F. Onimus , L. Dupuy , M. Gaumé , W. Kassem F. Mompiou...F. Onimus 19th International Symposium on Zirconium in the Nuclear Industry, 19–23 May 2019 | Manchester, UK 2 0 100 200

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

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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 ?


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


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


→ 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


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


(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


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


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.


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


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





→ Need for a better understanding of the interactions betweendislocation and loops to understand the observed deformation mechanisms




interactions


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


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


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)


bG=b2

bL=b1

𝜽 = 𝟐𝟏°



Screw type interaction, different Burgers vectors (bL=b1, bG=b2)


bG=b2

bL=b2

𝜽 = 𝟕𝟐°

→ Partial clearing / No pinning


Edge type interaction, same Burgers vectors (bL=bG)


bG=b2

bL=b1

𝜽 = 𝟕𝟐°

→ Full clearing / No pinning


Edge type interaction, different Burgers vectors (bL=b1, bG=b2)


For prismatic slip:Easy clearing of loops in the « edge-type » directionStrong pinning by loops in the « screw-type» direction


→ 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


bG=b2

bL=b2

𝜽 = 𝟏𝟎°


Simulations of dislocations gliding in Basal Plane

Screw type interaction, same Burgers vectors (bL=bG)


bG=b2

bL=b1

𝜽 = 𝟏𝟎°

→Weak pinning / No clearing


Screw type interaction, different Burgers vectors (bL=b1, bG=b2)


bG=b2

bL=b3

𝜽 = 𝟓𝟒°

→ Full clearing / No pinning


Mixed type interaction, different Burgers vectors (bL=b3, bG=b2)


bG=b2

bL=b2

𝜽 = 𝟖𝟒°

→ Partial clearing / No pinning


Edge type interaction, same Burgers vectors (bL=bG)


bG=b2

bL=b1

𝜽 = 𝟖𝟒°

→ Pinning/ No clearing




bG=b2

bL=b3

𝜽 = 𝟖𝟒°

→ Pinning/ No clearing





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.





→ Need for a better understanding of the interactions betweendislocation and loops to understand the observed deformation mechanisms




interactions


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


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



• 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


100 nm

Dislocation gliding in pyramidal plane (speed x2)

100 nm

𝑏


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


From Dislocation Dynamics → details of the interaction

Dislocation gliding in pyramidal plane at 350°C


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


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.


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.

Documents

F. Onimus , L. Dupuy , M. Gaumé , W. Kassem F. Mompiou...F. Onimus 19th International Symposium on Zirconium in the Nuclear Industry, 19–23 May 2019 | Manchester, UK 2 0 100 200