Strain-path change tests and physically based ... transient: Rapid deformationof the pellet ... materi F. Onimus ASTM 18th Zirconium in the Nuclear Industry, May 15-19, 2016, Hilton

ASTM International B10 18th International Symposium on Zirconium in the Nuclear Industry,

May 15-19, 2016, Hilton Head Island, SC, USA.

Strain-path change tests and physically

based polycrystalline modelling of the

behavior of recrystallized zirconium alloys

F. Onimus1, M. Bono2, J. Garnier1, A. Soniak2, R. Limon2,

D. Gilbon3, F. Bourlier4, A. Ambard5

1CEA, DEN, Section for Applied Metallurgy Research, 91191 Gif-Sur-Yvette, Cedex, France,2CEA, DEN, Section for Study of Irradiated Materials, 91191 Gif-Sur-Yvette, Cedex, France,

3CEA, DEN, Nuclear Material Department, 91191 Gif-Sur-Yvette, Cedex, France,4AREVA NP, 10 rue Juliette Récamier 69456, Lyon Cedex 06, France,

5EDF/R&D, Les Renardières, Ecuelles, 77818 Moret sur Loing Cedex, France.

F. Onimus ASTM 18th Zirconium in the Nuclear Industry, May 15-19, 2016, Hilton Head Island, SC, USA 2

Fuel pellet

Zr cladding

Fuel rod

Complex loading history during in-reactor operation

Fastneutrons

After 1 or 2 PWR cycles � mechanical contact

Water P=15.5 MPa� Creep down + pellet swelling� Pellet Cladding Mechanical Interaction

FissionProduct � high radiation damage

Power transient


During power transient :

�Rapid deformation of the pellet

�High stresses and plastic deformation of the cladding

Increasing renewable electricity � Enhanced maneuverability is required

�Need for a better knowledge and prediction of the effect of strain

path change on the mechanical behavior of thin cladding tubes.

Complex loading history during in-reactor operation

1) Principle of strain path change tests

2) Strain path change tests on non-irradiated material

3) Strain path change tests on neutron-irradiated material

4) Polycrystalline model for non-irradiated and neutron-irradiated materials

1) Principle of strain path change tests


Materials and mechanical tests

50 µm

9.5 mm

Cladding tube samples

Recrystallized zirconium alloys

RD (z)

TD (θ)

Two novel biaxial testing machines

in conventional lab … and in hot cell !


P

F

F

θθσσα zz=

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

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


NI-1 NI-2 NI-3 NI-4Step Biaxiality

ratioMaximum total strain

Biaxiality ratio

Maximum total strain

Biaxiality ratio


Biaxiality ratio


1 α=100 2% α=100 2% α=0 2% α=0.47 2%2 α=0 2% α=0.47 2% α=100 2% α=100 2%3 α=100 2% α=100 2% α=0 2% α=0.47 2%4 α=0 2% α=0.47 2% α=100 2% α=100 2%

Mechanical tests performed on non-irradiated recrystallized Zy-4.

Mechanical tests: change of loading path

� Study of the effect of change of loading path

2) Strain path change tests on

non-irradiated material


( ) ( )( ) ( )2

3

2

1

2

1 1 qbqbzz

qbzz

qbeqH HHH θθθθ σσσσσ +−+−=

Anisotropy: yield surface and strain direction

Measure of the flow stress for a plastic

strain offset of 0.1%

Hill criterion and comparison with

Von Mises criterion

Yield surface Strain direction

� strong plastic anisotropy (H3=0.14) (isotropic H3=0.5)

Negative axial strain rate for internalpressure test

� strong plastic anisotropy

-20°

α=0.47


Effect of change of loading path

Comparison between first and second stepsAxial tensile tests Pure hoop tensile tests

Internal pressure testsAxial tensile tests

� Significant effect of the previous step ! � Combined effect of kinematic and isotropic hardening

Effect of

kinematic

hardening

Effect of

isotropic

hardening

Hoop / Axialvs.

Axial

Axial / Hoopvs.

Hoop

Int. Press. / Axialvs.

AxialAxial / Int. Press.

vs.Int. Press.


θθσ

zzσ

θθσ

zzσIsotropic hardening Kinematic hardening

Expansion of the yield surface Translation of the yield surface

Decrease of the yield stress

Isotropic & kinematic hardening

Increase of the flow stress


Deformation mechanisms: Non-irradiated

1 µm

Pyramidal Π1

Basal B

Prismatic Pb=<c+a>

c

a2

a3

a1b=<a>

At the grain scale

Dislocation glide in the prismaticplanes mainly�Dislocation–dislocation interactions� Isotropic (strain) hardening

Grains with various crystallographicorientations + strong plastic anisotropy(difficult <c+a> glide)� Strain incompatibilities between grains� Composite effect � Back stresses� Kinematic hardening

At the polycrystalline scale

γγγγg=1% to 5%

Non irradiated

3) Strain path change tests on

neutron-irradiated material


50 nm

10 nm

Displacement cascade

Fast neutrons

n b

Dislocation loop

Deformation mechanisms: Neutron-irradiated

After testingAs-irradiated

� Clearing of loops by gliding dislocations� Local strain softening + localization of the plastic strain� Observation of Basal channels, no prismatic channel (internal pressure test)� Change of the easy slip system !


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

� Irradiation induced hardening due to high density of small dislocation loops

Non-irradiated

Irradiated

� Lower plastic anisotropy (H3=0.36) (vs. H3=0.14 for Non-Irradiated)

� Reduced plastic anisotropy afterirradiation !

Due to the easier activation of basal slip for internal pressure tests

+ Strain rate direction during internalpressure test : -8° (vs. -20° non-irradiated)


Comparison between first and second steps

Effect of change of loading path

Internal pressure testsAxial tensile tests

� No clear effect of the previous step (for these first two steps)

� No isotropic hardening

� No clear evidence of kinematic hardening

Int. Press. / Axialvs.

Axial

Axial / Int. Press.vs.

Int. Press.


Comparison with 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.

Stabilized hysterisis loops

Tension-compression tests in transverse direction at 350°C on recrystallized Zy-2

� Strong Bauschinger effect after irradiation

(note the scales)

� Significant kinematic hardening evidenced

during tension-compression tests

� The kinematic hardening remains lower than

the isotropic stress (1/2 size of the yield

surface)

Maximum stress(irradiated Zy-2)

� Cyclic strain softening after irradiation due

to the clearing of loops by dislocations

� During monotonic tests the kinematic

hardening balances the strain softening

� Important role of the kinematic hardening

for neutron-irradiated material

4) Polycrystalline model for non-irradiated

and neutron-irradiated materials


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


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


( )s

ncss

s Kτ

ττγ sign

−=&

totsdcs

cs b ρµαττ += 0 ∑=

sstot ρρ

−= ss

ss ybdt

d ρλ

γρ2

1& ( ) s 0 0 ∀= ρρ s

Parameter (unit) Value for non-irradiated material

(MPa)* 80000

(-)* 0.4

(-)* 10

(MPa)* 5

(-) 370

(-) 0.266

(MPa) 33

(MPa) 45

(MPa) 62

(MPa) 102

(-) 0.1

(µm) 0.1

(nm) 9

(m-2)* 9.6×1010

Eνn

KDδ

0Pτ0aπτ0Bτ0cπτdα

λy

)0(sρ

Flow law:

Strain hardening:

Dislocation density evolution:

xx =0≥x

0=x0<xif then

if then

Intra-granular constitutive laws: Non-irradiated

Pyramidal Π1

Basal B

Prismatic Pb=<c+a>

c

a2

a3

a1b=<a>


Fitting on monotonic first steps, then simulation of the full tests

Simulation of strain path change tests

Axial / Hoop /

Axial / Hoop

Hoop / Axial /

Hoop / Axial

Sim

Exp Sim

Exp

Sim

ExpSim

Exp

F. Onimus ASTM 18th Zirconium in the Nuclear Industry, May 15-19, 2016, Hilton Head Island, SC, USA 23� Good description of the behavior during strain path change


Internal pressure /

Axial / Internal

pressure / Axial

Axial / Internal

pressure / Axial /

Internal pressure Sim

Exp

Sim

Exp

Sim

Exp

Sim

Exp


Validation on tension-compression tests

Tension-compression tests in axial

direction at 350°C on recrystallized Zy-4

Tension-compression tests in transverse

direction at 350°C on recrystallized Zy-2

S.B. Wisner, M.B. Reynolds, R.B. Adamson, in: Zirconium in the Nuclear

Industry: 10th International Symposium, ASTM STP 1245, 1994, p. 499.

Stabilized hysterisis loops

� Very good prediction of the behavior during tension-compression tests.Note: the kinematic hardening is an outcome of the model.

Delobelle, P., Robinet, P., Geyer, P., Bouffioux, P. (1996).

J. Nucl. Mater., 238(2), 135-162.


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: Irradiated

( )ss

ncsss

s xK

x−

−−= τ

ττγ sign&

ssBsBs xDCx γγ &&& −=

Flow law and kinematic intra-granular hardening

γγγγlocal =10% to 100% γγγγg=1% to 5%

Irradiated Non irradiated

Armstrong–Frederick lawOnimus, F., Béchade, J.-L. (2009). J. Nucl. Mater., 384, pp. 163–174.


Coefficients for the irradiated material obtained after the refinement.

Coefficients of the model

Parameter (unit) Value for irradiatedmaterial

* (MPa) 80000* 0.4* 10

* (MPa.s1/n) 5(MPa) 230(MPa) 230(MPa) 300(MPa) 85* (m-2) 5×1014

0.540

(MPa) 105

30002800.53

Eν

nK

cPτc

a><πτc

ac >+<πτ0c

Bτ( )0bρ

Bα

Bk

BC

BD

Dδ

Basal

Prismatic

MPa1880 =+= lscs

cs b ρµαττ

�Lower critical shear stress and strain softening for basal slip�Constant critical shear stress for other slip systems

Fitting on monotonic first steps, then simulation of the full tests


�Good description of the behavior during strain path change (during these first cycles).


Internal pressure

/ Axial

Axial / Internal

pressure


Validation on tension-compression tests

S.B. Wisner, M.B. Reynolds, R.B. Adamson, in: Zirconium in the Nuclear

Industry: 10th International Symposium, ASTM STP 1245, 1994, p. 499.

� Good prediction of the Bauschinger effect and the cyclic strain softening.

� The simulation shows that during the first cycles the isotropic stress remains high compared to the kinematic hardening.

� This explains why the kinematic hardening is not evidenced during ourstrain path change tests.


Strain path change tests on non-irradiated material:

-anisotropic plastic behavior (due to difficult <c+a> glide)

-combined effect of isotropic hardening (dislocation-dislocation interactions) and

kinematic hardening (grain-grain interactions).

Strain path change tests on neutron-irradiated material:

-reduced plastic anisotropy due to easier basal slip for internal pressure tests

-no isotropic hardening (even cyclic strain softening due to clearing of loops)

-no significant evidence of kinematic hardening during our tests, despite its important

role. This is due to strong radiation induced hardening by loops �high isotropic stress

compared to kinematic hardening.

Polycrystalline model:

-good prediction of the effect of strain path change and good prediction of tension-

compression tests for both non irradiated and irradiated material.

Conclusions

Acknowledgements : Hot lab team for mechanical tests, P. Pilvin for providing the initial polycrystalline model.

Thank you for your attention !


Additional slides


First channels creation.High strain hardening rate.

1 µm

Σ

Ep0.5%0.2%

Propagation of channels

10 µm

Ductile failure mode

Localization of the deformation at the specimen scale

200 nm

In the neckingzone highlydeformedmaterial withoutirradiation defects

[Onchi et al. JNM 1980]

Mechanisms during mechanical tests


During axial tensile tests:�the Basal slip systems are not well orientated�Activation of Prismatic slip

� After irradiation Basal glide and clearing of loops easier, but Prismaticglide and clearing of loops occur when Basal slip not well orientated.

(z)

(θ)

{0002} pole figure

Prismatic channels, no B channel

Deformation mechanisms: Neutron-irradiated


Another evidence of kinematic hardening

Analysis of the unloading

� Non-linear behavior during unloading� Evidence of plasticity at the end of unloading� Evidence of high kinematic hardening (translation of the yield surface)

compared to a small isotropic stress (size of the yield surface)

Internal pressure testAxial tensile test


Kinematic hardening ?

Internal pressure testAxial tensile test

� No non-linear behavior at the end of the unloading� The kinematic hardening (translation of the yield surface) remains lower

than the isotropic stress (size of the yield surface).Because of the strong radiation induced hardening, the kinematic hardeningis not evidenced.

Analysis of the unloading

Documents

Strain-path change tests and physically based ... transient: Rapid deformationof the pellet ... materi F. Onimus ASTM 18th Zirconium in the Nuclear Industry, May 15-19, 2016, Hilton