f. onimus , l. dupuy , m. gaumé , w. kassem f. mompiou...f. onimus 19th international symposium on...
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19th International Symposium on Zirconium in the Nuclear Industry
19–23 May 2019 | Manchester, UK
Interaction between dislocation and irradiation induced loops in zirconium alloys
studied by in situ straining experiments in TEM, molecular and dislocation dynamics
simulations
F. Onimus1, L. Dupuy1, M. Gaumé1, W. Kassem1, F. Mompiou2
1 Service de recherches Métallurgiques Appliquées, CEA, Université Paris-
Saclay, 91191 Gif-sur-Yvette, France
2 Centre d'Elaboration de Matériaux et d'Etudes Structurales, CNRS, 29 Rue
Jeanne Marvig, 31055 Toulouse, France
This work has been funded by the project GAINE from the
French nuclear tripartite institute CEA EDF Framatome.
The development of Dislocation Dynamics has been funded
by the French Agence Nationale de la Recherche (ANR).
F. Onimus 19th International Symposium on Zirconium in the Nuclear Industry, 19–23 May 2019 | Manchester, UK 2
0
100
200
300
400
500
600
0% 2% 4% 6% 8% 10% 12%
Déformation circonférentielle
Co
ntr
ain
te
cir
co
nfé
ren
tiell
e (
MP
a)
Zy-4 Rx non irradiéZy-4 Rx irradié
Radiation effects on the mechanical behavior
Non irradiated
Irradiated
Necking
Necking
Internal pressure test at 350°C
Hoop strain (%) H
oo
p s
tre
ss (
MP
a)
Non irradiated
Irradiated
Fuel rod
Fastneutrons
Water
T=320°C,
P=155 bar
→ Irradiation induced hardening→ Decrease of the uniform elongation
(early necking but ductile failure mode)
Need for an understanding and prediction of the effect of irradiation on mechanical behavior
What is the origin of the change in the mechanical behavior ?
F. Onimus 19th International Symposium on Zirconium in the Nuclear Industry, 19–23 May 2019 | Manchester, UK 3
Displacement cascade
Fast neutrons
nb
Dislocation loop
Radiation effects on the microstructure
→ Creation of point defects& point defect clusters
Point defect clusters in zirconium: <a>-loops & <c>-loops
→ High density of small <a>-loops
<c>-loops, only Vacancy loops
<a>-loops, Vacancy and Insterstitial
50 nm
10 nm
<a>-loops are believed to act as obstacles against dislocation glide→ explaining the radiation induced hardening
F. Onimus 19th International Symposium on Zirconium in the Nuclear Industry, 19–23 May 2019 | Manchester, UK 4
Dislocation channelling mechanism
Thin foil Channel
→ Clearing of loops by gliding dislocations for sufficient applied stress
F. Onimus, J.-L. Béchade, D. Gilbon (2013) Metall. and Mater. Trans. 44 (1) 45 – 60.F. Onimus, J.-L. Béchade, C. Prioul, P. Pilvin et al. (2005) ASTM STP 1467, 14th B10 Int. Symp.
F. Onimus, I. Monnet, J.-L. Béchade, et al. (2004) J. Nucl. Mater. 328 (2-3) 165-179.
After transverse tensile test at 350°C
F. Onimus 19th International Symposium on Zirconium in the Nuclear Industry, 19–23 May 2019 | Manchester, UK 5
→ Change of the easy glide slip system !
TEM observations after Transverse Tensile test at 350°C
1 µm
Non irradiated + testing
Pyramidal P1
Basal B
Prismatic Pb=<c+a>
c
a2
a3
a1
b=<a>
After neutron irradiation + testing
Observation of Basal channels, no prismatic channel
.
Specimen 1
Grain 2
F. Onimus 19th International Symposium on Zirconium in the Nuclear Industry, 19–23 May 2019 | Manchester, UK 6
Observation of Basal channels.No prismatic channel.
g=0002
TEM observations after Internal Pressure test at 350°C
Specimen 2
Grain 1Specimen 2
Grain 3
F. Onimus 19th International Symposium on Zirconium in the Nuclear Industry, 19–23 May 2019 | Manchester, UK 7
(z)
(q)
→the Basal slip systems are not well orientated→Activation of Prismatic slip
→ More difficult activation of Prismatic glide after irradiation and only partial clearing of loops.
{0002} pole figure
Prismatic channels (+pyramidal), no B channel
TEM observations after Axial Tensile test at 350°C
F. Onimus 19th International Symposium on Zirconium in the Nuclear Industry, 19–23 May 2019 | Manchester, UK 8
A Multi-Scale Approach
TEM observations of grains→Deformation mechanisms
Mechanical tests→ Mechanical behavior
→ Study of interactions between dislocation and loops to understand the observed deformation mechanisms
Molecular Dynamics→ Details of dislocation–loop
interactions
Dislocation Dynamics→ Towards more complexand larger configurations
In situ straining in TEM vs. Dislocation Dynamics
F. Onimus 19th International Symposium on Zirconium in the Nuclear Industry, 19–23 May 2019 | Manchester, UK 9
Molecular & Dislocation Dynamics simulations
Following the work done by Serra & Bacon →MD simulations of interactions between loops and dislocation (only edge/screw dislocations in prismatic plane)
[Serra, A., & Bacon, D. J. (2013). Modelling and Simulation in Materials Science and Engineering, 21(4)]
Molecular Dynamics
6,000,000 DoF
LAMMPS
→Need for higher length scale simulations → Dislocation dynamics
LAMMPS
Dislocation Dynamics
300 DoF
→ Atomic scale informed Dislocation Dynamics simulations
DoF: Degree of Freedom Elastic coefficients, mobility coefficients & dislocation core energy.
F. Onimus 19th International Symposium on Zirconium in the Nuclear Industry, 19–23 May 2019 | Manchester, UK 10
Friction coefficient Value
𝐵𝑃 2.96×10-5 Pa.s
𝐵𝐵 4.56×10-5 Pa.s
𝑝 1.72×10-13 Pa.s.m
𝐵𝑒𝑓𝑓 = 𝐵𝑃 + 𝜌𝑛 𝐵𝐵ℎ𝑗𝑜𝑔
2+ 𝑝
𝜌𝑛 = 𝑛/𝐿
Molecular & Dislocation Dynamics simulations
Mobility coefficient measurement from MD simulations for « unjogged » and « jogged » edge dislocations gliding in the prismatic plane
Modeling of the effective friction coefficient of a jogged dislocation:
Taking into account additional friction on the constricted nodes (p)→ DD simulation are parametrized on MD simulations
(Number of constricted nodes per unit length)
𝑣 =𝜏𝑏
𝐵
F. Onimus 19th International Symposium on Zirconium in the Nuclear Industry, 19–23 May 2019 | Manchester, UK 11
Detailed comparison of dislocation – loop interactionsDislocation Dynamics vs. Molecular Dynamics
Edge dislocation Screw dislocationPrismatic Prismatic
Dif
fere
nt
Bu
rge
rs v
ec
tors
Sa
me
Bu
rge
rs v
ec
tors
LAMMPS
LAMMPS
LAMMPS
→ Validation of the Dislocation Dynamics by detailed comparison with MolecularDynamics simulations on pure screw/edge dislocations in the prismatic plane
→ Study of more complex configurations using DD simulations
F. Onimus 19th International Symposium on Zirconium in the Nuclear Industry, 19–23 May 2019 | Manchester, UK 12
A Multi-Scale Approach
TEM observations of grains→Deformation mechanisms
Mechanical tests→ Mechanical behavior
→ Need for a better understanding of the interactions betweendislocation and loops to understand the observed deformation mechanisms
Dislocation Dynamics→ Towards more complexand larger configurations
In situ straining in TEM vs. Dislocation Dynamics
Molecular Dynamics→ Details of dislocation–loop
interactions
F. Onimus 19th International Symposium on Zirconium in the Nuclear Industry, 19–23 May 2019 | Manchester, UK 13
𝜎23
𝜎23
y
xScrew type
interaction
Edge type
interaction
q
Mixed type
interactionbL=b2
bG=b2
Simulations of complex configurations
Dislocation Dynamics simulations of mixed dislocations gliding either in the prismaticor basal planes and interacting with loops
Large Frank-Read dislocation source - dislocation loop
F. Onimus 19th International Symposium on Zirconium in the Nuclear Industry, 19–23 May 2019 | Manchester, UK 14
y
xScrew type
interaction
Edge type
interaction
q
Mixed type
interactionbL=b2
bG=b2
Simulations of complex configurations
Dislocation Dynamics simulations of mixed dislocations gliding either in the prismaticor basal planes and interacting with loops
F. Onimus 19th International Symposium on Zirconium in the Nuclear Industry, 19–23 May 2019 | Manchester, UK 15
bG=b2
bL=b2
𝜽 = 𝟏𝟎°
→ Strong pinning / No clearing
Simulations of dislocations gliding in Prismatic Plane
Screw type interaction, same Burgers vectors (bL=bG)
F. Onimus 19th International Symposium on Zirconium in the Nuclear Industry, 19–23 May 2019 | Manchester, UK 16
bG=b2
bL=b1
𝜽 = 𝟐𝟏°
→ Strong pinning / No clearing
Simulations of dislocations gliding in Prismatic Plane
Screw type interaction, different Burgers vectors (bL=b1, bG=b2)
F. Onimus 19th International Symposium on Zirconium in the Nuclear Industry, 19–23 May 2019 | Manchester, UK 17
bG=b2
bL=b2
𝜽 = 𝟕𝟐°
→ Partial clearing / No pinning
Simulations of dislocations gliding in Prismatic Plane
Edge type interaction, same Burgers vectors (bL=bG)
F. Onimus 19th International Symposium on Zirconium in the Nuclear Industry, 19–23 May 2019 | Manchester, UK 18
bG=b2
bL=b1
𝜽 = 𝟕𝟐°
→ Full clearing / No pinning
Simulations of dislocations gliding in Prismatic Plane
Edge type interaction, different Burgers vectors (bL=b1, bG=b2)
F. Onimus 19th International Symposium on Zirconium in the Nuclear Industry, 19–23 May 2019 | Manchester, UK 19
For prismatic slip:Easy clearing of loops in the « edge-type » directionStrong pinning by loops in the « screw-type» direction
Simulations of dislocations gliding in Prismatic Plane
→ The expansion of the dislocation is impeded in the screw direction, leading to a difficultactivation of prismatic slip.
→ Clearing of loops is restricted to the edge direction, leading to a difficult formation of dislocation channels.
→ This explains the TEM observations of difficult activation of prismatic slip after neutron irradiation and partially cleared channels in the prismatic plane.
Light blue domain : weak interaction,
either partial clearing or no interaction
depending on the height of the loop
F. Onimus 19th International Symposium on Zirconium in the Nuclear Industry, 19–23 May 2019 | Manchester, UK 20
bG=b2
bL=b2
𝜽 = 𝟏𝟎°
→ Strong pinning / No clearing
Simulations of dislocations gliding in Basal Plane
Screw type interaction, same Burgers vectors (bL=bG)
F. Onimus 19th International Symposium on Zirconium in the Nuclear Industry, 19–23 May 2019 | Manchester, UK 21
bG=b2
bL=b1
𝜽 = 𝟏𝟎°
→Weak pinning / No clearing
Simulations of dislocations gliding in Basal Plane
Screw type interaction, different Burgers vectors (bL=b1, bG=b2)
F. Onimus 19th International Symposium on Zirconium in the Nuclear Industry, 19–23 May 2019 | Manchester, UK 22
bG=b2
bL=b3
𝜽 = 𝟓𝟒°
→ Full clearing / No pinning
Simulations of dislocations gliding in Basal Plane
Mixed type interaction, different Burgers vectors (bL=b3, bG=b2)
F. Onimus 19th International Symposium on Zirconium in the Nuclear Industry, 19–23 May 2019 | Manchester, UK 23
bG=b2
bL=b2
𝜽 = 𝟖𝟒°
→ Partial clearing / No pinning
Simulations of dislocations gliding in Basal Plane
Edge type interaction, same Burgers vectors (bL=bG)
F. Onimus 19th International Symposium on Zirconium in the Nuclear Industry, 19–23 May 2019 | Manchester, UK 24
bG=b2
bL=b1
𝜽 = 𝟖𝟒°
→ Pinning/ No clearing
Simulations of dislocations gliding in Basal Plane
Edge type interaction, different Burgers vectors (bL=b1, bG=b2)
F. Onimus 19th International Symposium on Zirconium in the Nuclear Industry, 19–23 May 2019 | Manchester, UK 25
bG=b2
bL=b3
𝜽 = 𝟖𝟒°
→ Pinning/ No clearing
Simulations of dislocations gliding in Basal Plane
Edge type interaction, different Burgers vectors (bL=b3, bG=b2)
F. Onimus 19th International Symposium on Zirconium in the Nuclear Industry, 19–23 May 2019 | Manchester, UK 26
Simulations of dislocations gliding in Basal Plane
For basal slip:Dislocations are only pinned for 1/3 cases in the screw direction. Weak interaction or clearing for 2/3 cases in the screw direction.Clearing of loops is possible both in the edge and screw (and mixed) directions.
→ The expansion of the dislocation is possible in the screw direction, leading to an easier activation of basal slip than prismatic slip.
→ Possible clearing in the screw direction → easier formation of dislocation channels.
→ Furthermore, for one basal plane, the three slip systems can be activated, potentially leading to a full clearing of loops in the basal plane.
→ This explains the TEM observations of easier activation of basal slip after neutron irradiation and fully cleared channels in the basal plane.
F. Onimus 19th International Symposium on Zirconium in the Nuclear Industry, 19–23 May 2019 | Manchester, UK 27
A Multi-Scale Approach
TEM observations of grains→Deformation mechanisms
Mechanical tests→ Mechanical behavior
→ Need for a better understanding of the interactions betweendislocation and loops to understand the observed deformation mechanisms
Dislocation Dynamics→ Towards more complexand larger configurations
In situ straining in TEM vs. Dislocation Dynamics
Molecular Dynamics→ Details of dislocation–loop
interactions
F. Onimus 19th International Symposium on Zirconium in the Nuclear Industry, 19–23 May 2019 | Manchester, UK 28
Zr +ion irradiation atJannus-Orsay (ARAMIS)Dose = 0.5 dpa (8. 1013 𝑖𝑜𝑛𝑠/𝑐𝑚2)
Temperature= 500°C Energy= 0.6 MeV
ZrTEM foil
ions Zr+
20 nm
0.5 dpa à 500°C
In situ tensile test at Toulouse (CEMES) at temperatures between 350°C and 500°C.
In situ straining in TEM
ARAMIS facility at Jannus-Orsay (CSNSM)
Recrystallized Zy-4
F. Onimus 19th International Symposium on Zirconium in the Nuclear Industry, 19–23 May 2019 | Manchester, UK 29
Dislocation dynamics simulations vs. in situ TEM observations
Dislocation
loop
Bv
=
→ Evaluation of the friction coefficient Bp~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 the kinetics → Evaluation of the velocity of the dislocation
Pyramidal plane
Tension
Burgers
vector
x7°
y
z
<a> loop
positions
<a> dislocation in pyramidal plane
Burgers
vector
F. Onimus 19th International Symposium on Zirconium in the Nuclear Industry, 19–23 May 2019 | Manchester, UK 30
Dislocation dynamics simulations vs. in situ TEM observations
• 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
Drouet, J., Dupuy, L., Onimus, F., Mompiou, F. (2016). Scripta Materialia, 119, 71-75.
Bp=0.3 MPa.s
BP=0.3 MPa.s
BB=3 MPa.s
Vacancy loopSame Burgers vectors
F. Onimus 19th International Symposium on Zirconium in the Nuclear Industry, 19–23 May 2019 | Manchester, UK 31
100 nm
Dislocation gliding in pyramidal plane (speed x2)
100 nm
𝑏
Dislocation dynamics simulations vs. in situ TEM observations
The loop seems to be pinned by solute atoms
Bp=0.3 MPa.s
BP=3 MPa.s
BB=30 MPa.s
Interstitial loopSame Burgers vectors
F. Onimus 19th International Symposium on Zirconium in the Nuclear Industry, 19–23 May 2019 | Manchester, UK 32
From Dislocation Dynamics → details of the interaction
Dislocation gliding in pyramidal plane at 350°C
Dislocation dynamics simulations vs. in situ TEM observations
Interstitial loopDifferent Burgers vectors
The loops seem to be pinned by solute atomsThe dislocation seems to undergo dynamic strain ageing due to solute atoms
Bp=3 MPa.s
BP=1 MPa.s
BB=10 MPa.s
F. Onimus 19th International Symposium on Zirconium in the Nuclear Industry, 19–23 May 2019 | Manchester, UK 33
Conclusions 1/2
-<a>-loops act as pinning point to dislocation motion leading to radiation induced hardening-For sufficient applied stress <a>-loops can be cleared by gliding dislocations leading to the formation of channels that are responsible for the early necking.-Slip systems are not affected in the same way by irradiation: easier basal slip activation and clearing of loops than for prismatic slip.
-DD simulations have been parametrized, with success, on MD simulations usingsimple configurations-DD simulations have been used to simulate more complex configurations-Systematic simulations of many different geometries, for basal and prismaticslip, have explained why basal activation and basal clearing is easier thanprismatic slip.
F. Onimus 19th International Symposium on Zirconium in the Nuclear Industry, 19–23 May 2019 | Manchester, UK 34
Conclusions 2/2
On good tracks towards a better understanding and a multi-scale modelling of the effects of irradiation on deformation mechanisms of zirconium alloys.In future prospects, this will help to improve the performance and safety of the nuclear fuel used in Light Water Reactors.
Thank you for your attention !
-In situ straining experiments in TEM have shown both the pinning of dislocations by loops and the clearing of loops by gliding dislocations.-In situ straining experiments have been correctly simulated by dislocation dynamics confirming the extrapolation ability of this numerical tool.
-Towards quantitative analysis of the strength of dislocation - loop interaction-Towards massive dislocation dynamics simulations involving many loops and many dislocations.
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