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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. MATGEN-IV Cargese, Corsica September 29, 2007.

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Multiscale Computer Simulations and Predictive Modeling of RPV Embrittlement

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  1. 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

  2. MATGEN-IV Cargese, Corsica September 29, 2007 Multiscale Modeling of RPV Embrittlement 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 80’s. Base Metal Weld Metal

  5. 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

  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 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

  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) <3x1018n/cm2 (60years, BWR) Neutron Fluence (n/cm2, E>1MeV)

  9. 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

  10. 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?

  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. ~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

  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. 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.

  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 @3.2ps @10.0ps Isolated subcascade formation Black dots : vacancies White circles : SIAs

  21. Large SIA & Small Vacancy Cluster Case 09 @0.1ps @11.0ps Overlapped subcascade formation (similar size subcascades) Black dots : vacancies White circles : SIAs

  22. Large SIA & Large Vacancy Cluster (1) Case 28 @3.2ps @10.2ps Overlapped subcascade formation (large & small subcascades) Black dots : vacancies White circles : SIAs

  23. 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

  24. 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>

  25. 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

  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. 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

  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 @ 500K 1.6ns @ 1000K 1D motion 1D motion + rotation (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. 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)

  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. 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.

  39. 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

  40. 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’)

  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 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.

  43. 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.

  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. 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

  47. ~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

  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 calculationsusing the VASP code. Vacancy – Solute Atom Binding Energy (eV) Vacancy – Solute Atom Binding Volume (A3)

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