2)



Large SIA & large vacancy cluster (3)



Channelling



Dispersed defect production



Summary of Cascade Database



Diffusivity

  • Diffusion simulation of a point defect by MD

  • Calculate Do and Em by MD



Diffusion Kinetics – Molecular Dynamics –











Binding Energies of Point Defect Clusters



Algorithm of KMC Simulation



Accumulation of Point Defect Clusters in Neutron Irradiated bcc-Fe



Microstructural evolution at different dose rates



Experimental observation of SIA loops – TEM observation –











Contribution of vacancy-type defects to embrittlement

  • Recoveries of Hv and S occur at different temperatures indicating that the vacancy type defect is not responsible for the Hv.



Summary of matrix damage



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



Formation of Cu-enriched Clusters



Thermal ageing of Fe-Cu-Ni-Mn-Si alloys



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



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.



Process of precipitation : KLMC result



Effect of Ni on cluster formation



Comparison between simulations and experiments

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



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



Hardening due to Cu precipitates – Molecular Dynamics –









What is the difference between the thermal ageing and irradiation?

  • 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.



0.12Cu 4x1019n/cm2



0.07Cu 6x1019n/cm2



0.03Cu 6x1019n/cm2



0.04Cu 3x1019n/cm2



Are the Ni-Si-Mn clusters responsible for embrittlement (hardening)?



Spacial Distribution Function, SDF(r)



Analysis of clustering using SDF

  • Slope becomes very weak at 500oC in good correspondence with the diffuse clustering.

  • Ni-Si-Mn clusters cause hardening.



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)


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?

  • 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



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.



Cu-vacancy clusters



Cu-SIA clusters



Mechanism Cu-SIA cluster formation



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 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



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 High Cu Material



Detailed Comparison of Surveillance Data and Test Reactor Irradiation Data of High Cu Material



SP1



SPT1



SPT2



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 at high dose region



DD simulations of flux effect in Fe



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

  • 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



Correlation between microstructure and mechanical property

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



Modeling of Mechanical Property Change



Comparison between the measured value and the prediction



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.





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