Multiscale Modelling of Microstructure Evolution under Radiation ...

Centre of Excellence for Nuclear Materials

Workshop Materials Innovation for Nuclear Optimized Systems

December 5-7, 2012, CEA – INSTN Saclay, France

Christophe DOMAIN EDF R&D (France)

Multiscale Modelling of Microstructure Evolution under Radiation Damage of Steels Based on Atomistic to Mesoscale Methods

Workshop organized by: Christophe GALLÉ, CEA/MINOS, Saclay – [email protected] Constantin MEIS, CEA/INSTN, Saclay – [email protected]

Article available at http://www.epj-conferences.org or http://dx.doi.org/10.1051/epjconf/20135102004

EPJ Web of Conferences 51, 02004 (2013) DOI: 10.1051/epjconf/20135102004 © Owned by the authors, published by EDP Sciences, 2013

Workshop Materials Innovation for Nuclear Optimized Systems December 5-7, 2012, CEA – INSTN Saclay, France

Multiscale Modelling of Microstructure Evolution under Radiation Damage of Steels Based on Atomistic to Mesoscale Methods Christophe DOMAIN1, 2 1

2

EDF R&D - MMC (Moret sur Loing, France) EDF-CNRS joint laboratory EM2VM (Study and Modeling of the Microstructure for Ageing of Materials)

Structural metallic materials used in nuclear facilities are submitted to irradiation which induce the creation of large amounts of point defects, which leads to modifications of the microstructure and the mechanical properties. In nuclear power plants, the main structural materials are: the pressure vessel (ferritic steels), the internal structure (austenitic steels). In order to simulate the microstructure evolution with the objective to predict it, multiscale modelling tools are developed (Fig. 1). For this purpose different simulation methods are used and developed in order to treat the different physical phenomena occurring at different time scales and length scales: ab initio, classical molecular dynamics, kinetic Monte Carlo, dislocation dynamics, phase field [1]. These simulations are very CPU demanding and take advantage of the development of High Performance Computing machines.

1nm3 0 - ps m3

(10-30nm)3

ab initio

ns

Molecular dynamics

40 years

Multi-scale modelling

Finite elements

s-h

cm3

Micro-macro

 (30-100nm)3

µm3 h-year

Dislocation dynamics



Mesoscopic

This is an Open Access article distributed under the terms of the Creative Commons Attribution License 2.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Workshop Materials Innovation for Nuclear Optimized Systems December 5-7, 2012, CEA – INSTN Saclay, France

Fig. 1: Multiscale modelling scheme applied within the PERFORM-60 project to the pressure vessel and internal material microstructure.

The microstructure evolution under irradiation is obtained starting from the neutron spectrum to obtain the primary damage (displacement cascades), followed by the evolution of the point defects formed and their accumulation (Fig. 2).

Flux (n/cm2/s)

1.E+11 1.E+10 1.E+09 1.E+08 1.E-08 1.E-06 1.E-04 1.E-02 1.E+0 1.E+0 0 2

1.E+04 PKA Flux (PKA/µm3/MeV/s)

Spectre de neutron 1.E+12

1.E+01

1.E-02 PWR 1.E-05

1.E-08 1E-05

1E-04

1E-03

1E-02

1E-01

1E+00 1E+01

EPKA(MeV)

Neutron spectrum

PKA spectrum

Primary damage

Short term evolution

Exper. resolvable defects

Interactions defects dislocations

Fig. 2: Microstructure modelling under irradiation.

The point defects created (vacancy and self interstitials) under irradiation often interact with the solute elements present in the materials. Solutes can precipitate and/or segregate on point defect clusters (loops or voids) or extended defects (dislocations, grain boundaries). These modifications of the microstructure affect directly the mechanical properties of the materials. Thus, modelling should take into account the most important solute elements in the chemical composition of the industrial alloys. For the pressure vessel steels (for which an important international efforts is done in particular thanks to the PERFECT [2] and PERFORM-60 european projects) the evolution of the microstructure of dilute Fe alloys as complex as Fe-CuNiMnSiP-C under irradiation are modelled using a multiscale approach based on ab initio, molecular dynamics and kinetic Monte Carlo (KMC) simulations. In these atomic KMC simulations, both self interstitials and vacancies, isolated or in clusters, as well as carbon atoms are modelled [3]. The short term evolution of the microstructure is simulated. The medium to long term evolution of the microstructure is obtained by object KMC and cluster dynamics, considering a “grey” material. The interaction of some of these defects with dislocations are characterised by molecular dynamics in order to be used in mesoscopic dislocation dynamics. A similar approach is developed for austenitic materials modelled by a concentrated FeCrNi alloy (γFe70Cr20Ni10). The thermal ageing (without irradiation) of FeCr alloys will also be presented. In the framework of the european projects dedicated to the pressure vessel steels and the austenitic steels, the multiscale modelling methods of the microstructure have been capitalised within two tools (RPV and INTERN) [4].

References [1] C. S. Becquart, C. Domain, Metallurgical and Materials Transactions A 42 (2011) 852. [2] Spetial Issue: PERFECT project. Journal of Nuclear Materials, 406 (2010). [3] C.S. Becquart, C. Domain, Phys. Status Solidi B 247 (2010) 9. [4] G. Adjanor et al., J. Nucl. Mater 406 (2010) 175.

Workshop Materials Innovation for Nuclear Optimized Systems MINOS, Saclay, Dec 2012

P ERFORM 6 0 F P 7 P r o jjee c t

Multiscale Modelling of Microstructure Evolution under Radiation Damage of Steels Based on Atomistic to Mesoscale Methods C. Domain1, C.S. Becquart2, G. Adjanor1, G. Monnet1, J.B. Piochaud2, R. Ngayam-Happy1,2 1 EDF R&D Dpt Matériaux & Mécanique des Composants Les Renardieres, Moret sur Loing, France 2 UMET, Université de Lille 1 Villeneuve d’Ascq, France

Lifetime extension: Materials ageing prediction • To improve quantitative predictions

of ageing of irradiated structural materials in nuclear power plants in order to gain margins. • Challenge: to predict the evolution

of hundred of tons over more than 40 years based on physical phenomena occurring at the nanometer scale and picosecond times (10-12 s) • Construction and improvement of

multiscale modelling methods allowing to better take into account the material composition and radiation damage

2

EDF R&D - Workshop MINOS - Saclay Dec 2012

Microstructure evolution of Fe alloys under irradiation Si P Mn Ni Cu

30 × 30 × 140 nm3 Si+P+Mn+Ni+Cu

RPV Fe ferritic alloys 25 nm

- plasticity

3 nm

25 nm

[H. Huang PhD SAT@GPM Rouen]

Austenitic alloys - FeNiCr AKMC RIS modelling

[A. Volgin PhD SAT@GPM Rouen ] EDF R&D - Workshop MINOS - Saclay Dec 2012

8 nm

29 nm

- microstructure modelling short & long term evolution

3

3 nm

1nm3 0 - ps m3

(10-30nm)3

ns

ab initio

40 years

Molecular dynamics

Multi-scale modelling

Finite elements

s-h

cm3

Barbu, CEA

+ experimental validation

Pareige, U. Rouen


KMC cohesive model & parameterisation

Micro-macro (30-100nm)3 µm3 h-year

Dislocation dynamics 4


Mesoscopic

Prog. de surveillance

Simulation tools Positon annhilation

SANS

Microscopy and chemical analysis

Time

h-year

Finite Elements 0.4 µm

Mesoscopic

Tomographic atom probe

(grain, set of grains)

Dislocation Dynamics

Kinetic Monte Carlo (diffusion) [Rate theory/cluster dynamics] (cf. T Jourdan)

s-h

Classical Molecular Dynamics ns

(atomic forces derived from empirical potentials)

Elementary Mecanisms

ab initio (forces and energies determined from the electronic structure -- Density Functional Theory (DFT))

0 - ps

1nn 001 100

System size

1nn

1nm3 5

(10-30nm)3


(30-100nm)3

µm3

cm3

Atomic Kinetic Monte Carlo of microstructure evolution Objective: Simulation formation of solute rich complexes (observed by TAP) under irradiation

Ni

Mn

Si

Cu

TAP, Pareige, U. Rouen

15x15x50 nm

Ab initio

εFe-V_1nn

Solute interactions (Cu, Ni, Mn, Si) (interface energies, mixing energies …)

Experimental data and Thermodynamical data

AKMC εFe-Si_2nn

Solute diffusion by - vacancy mechanisms - interstitial mechanisms

Parameterisation cohesive model

1) (2) (1) ( 2) (1) (2) Emixing = −4ε ((Fe − Fe ) − 3ε ( Fe − Fe ) + 8ε ( Fe − X ) + 6ε ( Fe − X ) − 4ε ( X − X ) − 3ε ( X − X )

E formation (V Z ) = 8ε ((V1)− Z ) + 6ε ((V2)− Z ) − 4ε ((Z1)− Z ) − 3ε ((Z2)− Z ) (1) (1) (1) (1) (1) Ebinding (V − X ) = ε ( Fe −V ) + ε ( Fe − X ) − ε ( Fe − Fe ) − ε (V − X )

Experimental validation: TAP, SANS, SAXS, PA, TEP 6


Atomistic Kinetic Monte Carlo (AKMC) Vincent et al. NIMB 255 (2007) 78 Vincent et al. JNM 382 (2008) 154

Treatment of multi-component systems on a rigid lattice

Substitutional elements Interstitial elements

Code: LAKIMOCA

Diffusion by 1nn jumps

Via vacancies Via interstitials

Jump Probability:

 Ea  ΓX = ν X exp −  kT  

νX = attempt frequency

Residence Time Algorithm applied to all events

Vacancy and Interstitial jumps Frenkel Pairs and Cascade flux for irradiation

Γ1,2

v2

v1

1 Average time step: ∆t = ∑ Γ jk

Γ3,1

Γ2,2

v3 Γ2,1

Γ1,1

Γ3,2 Γ3,2

j ,k Γ1,1

Environment dependant form of activation energy Ea

Ea = Ea ( X i ) + 7


Γ1,8 Γ2,1

Ef − Ei 2

Γ2,7

Γ3,7

AKMC irradiation simulation conditions For electron irradiation: Frenkel Pair (FP) flux For neutron irradiation: flux of • 20 keV and 100 keV cascades debris obtained by Molecular Dynamics (R. Stoller, J. Nucl. Mater. 307-311 (2002) 935)

• Frenkel Pairs cascades Cascades

surface

Typical simulation box:

PBC

PBC

1.01 × 10-17 cm3 boxes 8.65 106 atoms

Frenkel Paires de

pairs Frenkel

surface

8


8

Cohesive energy model (bcc) Ea = Ea( X i ) + Ef Vacancy:

εFe-V_1nn

− Ei 2

i) (i ) (i) (i ) (i ) (i ) E = ∑ ε ((Fe − Fe ) + ∑ ε (V −V ) + ∑ ε ( Fe −V ) + ∑ ε ( Fe − X ) + ∑ ε (V − X ) + ∑ ε ( X −Y ) j

k

εFe-Si_2nn

l

m

n

p

• RPV: 1nn and 2nn pair interactions • FeCr: 2BM potential

• solute - dumbbell

El1nnComp (dumbi − X j )

Elmixed ( X j − X k )

El1nnTens ( X j )

+

+

SIA: Eb (dumb - dumb) 1nn & 2nn

• dumbbell - dumbbell

Solute atoms Fe atom

  E dumb = ∑  E f + ∑ E l1nnComp (dumbi − X j ) + ∑ E l1nnTens ( X j ) + ∑ E lmixte ( X j − X k ) + ∑ E l (dumb − dumb)  i  j j i, j 

+

FIA (C): FIA

+ vacancy

+ solute

SIA

~ 100 ab initio data considered in the model 9


9

Cohesive model: εX-Y and εV-X determination Binary alloys

• • • •

2) (1) ( 2) (1) ( 2) Emélange = −4ε ((1Fe) − Fe) − 3ε ((Fe + 8 ε + 6 ε − 4 ε − 3 ε − Fe) ( Fe− X ) ( Fe− X ) (X −X ) (X −X ) 2) (1) ( 2) (1) ( 2) Eint erface(100) = −2ε ((1Fe) − Fe) − ε ((Fe − Fe ) + 4ε ( Fe − X ) + 2ε ( Fe − X ) − 2ε ( X − X ) − ε ( X − X )

Ecohésion ( Z ) = 4ε ((1Z)− Z ) + 3ε ((Z2)− Z ) Z

• E formation (lac ) •

1) = 8ε ((lac −Z )

2) + 6ε ((lac −Z )

i = 1 or 2

− 4ε ((1Z)− Z )

− 3ε ((Z2)− Z )

X, Y = solute atoms

Z = Fe or solute atom

(i ) (i ) (i ) (i ) Eliaison = 2 ε − ε − ε ( lac − lac ) ( Fe −lac ) ( Fe − Fe ) ( lac −lac )

(1) (1) (1) (1) (1) Eliaison = ε + ε − ε − ε (lac − X ) ( Fe−lac ) ( Fe− X ) ( Fe− Fe) (lac − X ) εFe-Cu_1nn Ternary alloys… εSi-Si_2nn

(i ) (i ) (i ) (i ) (i ) Eliaison = ε + ε − ε − ε ( X −Y ) ( Fe − X ) ( Fe −Y ) ( Fe − Fe ) ( X −Y )

Ab initio data

Parameters Adjustment on thermal annealing experiment

10


10

DFT: point defect & point defect cluster properties (stability & mobility) Fe-C 1nn 001

Phys. Rev. B 69 (2004) 144112

1nn

100

Local magnetic moment (µB)

Phys. Rev. B 65 (2002) 024103

BGL run 512 CPU - ~24h

1,2 1 0,8

Fe-CuNiMnSi

0,6 0,4 0,2 0 -0,2

Nucl. Inst. Meth. Phys. Res. B: 228 (2005) 137-141

11

Fe Cu

Ni

Mn

Si

Cr

Co

Mo


686+19 Fe atoms PAW GGA 300 eV - 1 kpoints

Neutron irradiation of FeCuNiMnSi alloys Medium term evolution by atomic Kinetic Monte Carlo Fe-0.2Cu-0.53Ni-1.26Mn-0.63Si (at.%) at 300°C Flux: 6.5 10-5 dpa.s-1 Dose: 1.3 10-3 dpa

V-solute complex SIA-solute complexes Small solute clusters

Cu

Ni

Si

V

Mn

SIA

12

Point defect clusters = germs for precipitation


[> 1 month on 1 CPU]

Fe – CuMnNiSiP (at.%) alloys V-Solute

SIA-Solute

Pure solute

25

0.18Cu 1.38Mn 0.69Ni 0.43Si 0.01P 5.79x10-5 dpa/s - 300°C - 18.05 mdpa

SIA Vac

Répartition des espèces

20

P

Ni Mn

15

Si Cu

10

5

0 1

•

13

19

25

31

37 43 49 Cluster de ID l'amas Numéro

55

61

67

73

The biggest solute clusters are associated with PD clusters −

• • •

7

In agreement with induced segregation mechanism to account for solute clusters formation

Clusters associated with interstitial clusters are enriched in Mn, and P/Ni Clusters associated with vacancy clusters are enriched in Si/Cu/Mn (mostly) and Ni I-Solute complexes > V-Solute complexes 13


[R. Ngayam happy PhD]

79

Average composition (nb solute & vac & int / cluster) 18,09 mdpa

20

5,1 mdpa 20

18,53 mdpa

10

14,38 mdpa

15

SIA Vac P Ni Mn Si Cu

18,09 mdpa

15

18,53 mdpa

5,1 mdpa 10

0

5

0 Fe - Cu

Fe - M n

Fe - M nNi

Fe - CuMnNi

Fe CuM nNiSiP

Vacancy - solute 15

24,33 mdpa

Nombre moyen par amas

30




40

5,1 mdpa

10

14,38 mdpa

18,09 mdpa 24,33 mdpa

18,53 mdpa

Fe - M nNi Fe - CuMnNi

Fe CuMnNiSiP

5


0

Fe - Cu

Fe - Mn

Fe - MnNi

Fe - CuMnNi

Fe CuMnNiSiP

Fe - Cu

Fe - Mn

Solute clusters

Interstitial - solute

5,1 mdpa

80

10

14,38 mdpa

24,33 mdpa

18,09 mdpa 18,53 mdpa

5


62 mdpa 60

62 mdpa

P Ni Mn 40 Si Cu

P Ni Mn Si Cu

62 mdpa

62 mdpa

20

100 mdpa 0

0 Fe - Cu

14

Fe - Mn

Fe - MnNi

Fe - CuMnNi

Fe CuMnNiSiP

Fe - Cu

Fe - Mn

Fe - MnNi

Fe - CuMnNi

16MND5

All Solute clusters AKMC

Solute clusters Atom Probe [Meslin et al.]

Simulation

Experimental results


[R. Ngayam happy PhD]

Cohesive energy model (fcc) E = ∑ε + ∑ε + ∑ε +∑ ε + ∑ε (i ) ( Fe − Fe )

j

(i ) (V −V )

k

(i ) ( Fe −V )

l

(i ) ( Fe − X )

m

X

(i ) (V − X )

+ ∑ ε ((Xi ) −Y )

n

p

Vacancy

X

Y

1nn (and 2nn) pair interactions (no reliable FeNiCr EAM potentials for thermodynamical and defect properties)   E dumb = ∑  E f + ∑ E l1nnComp (dumbi − X j ) + ∑ E l1nnTens ( X j ) + ∑ E lmixte ( X j − X k ) + ∑ E l (dumb − dumb)  i  j j i, j 

Tensile atoms SIA Compressive atoms

Y Y SIA

15


X

FeNiCr interaction parameters adjustment on DFT data (Fe70Ni10Cr20) Chemical interactions in the Bulk Cohesive energies X-X terms

Binding energies in dilute γ-Fe X-Y terms

Vacancy-solute interactions

16

Fe Cr Ni 256 at


TNES & RIS profil Electron irradiation 0.6 dpa 723 K RIS

TNES

TNES results: Cr enrichment Ni depletion

RIS results: Cr depletion Ni enrichment

→ Coherent with experimental results 17


[J.B. PIochaud PhD]

Long term microstructure modelling Object Kinetic Monte Carlo Objects:

Precipitatio n SIA-Loop Nanovoi d trix a M ge a m Da

Solute clusters on i t a g e gr s e B S G at

Psegregatio n

- vacancy - self interstitial - dilute solute (with vacancy interactions) - sink (e.g. grain boundaries, …) - trap (e.g. impurities, …) - dislocation - foreign interstitial atoms He in austenitic alloys C or N in ferritic or austenitic alloys Recombination Emission

Electrons

+

+

Traps Interstitial

Frenkel pairs

loop

PBC or

Emission

dislocation

Vacancy

surface

Interstitial

cluster Neutrons

cluster Annihilation +

Mixed He vacancy cluster

200nm

He cluster

18


Migration

cascade

Long term simulation of the microstructure under irradiation of Fe by object kinetic Monte Carlo Recombination +

Emission traps Interstitial loop

dislocation PBC or surface

Emission Vacancy cluster

Interstitial cluster

sinks +

>300nm

Annihilation

Vacancy loop

Migration

Input required: 1E+26

Mobility: diffusion coefficient Local interaction rules: Interaction and binding energies

set 1 PBC set 2a PBC

Density (m-3)

set 3a PBC experimental

1E+25

min

3.5

max 3 2.5 2

1E+24

1.5

HFIR n irradiation

1 0.23 0.5 0.009

1E+23 0.0001

0

0.001

0.01

0.1

1

0.0009 0.22-0.44 0.45-0.64

19

EDF R&D - Workshop MINOS - Saclay Dec 2012 dpa

0.0001

0.65-0.82 0.83-0.92 0.92-reste

Long term simulation of the microstructure: Application example: flux effect study in bcc Fe DEFECT POPULATION at 0.1 dpa

7 10-5 dpa/s

343K

7 10-11 dpa/s

(param Set II) 20


Multiscale modeling of plasticity: phenomenological scales Mechanical properties

Physics modeling

RVE mechanics Irrad. microstructure

Collective dislocation behavior

Dislocation-defect

10 nm

10 µm

10 µm

Atom-meso transition 21

Meso-continuum transition

Multiscale approach EDF R&D - Workshop MINOS - Saclay Dec 2012

Homogenization

Dislocation at the atomic scales [Domain et al.]

500

Critical Stress (MPa)

[Terentyev et al.]

800

τ c (MPa)

400

600 MD Simulations

300

400

Antitwinning direction

200

Twinning direction 200

100 Experiments

T (K)

0

Screw core structure: compact ab initio EAM: Mendelev03 EAM: Ackland04

Screw 22motion by DK

0

100

200

300

Critical stress for (110) screw dislocation (temperature, strain rate)


400

Τ (Κ) 0 0

50

100

150

Critical stress for (112) edge dislocation (temperature, strain rate )

200

Irradiation strengthening in RPV Shear stress (MPa)

150

125

∆CRSS

voids

Lath geometry

Carbides

100

75

Forest dislocation

50

25 Alloy Friction

0 [Queyreau et al.] 23

Initial1state EDF R&D - Workshop MINOS - Saclay Dec 2012

2 Irradiated state

Integration: RPV & INTERN plateforms neutron spectrum IRRAD

RPV-2 INTERN-1

pka spectrum

RPV-2 or INTERN-1

temperature + composition CONVOLVE


source term

LONG_TERM

composition + mobility rules and diffusion coefficients + energetics of clusters + sinks densities + time steps and total irradiation time

clusters distributions f(t)

HARD

pinning forces of the clusters + slip system + shear modulus

∆τ(t) ∆τ

[Adjanor et al., JNM 406 (2010) 175] 24


Dislocation dynamics cristalline law of Fe alloys (at low temperature) Orowan Law for plastic flow

DD velocity of scew dislo

υ screw (τ , T ) =

ν Db 2 lc2

γ&s = bρ scs vscs (τ , T ) + bρ eds υ eds (τ , T )

 ∆G (τ app )  s  lsc exp  − kT  

[Naamane, Monnet, Devincre]

γ&s = 4 ρ

s sc

υ Db3 lc2

 ∆G τ s ∆ G   eff o o lscs exp −  sinh   kT τo  kT  

   

Dislocation density evolution law

ρ& s =

γ&s  b  

∑a K

su

ρu

 − gc ρs   

[Monnet, Vincent, Mécanique & Industries 12, 193–198 (2011)] 25


Finite elements simulations: stress strain curves Stress (MPa) 50K

300 100K

200 150K 200K

100

250K 350K

0 0

10

20

30

40

50

γ (%) [Kuramoto 1979]

[Monnet, Vincent, Mécanique & Industries 12, 193–198 (2011)] 26


Material Multiscale Modeling Challenge

Complexity (chemistry, clusters, interfaces)

Integration

Length-scale

(codes, database, methods, …)

(Angstrom, meter)

Accuracy (ab initio, semi-empirical potentials, cohesive models)

Time-scale (fs, ps, years)

Uncertainties Statistics 27


Conclusions & perspectives A multi-scale modelling approach is developed for more than 10 years (e.g.

through internal & EURATOM European project SIRENA, PERFECT & PERFORM60, GETMAT): RPV & INTERN plateform. Improvement of the knowledge elementary properties allow to better predict

material evolution. Some important progress thanks to the use of HPC machines. The prediction of the evolution of the mechanical properties requires to know the

plasticity of the materials. The prediction of the evolution of the irradiated microstructure requires as input

physical parameters the properties of each point defect clusters (mobility and stability). The properties of each point defect clusters (size, configurations, chemistry) need

to be defined by ab initio calculations. Represent numerous configurations / mechanisms to be investigated.

28
