Mécanismes de déformation et dommage d’irradiation...

13/06/2016

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Rencontres Franciliennes de Mécanique,

13-14 juin 2016, France

Mécanismes de déformation et

dommage d’irradiation dans les

alliages de zirconium : une approche

multi-échelle

F. Onimus1, L. Dupuy1, F. Mompiou2, M. Bono3

1Service de Recherches Métallurgiques Appliquées, CEA-Saclay, 91191 Gif-sur-Yvette, France2CEMES, CNRS, 29 rue Jeanne Marvig, 31055 Toulouse, France3Service d’Etude des Matériaux Irradiés, CEA-Saclay, 91191 Gif-sur-Yvette, France

Acknowledgements :

J. Drouet, M. Blétry, M. Fivel, E. Ferrié for help in DD developments and simulations.

C. Bachelet, S. Picard for ion irradiation.

C. Duguay, R. Limon, A. Soniak, B. Verhaeghe and SEMI for mechanical tests and thin foils.

I. Monnet, T. Vandenberghe and SRMA for support in TEM.

B. Doisneau, L. Guetaz for help in initial in situ TEM.

P. Pilvin for the initial polycrystalline model.

EDF and AREVA for financial support.

F. Onimus Rencontres Franciliennes de Mécanique, 13-14 juin 2016, France 2

Zirconium alloys in PWR core

Fuel assembly

Vessel

Internals

Control bars

Guide tubes (Zr)

Grids (Zr)

Top nozzle

Fuel cladding(Zr)

Bottom nozzle

Fuel rod

Main Function : Confinement of the nuclear fuel and Fission Products

Fastneutrons

Water (primary circuit)

T=320°C, P=155 bar

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50 µm

A Multi-Scale Approach

50 nm

In situ tensile test in TEM� dislocation motion

TEM observations of grains�Deformation mechanisms

Dislocation Dynamics

Mechanical tests� Mechanical behavior

Polycrystalline model

Homogeneous Equivalent Medium (HEM)

Polycrystal50 µm


� Irradiation induced hardening�Decrease of the uniform elongation (early localization of the plastic strain but ductile failure mode)

(z)

(θ)

Radiation effects on the mechanical behavior

Non irradiated

necking

neckingIrradiated

Internal pressure test @350°C

50 µm

9.5 mmRD (z)

TD (θ)

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F. Onimus Rencontres Franciliennes de Mécanique, 13-14 juin 2016, France 5Before irradiation After irradiation

50 nm200 nm

Radiation effects on the microstructure

10 nm

Displacement cascade

Fast neutrons

n b

Dislocation loop a3

a1

a2

bL


� Clearing of loops by gliding dislocations

TEM observations after Transverse Tensile test at 350°C

After neutron irradiation + testing

� Dislocation channelling mechanism

Recrystallized Zy-4 at 350°C

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Dislocation channelling mechanism

Thin foil Channel

In many irradiated metals and alloys

� Local strain softening + Localization of the plastic strain


� Change of the easy glide slip system !

TEM observations after Transverse Tensile test at 350°C

1 µm

Non irradiated + testing

Pyramidal Π1

Basal B

Prismatic Pb=<c+a>

c

a2

a3

a1

b=<a>

After neutron irradiation + testing

Observation of Basal channels, no prismatic channel

.

Specimen 1Grain 2

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�the Basal slip systems are not well oriented�Activation of Prismatic slip

� After irradiation Basal glide and clearing of loops easier, but Prismatic glide and clearing of loops occur when Basal slipnot well oriented.

(z)

(θ)

{0002} pole figure

Prismatic channels, no B channel

TEM observations after Axial Tensile test at 350°C

Prismatic channel -> partial clearing of loops


50 µm


50 nm




�Need for a better understanding of the dislocation channelling process& origin of the change of the easy glide slip system.

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Zr +ion irradiation atJannus-Orsay (ARAMIS)Dose = 0.5 dpa (8. 10��/ ��)Temperature= 340°C Energy= 0.6 MeV

ZrTEM foil

ions Zr+

20 nm

0.5 dpa à 340°C

In situ tensile test at Grenoble (SIMAP) and Toulouse (CEMES) at temperatures between 350°C and 500°C.

Study of the dislocation-loop interactions

ARAMIS facility at Jannus-Orsay (CSNSM)

Recrystallized Zy-4


In situ tensile test at 350°C of ion irradiated recrystallized Zy-4

Annihilation of a loop by a <a> edge dislocation gliding in a prismatic plane

50 nm

Tests at SIMAP/INP Grenoble

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In situ tensile test at 450°C of ion irradiated recrystallized Zy-4

Annihilation of a <a> loop by a <a> edge dislocation gliding in a pyramidal plane. The super jog transforms into an helix turn on the screw part.

Edge part of the dislocation

Screw part of the dislocation


In situ tensile test at 450°C of ion irradiated recrystallized Zy-4 (~0.5 dpa at 500°C)

Annihilation of a <a> loop by a <a> screw dislocation gliding in a pyramidal plane. An helix turn appears on the screw part.

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50 µm


50 nm




Nodal DD code Edge-screw DD code

Dislocation DynamicsNew nodal Dislocation Dynamics code:

NUMODIS


Force calculationξσ ×⋅= )( bf

Stress calculation

Velocity

Discrete events

Discretization

)(vBf =

Nodal structure

Peach-Koehler

Explicit algorithm

Strain or stress control

Dislocation dynamics: NUMODIS

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Dislocation dynamics simulations:

Interactions between dislocation and loopsD

iffer

ent B

urge

rs v

ecto

rs

PrismaticPrismatic

Diff

eren

t Bur

gers

vec

tors Basal

Sweeping of loops easier in the basal plane than in the prismatic plane.� In agreement with the easy basal channeling observed by TEM.

Edge dislocation Screw dislocation

Prismatic � 3/6 clearing Basal � 5/6 clearing

Edge dislocation

Basal

Screw dislocation


Dislocation dynamics simulations vs. in situ TEM observations

Dislocation

loop

Bv

τ=

� Evaluation of the friction coefficient B~0.3 MPa.s

Dislocation dynamics simulation of a real interaction observed in situ

From diffraction pattern indexing � Orientation of the grains vs. tensile axis

From movie� Dimensions and positions of the dislocation and loop

From curvature of the dislocation (DISDI software)

�Evaluation of shear stress ~ 50 MPa�And applied tensile stress ~160 MPa

From movie space and time scale � Evaluation of the velocity of the dislocation

Pyramidal plane

Tension

Burgers vector

x7°

y

z

<a> looppositions

<a> dislocation in pyramidal plane

Burgers vector

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�� Good agreement between simulation and experiment

L. Dupuy : DD code NUMODIS

• Careful spatial and time scaling

• Systematic analysis of the effect of the loop nature, loop Burgers vector and position

• Careful comparison of the detailed shape of the dislocation

�� vacancy loop with same Burgers vector as the dislocation



�� Great agreement between simulation and experiment !

L. Dupuy

3D overlaping of the two films !


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50 µm


50 nm



Dislocation Dynamics


Polycrystalline model


Polycrystal50 µm



Polycrystal50 µm

Polycrystalline modelling

(z)

(θ)

Set of 240 crystallographicorientations representative of

the texture

Experimental {0002}pole figure

Σ

Σ

Σ

+

Σ

Σ

+ …=

Σ

HEMHEMHEM

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Σ

gσ p

gε&

pE&

Homogenization

Intra-granularconstitutive laws

Localization( ) ∑

∈

=

−−+Σ=

Ggg

ggg

fBB βββµσ with 12

p

g

p

gg

p

ggD εεδβεβ &&&

−−=

( )ssssgs nmmn ⊗+⊗= :2

1στ

( )∑∈

⊗+⊗=Ss

sssssp

gnmmnγε &&

2

1

∑∈

=Gg

p

gg

pfE ε&&

( )p

Gggg EEIIσfΣ −

⊗

−+==∑

∈ ννµ21

2 I

More on the polycrystalline model

*

*so-called beta-model proposed by G. Cailletaud and P. Pilvin described in :G. Cailletaud, Int. J. Plasticity 8 (1992) 55.P. Pilvin, in: Proceedings of the International Conference on biaxial/multiaxial fatigue ESIS/SF2M, 1994, p. 31.P. Geyer, X. Feaugas, P. Pilvin, in: Proceedings of Plasticity'99, Cancun, 1999.X Feaugas, P Pilvin, M Clavel, Acta Materialia, Volume 45, Issue 7, July 1997, Pages 2703–2714F. Onimus, J.L. Béchade, Journal of Nuclear Materials Volume: 384, Issue: 2, Pages: 163-174, 2009.M. Priser, M. Rautenberg, J.-M. Cloué, Ph. Pilvin, X. Feaugas, D. Poquillon, Journal of ASTM International, 8 (1) ( 2011 ) 10-19


Ndl =ρwith

−= ∑∈Bs

slBl k

dt

d γρρ&

( ) dNl 00 =ρ

bHkB /=

Strain softening inside basal channels

H

l

Irradiation induced hardening

lscs

cs

cs

cs b ρµαττττ +=∆+= 00

Ndl =ρ =0N =d5×1022 m-3 10 nmwith ld

Intra-granular constitutive laws

( )ss

ncsss

s xK

x−

−−= τ

ττγ sign&

ssBsBs xDCx γγ &&& −=

Flow law and kinematic intra-granular strain hardening

γγγγlocal =10% to 100% γγγγg=1% to 5%

Irradiated Non irradiated

Armstrong–Frederick law

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Coefficients for the irradiated material obtained after the refinement.

Fitting on monotonic tests

Prismatic

Basal

Parameter (unit) Value for irradiatedmaterial

* (MPa) 80000* 0.4* 10

* (MPa.s1/n) 5(MPa) 240(MPa) 240(MPa) 300(MPa) 85* (m-2) 5×1014

0.540

(MPa) 105

30002800.53 MPa1880 =+= ls

cs

cs b ρµαττ

Eν

nK

cPτc

a><πτc

ac >+<πτ0c

Bτ( )0bρ

Bα

Bk

BC

BD

D

δ

� Lower critical shear stress and strainsoftening for basal slip

� Constant critical shear stress for otherslip systems


Validation on cyclic tests. Literature results.

S.B. Wisner, M.B. Reynolds, R.B. Adamson, in: Zirconium in the Nuclear Industry: 10th International Symposium, ASTM STP 1245, 1994, p. 499.

� Strong Bauschinger effect after irradiation � Cyclic strain softening after irradiation

Stabilized hysterisis loops

Maximum stress

-600

-400

-200

0

200

400

600

-1.0% -0.5% 0.0% 0.5% 1.0%

Plastic strain

Stre

ss (M

Pa)

Unirradiated (Exp)Irradiated (Exp)

Unirradiated (Sim)Irradiated (Sim)

0

100

200

300

400

500

600

0 5 10 15 20 25 30Number of cycles

Max

imu

m s

tress

(M

Pa)

Unirradiated (Exp)

Irradiated (Exp)

Unirradiated (Sim)

Irradiated (Sim)

� Good prediction of both the kinematic strain hardening and the cyclic strain softening.

Polycrystalline model simulations

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Validation on TEM observations

Transverse tensile test

Computed shear strain rate (slip activities) / TEM observations

Grain 2

Grain 6

Basal Prismatic Pyramidal <c+a>


Validation on TEM observations

� Good prediction of the slip system activitiesOnly 7 disagreements out of 71 cases ( > 90% good predictions) !

Internalpressure test

Computed shear strain rate (slip activities) / TEM observations

� Validation of the model both at microscopic and macroscopic scales

Grain 1 Grain 7

Basal Prismatic Pyramidal <c+a>

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θθσσα zz=

Tests performed at 350°C with strain rate of 3x10-4 s-1

P

F

F

Mechanical tests: biaxiality

Controlled Biaxiality ratio:

+

≈100

000

000

2/100

010

000

2 m

mqb

De

F

e

PD

πσ

Tests analyzed as a quasi-biaxial test :

� Study of the plastic anisotropy & the effect of change of loading path

A novel biaxial testing machines in hot cell !


IR-1 IR-2Step Biaxiality ratio Total strain

incrementBiaxiality ratio Total strain

increment1 α=0.47 0.5% α=100 1%2 α=100 1% α=0.47 0.6%

Mechanical tests performed on a neutron-irradiated recrystallized zirconium alloy.

Mechanical tests: effect of irradiation

� Simulation of these new tests with the polycrystalline model

+ Slight additional adjustment of Primatic and <a>-pyramidal CRSS : 240 MPa � 230 MPa

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�Good description of the behavior during strain path change (during these first cycles). Yielding in axial tension to be improved.

Simulation of strain path change tests

Internal pressure

/ Axial

Axial / Internal

pressure


TEM observations after neutron irradiation + testing:-In many grains � Basal channels � Change of easy glide slip system (B vs. P)-Clearing of the loops easier in the basal plane than in the prismatic plane.

In situ straining in TEM after Zr ion irradiation:-In situ observation of annihilation of loops by <a> dislocations gliding in prismatic and pyramidal planes. Incorporation of the loops as super-jog or helix turn.

Dislocation Dynamics simulations:-Clearing of loops easier in the basal plane than in the prismatic plane. In agreement with TEM observations.-Simulation of a real interaction observed in situ. Good agreement with in situ TEM.

Polycrystalline model adapted for irradiated material :�Good fitting on monotonic transverse tensile and internal pressure tests.�Good prediction of cyclic tests : Bauschinger effect and cyclic strain softening�Good prediction of the anisotropy and effect of change of loading path�Good prediction of slip system activities compared to TEM observations

Conclusions

Thank you for your attention !

Mécanismes de déformation et dommage d’irradiation...

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