Evaluation of the Oxygen-Induced Zircaloy Embrittlement in ICARE/CATHARE

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11th International QUENCH Workshop, October 25-27, 2005, Forschungszentrum Karlsruhe, Germany

Evaluation of the Oxygen-Induced Zircaloy

Embrittlement in ICARE/CATHARE

Ladislav Belovsky

ALIAS CZ s.r.o., Czech [email protected]

Presented at the 11th International QUENCH Workshop, October 25-27, 2005, Forschungszentrum Karlsruhe, Germany

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Motivation for Development of a New Model (ZROB)

• ICARE/CATHARE: … applicable also for LOCA and beyond DBA analyses

• Acceptance criteria for ECCS for LWRs ( 10CFR50.46 ): Evaluation of post-quench cladding embrittlement (17% ECR by B-J since 1973).

• The 17% ECR criterion currently under revision by USNRC:– High burnup (hydrogen, pre-oxide).

– New Zr-based alloys

• Exp. research indicates that embrittlement is a combined function of :– Oxygen content & distribution metal (beta phase)– Hydrogen content (& distribution ?) in metal

• Modeling of Zircaloy embrittlement in ICARE/CATHARE in two steps:– 1. step: Oxygen-induced embrittlement (O-diffusion in beta phase)– 2. step: Impact of hydrogen onto embrittlement (O-solubility & diffusion, hydrides, …)

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Modeling Features & Assumptions

• ZROB receives beta layer boundaries from oxidation module (ZROX or UZRO)

• ZROB calculates 1D oxygen diffusion in beta layer >970 °C (oxygen-free ZR in ZROX):

– Oxidizing surface: - Beta layer (ZR) always covered with O-stabilized alpha layer (ZRO). - Boundary concentration at ZR/ZRO: Zircaloy-Oxygen phase

diagram

– Non-oxidizing surface: Zero oxygen flux.

– Uniform meshing, Cylindrical coordinates, Implicit finite-difference method, Gauss elimination.

– Initial condition: Constant concentration profile (as-received material).

• ZROB deduces from the oxygen concentration profile in the beta layer :

1. Thickness of beta layer with less than specified O-concentration ( …, 0.6, 0.7, … wt% O ).

2. Fractional saturation of beta layer.

3. embrittled Zircaloy components after quenching (Chung-Kassner 1 and/or Pawel 2 criterion).

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Diffusion Equation for Oxygen in ZR Layer

• Oxygen mass balance in ith segment:

• Oxygen fluxes at segment boundaries: Ji = Di ·ΔC/ΔR

CN

CN-1

Ci+1 CiCi-1

C2

C1

RN RN-1 Ri+1 Ri Ri-1 R2 R1

rN rN-1 ri+1 ri ri-1 r2 r1rN+1

i-th segment (regular)

inner segment

outer segment

r

C

thickness of ZR layer

Ji+1 JiJN+1 J1

ii

i

ii JJt

Crr

122

1

Example of two-sided oxidation

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Oxygen diffusion coefficient in ZR layer

> 970 °C (-Zr) : D = 2.63·10-6 exp(-28200/(1.987·T)) J. Nucl. Mat. 68 (1977)

< 820 °C (-Zr) : D = 1.32·10-4 exp(-48200/(1.987·T)) J. Nucl. Mat. 67 (1977)

1.E-18

1.E-16

1.E-14

1.E-12

1.E-10

1.E-08

4 6 8 10 12 14

10000 / T [ 1/K]

D [

m2/s

]

beta-Zralpha-Zr(a+b)-Zr

970 820 °C

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Oxygen solubility SO in ZR layer at ZR/ZRO interface

• >1007 °C : SO = exp(5.02 – 8220 / T[K]) [wt%] As-received Zircaloy (Chung-Kassner 3)

• 970-1007 °C : SO = 5.246·10-3·(T[K]-1233)

• < 970 °C : SO = 0

T [

C ]

Oxygen concentration [ at% ]

-Zr

ZrO2

-Zr

inner clad surface

outer surface

Phase diagramZry-O

SO

ZRO

ZR

700

900

1100

1300

1500

1700

1900

2100

0.0 0.4 0.8 1.2 1.6 2.0 2.4

Oxygen concentration [ wt% ]

Tem

per

atu

re [

C]

Zr-O

Zry: Chung-KassnerI/C UZRO: Berdyshev

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Input & Output Data

• Input: – MACR xxxx User name of the oxidizing Zircaloy macro-component (eg. CLAD1).– CINI Initial O-concentration in as-received Zircaloy: 0.1 wt% ( 0 -

1.5 )– COXX User defined critical O-concentration: 0.55 wt% ( 0 - 2 )– DTMX Max. length of internal sub-time step within global Δt: 0.5 s ( 0.001 - 10 )– NMAX Max. number of concentration points in ZR: 15

( 4 - 100 )

• Output:

– Fractional saturation of beta layer FBS = CAV / SO

– CAV : Average concentration of oxygen in ZR layer

– SO : Boundary concentration of oxygen in ZR (oxygen solubility)

– Thickness THICXX within ZR with max. COXX [wt%] oxygen(another six variables THIC04 to THIC09 are automatically calculated for 0.4 to 0.9 wt%)

– If embrittlement criterion fulfilled < 400 K (Chung-Kassner 1 or Pawel 2), component state DISLOCAT.

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Results: Numerical Against Analytical Solution

• Non-moving boundary diffusion problem in a slab, thickness l = 0.7 mm

– Outer surface: oxidizing, boundary concentration from Chung-Kassner 3 correlation– Inner surface: zero oxygen flux– Initial O-conc.: 0.1 wt% (1000 wt ppm)– Constant temperature 1000 °C, 1400 °C

• Analytical solution (Carslaw & Jaeger 4): – Oxygen concentration C(x, t) after t seconds at distance x from the surface:

• Numerical solution by ZROB :– Clad diameter 9 m ( slab)– Default input data

• Comparison: Good agreement (see next figures)

02

2200 2

)12(cos4

)12(exp12

)1(41,

k

k

B l

xk

l

tDk

kCCCtxC

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Results: Numerical Against Analytical Solution Cont’d

Temperature

1000 °C

-4

-2

0

2

4

6

8

10

12

14

16

18

0 100 200 300 400 500 600 700

Distance from the outer cladding surface [micron]

Ox

yg

en

co

nc

en

tra

tio

n

[kg

/m3 ]

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

Re

l. d

iffe

ren

ce

(A

- Z

RO

B)

/ A

[%

]

AnalyticalZROBRel. difference [%]60 s

400 s 1140 s

60 s

400 s

1140 s

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Results: Numerical Against Analytical Solution Cont’d

Temperature

1400 °C

-20

-10

0

10

20

30

40

50

60

70

80

90

100

0 100 200 300 400 500 600 700

Distance from the outer cladding surface [micron]

Ox

yg

en

co

nc

en

tra

tio

n

[kg

/m3 ]

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

Re

l. d

iffe

ren

ce

(A

- Z

RO

B)

/ A

[%

]

AnalyticalZROBRel. difference [%]

40 s

480 s

480 s

40 s

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Results: Sensitivity to Meshing and Time step

• Temperature 1400 °C

-1

0

1

2

3

4

5

6

7

8

0 10 20 30 40 50 60 70 80 90 100

Number of concentration points NMAX [-]

Ma

x.

rela

tiv

e d

iffe

ren

ce

[%

] 40 s

480 s

-1

0

1

2

3

4

5

6

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Internal sub-time step DTMX [ s ]

Ma

x.

rela

tiv

e d

iffe

ren

ce

[%

]

40 s

480 s

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Results: Isothermal Oxidation (As-received Zircaloy)


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Results: Isothermal Oxidation (As-received Zry) Cont’d


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Results: Transient Oxidation (As-received Zry)

• Linear heat-up and cool-down between 800 and 1300 °C at 1 °C/s

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• Absorbed hydrogen CH increases the oxygen solubility SO in beta phase.

• CEA 5, 6 experimental data available for 1200 °C.

• Saturation of this effect at 600 wppm H.

• Billone (ANL, 2005) 7: Fit to CEA data (additive term to Chung-Kassner 3 correlation):

SO = exp(5.02 – 8220 / T) + 0.6· (1 - exp[-0.006· CH]) [wt%] T[K], CH [ wppm].

• The increased solubility limitaccelerates the filling of betaphase with oxygen.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 200 400 600 800 1000

H [wppm]

O-s

olu

bili

ty in

bet

a [w

t%]

CEA Experiment

ANL Fit to data

Oxygen Solubility in Hydrided Zircaloy

0.6

1200 °C

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• Beta layer poor in oxygen (~ < 0.6 wt%) disappears faster in hydrided Zircaloy.

FBS = CAV / CB, FBSA = (CAV – CINI) / (CB - CINI), where CINI … initial oxygen conc. in as received Zry.

Results: Isothermal Oxidation (Hydrided Zircaloy)

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Conclusions

• Zry embrittlement module ZROB available since mid 2005 (ICARE2-V3mod1.4).

– Applied embrittlement criteria: Chung-Kassner (1980) & Pawel (1974) … to be revised.

• Effect of hydrogen is under testing:– Increased oxygen solubility due to H: ready for implementation into ZROB– Increased oxygen diffusion coefficient : – Impact of hydrides onto embrittlement :

• References

[ 1] H. M. Chung, T. F. Kassner: NUREG/CR-1344 (1980).

[ 2] R. E. Pawel: Oxygen diffusion in beta Zircaloy during steam oxidation. J. Nucl. Mat. 50 (1974).

[ 3] H. M. Chung, T. F. Kassner: Pseudobinary Zircaloy-Oxygen Phase Diagram. J. Nucl. Mat. 84 (1979)

[ 4] H. S. Carslaw, J. C. Jaeger: Conduction of Heat in Solids. Oxford, Clarendon Press, 2nd edition (1959), p.100.

[ 5] L. Portier et al.: 14th Int. Symp. Zirconium Nucl. Ind., June 13-17, 2004, Stockholm, to be published by ASTM.[ 6] J-C. Brachet et al.: NRC Nucl. Safety Research Conf., Oct. 25-28, 2004, Washington.[ 7] M. C. Billone: LOCA Embrittlement Criterion. Argonne National Laboratory (April 2005).

… to be experimentally investigated

Evaluation of the Oxygen-Induced Zircaloy Embrittlement in ICARE/CATHARE

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