mécanismes de déformation et dommage d’irradiation...
TRANSCRIPT
13/06/2016
1
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
13/06/2016
2
F. Onimus Rencontres Franciliennes de Mécanique, 13-14 juin 2016, France 3
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
F. Onimus Rencontres Franciliennes de Mécanique, 13-14 juin 2016, France 4
� 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)
13/06/2016
3
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
F. Onimus Rencontres Franciliennes de Mécanique, 13-14 juin 2016, France 6
� 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
13/06/2016
4
F. Onimus Rencontres Franciliennes de Mécanique, 13-14 juin 2016, France 7
Dislocation channelling mechanism
Thin foil Channel
In many irradiated metals and alloys
� Local strain softening + Localization of the plastic strain
F. Onimus Rencontres Franciliennes de Mécanique, 13-14 juin 2016, France 8
� 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
13/06/2016
5
F. Onimus Rencontres Franciliennes de Mécanique, 13-14 juin 2016, France 9
�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
F. Onimus Rencontres Franciliennes de Mécanique, 13-14 juin 2016, France 10
50 µm
A Multi-Scale Approach
50 nm
In situ tensile test in TEM� dislocation motion
TEM observations of grains�Deformation mechanisms
Mechanical tests� Mechanical behavior
�Need for a better understanding of the dislocation channelling process& origin of the change of the easy glide slip system.
13/06/2016
6
F. Onimus Rencontres Franciliennes de Mécanique, 13-14 juin 2016, France 11
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
F. Onimus Rencontres Franciliennes de Mécanique, 13-14 juin 2016, France 12
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
13/06/2016
7
F. Onimus Rencontres Franciliennes de Mécanique, 13-14 juin 2016, France 13
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
F. Onimus Rencontres Franciliennes de Mécanique, 13-14 juin 2016, France 14
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.
13/06/2016
8
F. Onimus Rencontres Franciliennes de Mécanique, 13-14 juin 2016, France 15
50 µm
A Multi-Scale Approach
50 nm
In situ tensile test in TEM� dislocation motion
TEM observations of grains�Deformation mechanisms
Mechanical tests� Mechanical behavior
Nodal DD code Edge-screw DD code
Dislocation DynamicsNew nodal Dislocation Dynamics code:
NUMODIS
F. Onimus Rencontres Franciliennes de Mécanique, 13-14 juin 2016, France 16
Force calculationξσ ×⋅= )( bf
Stress calculation
Velocity
Discrete events
Discretization
)(vBf =
Nodal structure
Peach-Koehler
Explicit algorithm
Strain or stress control
Dislocation dynamics: NUMODIS
13/06/2016
9
F. Onimus Rencontres Franciliennes de Mécanique, 13-14 juin 2016, France 17
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
F. Onimus Rencontres Franciliennes de Mécanique, 13-14 juin 2016, France 18
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
13/06/2016
10
F. Onimus Rencontres Franciliennes de Mécanique, 13-14 juin 2016, France 19
���� 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
Dislocation dynamics simulations vs. in situ TEM observations
F. Onimus Rencontres Franciliennes de Mécanique, 13-14 juin 2016, France 20
���� Great agreement between simulation and experiment !
L. Dupuy
3D overlaping of the two films !
Dislocation dynamics simulations vs. in situ TEM observations
13/06/2016
11
F. Onimus Rencontres Franciliennes de Mécanique, 13-14 juin 2016, France 21
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
F. Onimus Rencontres Franciliennes de Mécanique, 13-14 juin 2016, France 22
Homogeneous Equivalent Medium (HEM)
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
13/06/2016
12
F. Onimus Rencontres Franciliennes de Mécanique, 13-14 juin 2016, France 23
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
F. Onimus Rencontres Franciliennes de Mécanique, 13-14 juin 2016, France 24
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
13/06/2016
13
F. Onimus Rencontres Franciliennes de Mécanique, 13-14 juin 2016, France 25
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
F. Onimus Rencontres Franciliennes de Mécanique, 13-14 juin 2016, France 26
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
13/06/2016
14
F. Onimus Rencontres Franciliennes de Mécanique, 13-14 juin 2016, France 27
Validation on TEM observations
Transverse tensile test
Computed shear strain rate (slip activities) / TEM observations
Grain 2
Grain 6
Basal Prismatic Pyramidal <c+a>
F. Onimus Rencontres Franciliennes de Mécanique, 13-14 juin 2016, France 28
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>
13/06/2016
15
F. Onimus Rencontres Franciliennes de Mécanique, 13-14 juin 2016, France 29
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 !
F. Onimus Rencontres Franciliennes de Mécanique, 13-14 juin 2016, France 30
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
13/06/2016
16
F. Onimus Rencontres Franciliennes de Mécanique, 13-14 juin 2016, France 31
�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
F. Onimus Rencontres Franciliennes de Mécanique, 13-14 juin 2016, France 32
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 !