2055-38

Joint ICTP/IAEA School on Physics and Technology of Fast ReactorsSystems

M. Vijayalakshmi

9 - 20 November 2009

Indira Gandhi Center for Atomic ResearchKalpakkam

India

Introduction to structural materials and their behaviour in a fast reactor fuelassembly

2 Radiation Damage Principles of Design of Radiation Resistant Materials for Fast Reactor Fuel

Assembly

Introduction to structural materials and their behaviour in a fast reactor fuel assembly 

2.    Radiation Damage2.    Radiation Damage

Principles of Design of Radiation Resistant Materials for Fast Reactor Fuel Assembly

IRRADIATIONCREEP

IRRADIATIONHARDENING

IRRADIATIONEMBRITTLEMENT

IRRADIATIONGROWTH

VOID SWELLING

MATERIALS DEGRADATION

INREACTORS

DISTORTION IN SHAPERETAINING SAME VOLUME

MODULE 2: RADIATION DAMAGE MODULE 2: RADIATION DAMAGE ‐‐SCOPE SCOPE 

• DOSE;• TEMPERATURE;• DOSE RATE;• COLD WORK• CHEMISTRY

VOID SWELLING: NUCLEATION & VOID SWELLING: NUCLEATION & GROWTH OF VOIDSGROWTH OF VOIDS

DO ALL  SINKS REACT WITH DEFECTS THE SAME WAY?

NATURE OF SINKS IN VOID GROWTH;

TYPE OF SINKS: NEUTRAL, BIASED & 

VARIABLE BIAS 

NEUTRAL 

G.B.’s

INCOHERENTPRECIPITATES

absorption α Di.v & (C i/v xal – C i/v sink surface  ) rate

BIASED  SINKS  BIASED  SINKS  ‐‐ DISLOCATIONSDISLOCATIONS

2% more bias For I’s than V’s.

I’s drift towards Core driven byStress gradient

I’s enhance climb;   So unsaturable sink

TYPE OF SINKS VARIABLE BIAS SINKS:    COHERENT PRECIPITATES & IMPURITY ATOMS

TTiiCC pprreecciippiittaattee

AAuusstteenniittee mmaattrriixx

CAPTURES I OR V’s ;  RETAINS ITS IDENTITY TILL IT ANNIHILATES WITH THE OPPOSITE !!!!

INCREASES RATE OF  V + I  RECOMBINATION PROBABILITY

VOID SWELLING: solution to growth rate equations

ρV = ∫ ρV ® dR

Total Number Density of voids Number of voids / cm2 of

radii R & R+dR

Rav = (1/ ρV ) ∫ R ρV ® dR

Volumetric swelling rate

dV/dt = 4Π R2 (dR/dt)

∆V / V = (4/3) Π Rav3 ρV

VOID SWELLING

DOSE;

TEMPERATURE;

COLD WORK &

DOSE RATE.

Void swelling – dose dependence

• LOW DOSES ‐ LOW AMOUNT PRODUCTION OF POINT DEFECTS ; NOT ENOUGH TO FORM MORE VOIDS & ALLOW THE AMBRYOS TO GROW.

• HIGH DOSES ‐‐ LOSSES  TERM TO (RECOMBINATION + SINKS) 

IS OFFSET BY PRODUCTION

Transient Swelling Regime

Threshold

dose

Linear Swelling Regime

Sw

ellin

g

Fluence (dpa)

JOB OF MATERIALS SCIENTISTS JOB OF MATERIALS SCIENTISTS ---- IDENTIFY A MATERIAL WITH IDENTIFY A MATERIAL WITH AS HIGH THRESHOLD AS POSSIBLEAS HIGH THRESHOLD AS POSSIBLE

VOID SWELLING: TEMPERATURE DEPENDENCEVOID SWELLING: TEMPERATURE DEPENDENCE

STRONG DEPENDENCE  ON TEMPERATURE

• VACANCY DIFFUSION COEFFICIENT ‐ DDvv

• EQUILIBRIUM  THERMAL VANCANCY CONCENTRATION –CCvv

00

LOW TEMPERATURE

• LOW (Dv)MOBILITY OF VACANCY CONCENTRATION

• BUILD UP OF FREE VACANCIES & INTERSTITIALS

• HIGHER RECOMBINATIONS

• NO EXCESS CONCETRATION OF VACANCIES

• LESS  VOIDS

HIGH TEMPERATURE

• DEFECT CONCENTRATION   ~   THERMAL EQUILIBRIUM CONCENTRATION

• LESS SUPERSATURATION (S = CV / CV0 )

• LESS DRIVING FORCE FOR VOID FORMATION

• EMISSION OF VACANCIES FROM VOIDS; 

• LESS NO OF VOIDS

Regularity of swellingRegularity of swelling

The dependence of swelling on The dependence of swelling on irradiation temperature of steelirradiation temperature of steelChSChS--68 68 of fuel pinof fuel pin cladding material of the first modernization cladding material of the first modernization

corecore ofof BNBN--600600..

0

5

10

15

20

25

30

35

400 420 440 460 480 500 520 540 560 580 600

Temperature (0С)

Swel

ling

(%)

–– D = 60D = 60 dpadpa–– D = 70D = 70 dpadpa–– D = 80D = 80 dpadpa–– D = 90D = 90 dpadpa

13

TEMPERATURE     EFFECT

AS ‘T’ INCREASES, VACANCIES BECOME MORE AND MORE MOBILE;   NET ARRIVAL OF VACANCIES TO VOIDS INCREASE;    VOIDS GROW.

AT HIGH ENOUGH TEMPERATURES, CV0 INCREASES, S REDUCES, THERMAL EMISSION OF VACANCIES FROM VOID SURFACE INCREASES. VOID SHRINKS.

BALANCE IS VOID GROWTH.

VOID SWELLING: EFFECT OF DOSE RATE

1010--44……1010--2 2 dpa/sdpa/s

11⋅⋅1010--77…… 22⋅⋅1010--33 dpa/sdpa/s

1010--1010……1010--66 dpa/sdpa/s300 (800)300 (800)

11⋅⋅10101111

11⋅⋅10101515

3333

33⋅⋅10101515

66⋅⋅10101919

44⋅⋅1010 55 (Fe(Fe++))99⋅⋅1010 55 (Cr(Cr++))

22⋅⋅10101414

22⋅⋅10101616

Damage cross-section, barn10 10 2 10 3 10 4 10 5 10 61

DOSE RATE DIFFERENCE USING DIFFERENT INCIDENT PROJECTILESDOSE RATE DIFFERENCE USING DIFFERENT INCIDENT PROJECTILESDOSE RATE DIFFERENCE USING DIFFERENT INCIDENT PROJECTILES

Flux density, particle/(cm2⋅s)

10 10 10 12 10 14 10 16 10 18 10 2010 8

nnn

e-ee--

i+ii++

[ ]224

22

101 cmbarnscm

particlecmsdpa

Фk−=

⎥⎦⎤

⎢⎣⎡

⋅⋅=⎥⎦

⎤⎢⎣⎡

⋅=σ

1515

Electrons Light ions Heavy ions

High dose rate(10-3 dpa/s)

High dose rate

no cascades

Very limited depth of penetration

Strongly peaked damage profile

Cascade production

moderate dose rate(10-4 dpa/s)

Good depth of penetration

Flat damage profile over tens of μm

Smaller, widely separated cascades

Insitu analysis (TEM)

Fast Reactor

Time to build up dose:  Reactor vs other irradiation sources

• 10‐6 to 10‐7 dpa/s in a reactor

• Time for 10 dpa – 4 to 5 months against one day in heavy ion accelerator

• few hrs in HIGH VOLTAGE electron microscope

Void Swelling : - Dose Rate

Peak Swelling Temperature depends on Irradiation Dose rate

⎟⎟⎠

⎞⎜⎜⎝

⎛ΦΦ

=1

2

2

1 lnATT

WHY ? OF DOSE RATE BEHAVIOUR

• HIGHER DOSE RATE  INCREASES   RATE OF PRODUCTION OF CONCENTRATION  OF POINT DEFECTS ;

• RECOMBINATION RATE       α PRODUCTION RATE  ‐ DOSE RATE;

• SUPERSATURATION  REDUCES  &  HIGHER  TEMPERATURE  IS REQUIRED  TO  INTRODUCE  THE  DIFFERENCE  IN  THE PRODUCTION  /  LOSS  TERM,  TO  ACHIEVE    REQUIRED SUPERSATURATION

• Tmax SHIFTS TO HIGHER TEMP.

EFFECT OF DISLOCATIONS

dRo/dt = [(Ko (Zi-Zv)ρd Ω ] / [R ( Zv ρd + 4π R ρv + 4π Rcp ρcp)]

Void growth rate in a lattice with biased sinks, like dislocations

Bias due to dislocations Vacancies absorption at dislocations

If Zi= Zv , voids do not grow.

EFFECT OF DISLOCATIONS

Q : RATIO OF SINK STRENGTH

Let Q = dislocation sink strength / void sink strength

VOIDG

ROWTH

RATE

LOW DISLOCATION DENSITYHIGH VOID DENSITY

HIGH DISLOCATION DENSITYLOW VOID DENSITY

MAX. SWELLINGMAX. SWELLING

Void Swelling : Temperature & Dislocation Density

Low Mobility

Super saturation difficult

Thermal Emission of Vacancies from voids

Hyderabad, July 2-4, 2008

Structural approach – dislocation factor

Влияние степени х.д. на распухание

0

2

4

6

8

10

12

14

16

0 10 20 30 40 50 60

Степень х .д., %

Распу

хани

е, %

ε = 15 %

ε = 18 ±2 %

ε = 20 ±3 %

ε = 20-25 %

Effect of cold work level on EI847 swelling

BN-350 , 500 0C, 60 dpa

Cold work level, %

Progress in c.w. levelof austenitic steel

Swel

ling,

%

What is the limiting doseat which the favourableeffect of C.W. increasedisappears?

METHODS TO STUDY VOID SWELLING

•• MODELLING : MODELLING : MONTE‐CARLO METHODS, MOLECULAR DYNAMICS, CONTINUUM MECHANICS, RATE THEORY, DISLOCATION DYNAMICS

•• EXPERIMENTAL METHODS:  EXPERIMENTAL METHODS:  DENSITY MEASURE‐MENTS, STEP‐HEIGHT , POSITRON ANNIHILATION, RESISTIVITY, TEM UNDER NEUTRON, ION IRRADIATION CONDITIONS.

METHODS TO STUDY VOID SWELLINGMETHODS TO STUDY VOID SWELLING

0 30000 60000 90000 120000 150000120

130

140

150

160

Posi

tron

lifet

ime

(ps)

Annealing time (s)

623 k

573 k

523 k

POSITRON STUDIESPOSITRON STUDIES

450 500 550 600 650 7000.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Swel

ling

(%)

Temperature (oC)

30 ppm He, 100 dpa

STEP HEIGHT AFTER Ni ION IRRADIATION IN AN ACCELERATOR

Materials ModelingMaterials Modeling

Molecular Dynamics

Density Functional Theory calculation of Physical Properties

Car- Parinello MD

ABINIT

VASP

SIESTA

WIEN-2K

MDCASK

Codes Installed, Codes Installed, ParallelisedParallelisedCascades for 5, 10, and 100 keV cascades in Cu at 100K

Hot cells at for PIE of FBTR Fuel & Structural Materials 

IN-SERVICE PERFORMANCE – WRAPPER OF FBTR

VOIDS in 20 % CW 316 SS AFTER 40 dpa

200nmNi3Si – G Phase formed ONLY during irradiation – due to RIS

VOID SWELLINGDOSE;

TEMPERATURE;

COLD WORK &

DOSE RATE.

IRRADIATIONCREEP

IRRADIATIONHARDENING

IRRADIATIONEMBRITTLEMENT

IRRADIATIONGROWTH

VOID SWELLING

MATERIALS DEGRADATION

INREACTORS

IRRADIATION GROWTH

30 CM

1 CM0.58 CM

10 CM 1020 n/cm2

Volume remains sameVolume remains sameDistortion increasesDistortion increases

shape changesshape changesHCP LATTICE

BASAL PLANE – (0001) - VACANCY LOOPS

PYRAMIDAL PLANE –(11. 0) –

INTERSTITIAL LOOPS

ATOMS ARE REMOVED FROM BASAL PLANES & DEPOSITED IN THE (11-0) PLANES

IRRADIATION HARDENINGMECHANICAL BEHAVIOUR OF MATERIALS (FORGET IRRADIATION FOR A MOMENT)

Generation of dislocationsGeneration of dislocations

Pinning by obstaclesPinning by obstacles

Unpinning of immobile dislocationsUnpinning of immobile dislocations

Build up of stress ahead of pileBuild up of stress ahead of pile--upup

crackingcracking

IRRADIATION HARDENING

n + =

= source hardening + friction hardening

Unpin the immobiledislocations

Obstacle to mobile disolcations

IRRADIATION HARDENING

Δσsirrad. = (ϕ t )1/2

Effect of dpa

IN-SERVICE PERFORMANCE – WRAPPER OF FBTR Tensile Testing of Irradiated Cladding

Remote tensile test system

Shear Punch testing of Irradiated WrapperSmall disk specimen extracted in hot cell

Test machine with lead shielding

0.0 0.2 0.4 0.6 0.8 1.00123456789

Unirradiated

2 dpa

56 dpa

Load

, kN

Punch Displacement, mm

Shear punch test plot for various dpa

Stress-strain curves for various dpa and test temperatures

Effect of Test Temperature

0.00 0.05 0.10 0.15

100

300

500

700Unirradiated Clad (T = 470C)

(50 dpa,450C)(56 dpa,

430C)Stre

ss, M

PaStrain

Test Temperature = Irradiation Temperature

IRRADIATION CREEP

• WHAT IS CREEP ?

• WHAT ARE CREEP MECHANISMS ?

• WHAT IS IRRAD. CREEP ?

• SIPN & SIPA – IRRAD. CREEP MECHANISMS

• IDENTIFICATION OF IRRAD. CREEP

Typical Creep-curve: THERMAL ONLY

CREEP MECHANISMS

HARDENING MECHANISMSGRAIN BOUNDARY CREEP MECHANISMS

IRRADIATION CREEP

• AUGMENTATION OF THERMAL CREEP BY IRRADIATION OR

• INTRODUCING CREEP AT T’s WHERE THERMAL CREEP IS KNOWN ‘NOT TO OCCUR’

• CREEP RATE CHANGED WITH DOSE, DOSE RATE – SIGN OF IRRAD. CREEP

IRRADIATION CREEP IN EBR‐II

IRRADIATION CREEP MECHANISMS: SIPA & SIPN• V ‘s & I’s ABSORBED PREFERENTIALLY

• I’s TO ⊥ s WITH EXTRA HALF PLANE ⊥ σ

• V’s TO OTHER ⊥s

σ⊥

⊥

⊥

⊥

⊥

• LOOPS NUCLEATE PREFERENTIALLY

• (INT.LOOPS)PLANES ⊥ σtensile >>>

same in planes ll σtensile

• (VAC.LOOPS)PLANES ⊥ σtensile<<<<<

same in planes ll σtensile

σtensile () () () ()

()

()

σtensile() ()

()

()()()

Swelling assisted creep•• Swelling enhances creep rate at smaller dose Swelling enhances creep rate at smaller dose levelslevels

•• Creep disappears beyond certain doseCreep disappears beyond certain dose

•• After this dose, swelling continues, creep After this dose, swelling continues, creep disappearsdisappears

•• when voids form, V + I are absorbed in large numbers by when voids form, V + I are absorbed in large numbers by the voids.the voids.

•• Less I flow to dislocations Less I flow to dislocations ‐‐ creep reducescreep reduces

•• Swelling saturates due to low excess vacancy absorptionSwelling saturates due to low excess vacancy absorption

Swelling assisted creep: Mechanisms

Irradiation embrittlement

Tc = C-1 [ln Bksd1/2 / (βγμ - kyks)

RADIATION DAMAGERADIATION DAMAGE

IRRADIATIONCREEP

IRRADIATIONHARDENING

IRRADIATIONEMBRITTLEMENT

IRRADIATIONGROWTH

VOID SWELLING

MATERIALS DEGRADATION

INREACTORS

THANQ 4 THANQ 4 UR ATTENTIONUR ATTENTION

Introduction to structural materials and their behaviour in a fast reactor fuel assembly 

Radiation Damage

Principles of Design of Principles of Design of Radiation Resistant Materials for Radiation Resistant Materials for 

Fast Reactor Fuel AssemblyFast Reactor Fuel Assembly