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In-situ SEM Observation and FEM Analysisof Delayed Hydride Cracking Propagation in
Zircaloy-2 Fuel Cladding Tubes
*Toshio Kubo (NFD)Hiroaki Muta, Shinsuke Yamanaka (Osaka University)Masayoshi Uno (Fukui University)Keizo Ogata (JNES)
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Outside-in crackingin ramp tests of BWR fuel rods
Cross-sectional view of a failed segmented rodBurnup, 61 GWd/t, Maximum power, 43 kW/m
100 µm
Outside-in crack propagationby DHC
(Delayed Hydride Cracking)
Radialhydrides
Overview images of an axial crack
Axial direction
1mm
Outer surface
1mm
Outersurface
Innersurface
Crack
Fracture surface
Axial crack
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(1) DHC tests were carried out in the chamber of an SEMfor Zircaloy-2 BWR fuel cladding tubes,●to directly observe the propagation process of DHC, and●to measure the crack propagation rate in the radial
direction of the cladding tubes
(2) FEM analyses of stress distribution and hydrogen diffusionaround a crack tip were made to estimate the crack velocity.The DHC mechanism was considered by comparison betweenexperimental and analytical results.
Objectives
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Apparatus for the DHC tests in an SEM
Objective
Tensile load
Micro-heater
Infrared thermometer
Ring specimen
Objective
Tensile load
Micro-heater
Infrared thermometer
Ring specimen
Objectivelens
Micro-heater
Tensile load
Infrared thermometer
Video
Objectivelens
Pre-crack
40°
GripTensileload
Ring specimen with a pre-crack
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Test specimens
Test materials
Hydrogencharge
Thermal cyclingto obtain radial hydrides
DHC tests
●Cold-worked Zry-2 BWR fuel cladding tubes●Some were stress relieved at 723K and 783K
●Heated at 588K for 24h in LiOH aqueous solution●Hydrogen concentration ; 90-130 ppm
in Zry-2 matrix
Hoop stress of160MPa
Tem
pera
ture
/Str
ess
Time
663K
423K
Pre-cracking on outer surfaces
DissolutionPrecipitation
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Zry-2matrix
Zr liner
100 µm
(a)Circumferentially-hydrided(After hydrogen charge)
(b)Radially-hydrided(After the thermal cycling)
Hydride distribution
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Pre-cracking on specimen outer surfaces
This transverse cross section was polishedfor the observation under an SEM
Cyclic loading Methanol solution of iodine
Pre-crack
Cut at the middle of pre-crack
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a
W Uniform crack
Pre-crack
A
Axial direction
Outer surfaceLc
Inner surface
Evaluation of stress intensity factor, KⅠ
8
KⅠA for a long shallow crack≒ KⅠ for a uniform crack,when a/Lc < 0.2
M’ = ( 1.13 – 0.09α ) + ( - 0.54 + ) β2
α = a/Lc β = a/W
+ (0.5 – + 14.0(1-α)24)β2
ξ2 = 1 + 1.464α1.65
KⅠA =σ√πa M’ξ
0.89(0.2 +α)
1(0.65 +α )
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●Test method : Ring tensile tests in an SEMat a constant crosshead speed
●Crosshead speed : 0.002 mm/min ( 2 µm/min )●Temperature : 523K and 548 K●Temperature cycling: Pre-heated at 598 K for 0.5 h
Test conditions
Time
598K/0.5h
Tem
pera
ture
/Str
ess
548K
Radially-hydrided material
Circumferentially-hydrided material
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50
100
150
200
0 100 200 300 400Time (min)
Cra
ck d
epth
(µm
)
500750
250
①
⑥
Cra
ck d
epth
(µm
)
Time (min)
Stre
ss (M
Pa)
Crack depth
Stress
Time dependency of crack depth and stress
10
Temperature; 523 K, Circumferentially hydrided material
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Observation of crack propagation
11
Temperature; 523 K,Circumferentially hydrided
0
25
50
200 250 300 350
Time (min)
Ave
rage
crac
k ve
loci
ty (
x 1
09 m/s)
①
②
③ ④
⑤
⑥
Prop
agat
ion
dist
ance
(µm
)
①
②
③
②
③④
Sharp crack
Crack blunting
③ ④
③④
⑤
Sharp crack
⑤
③④
⑤
⑥
Crack blunting
⑥
10µm
②
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Effects of yield stress on DHC
12
Temperature; 548 K, Circumferentially hydrided materials
1.E-10
1.E-09
1.E-08
1.E-07
1.E-06
0 10 20 30
KⅠ (MPam1/2)
Cra
ck v
eloc
ity (
m/s
)○ Cold-worked△ 723KSR◇ 783KSR
Yield stress(MPa)
○ Cold worked 600△ Stress relieved at 723K 520◇ Stress relieved at 783K 310
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Effects of hydride orientation on DHC
13
Temperature; 523 K
1.E-10
1.E-09
1.E-08
1.E-07
1.E-06
0 10 20 30
KI (MPam1/2)
Cra
ck v
eloc
ity (
m/s)
Hydride orientation○ Circumferential▲ Radial
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DHC propagationin the radially hydrided material
BSE image taken after a DHC test. Test temp.; 523 K
10µm
Pre-existing radial hydride
Crack
Radial direction
Pre-crackCrack propagation
Pre-existing radial hydrides
Hydrogen diffusion
Hydrideprecipitation
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Fracture of radial hydrides at room temperature
15
Crack
Fracture of radial hydrides
10μm
BSE image taken at room temperature
Radial direction
From The International Topical Meeting on Light Water ReactorFuel Performance, ANS, Seoul, Korea, October 19-23, 2008
Contour lines ofstress
Fracture of radial hydrides
Crack
NIPPON NUCLEAR FUEL DEVELOPMENT CO., LTD.BSE image taken after a DHC test. Test temp.; 523 K 16
Circumferential hydride
Crack
Radial direction
10µm
Radial hydride
DHC propagationin the circumferentially hydrided material
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SOFTWARE : ABAQUS Ver.6.7-1
STRESS DISTRIBUTION ANALYSES :●Zircaloy-2 ; Isotropic elastic- plastic body●Stress strain curve ;
●Yield stress ; Present experimental values●Others ; MATPRO HANDBOOK
HYDROGEN DIFFUSION ANALYSES
J ; Hydrogen fluxΦ; Normalized hydrogen concentrationp ; Hydrostatic pressures ; Hydrogen solubilityD ; Diffusivitykp ; Pressure stress factor
mnK ÷
øö
çèæ= -310
'ees
÷øö
çèæ
¶¶
+¶¶
-=xp
xsDJ pk
f
FEM ANALYSESon stress distribution and hydrogen diffusion
17
Hydrogen concentration is fixed at 100 ppm
Stress
Crack
W
L
W : 0.7 mmL : 0.05, 0.1 and 0.2 mm
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Distribution of hydrostatic pressureand hydrogen concentration
18
98 ppm 155 ppm+20 MPa -970 MPa
Hydrostatic pressure Hydrogen concentration
Temperature : 523K Stress : 100 MPa
10 mm
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Hydrogen flux rate versus KⅠ
19
KⅠ (MPam1/2)
Temperature : 523 K
0.15μm
Hydride
Thickness of the hydride at the crack tip:0.1 – 0.2μm ( from the observation)
1E-17
1E-16
1E-15
1E-14
0 5 10 15 20
KⅠ (MPam1/2)
Hyd
roge
n flu
x ra
te (g
/μm
2 /s)
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V-KⅠ curvesCalculations and measurements
20
Temperature : 523 K
1.E-10
1.E-09
1.E-08
1.E-07
0 10 20 30
KⅠ (MPam1/2)
Cra
ck v
eloc
ity (m
/s)■ Calculation○ Experiment
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Crack velocity versus yield stress
21
Temperature : 548 K
0
2
4
6
200 400 600 800
0.2% offset yield stress (MPa)
Cra
ck v
eloc
ity (
x108 m
/s)
Yield stress (Mpa)600 520 310● ▲ ■ Experiment● ▲ ■ Calculation
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Hydrostatic pressure distributionin front of a crack tip
22
-1000
-750
-500
-250
0
0 2 4 6
Distance from crack tip (µm)
Hyd
rosta
tic p
ress
ure
(MPa
)
Yield stress (Mpa)◇ 310△ 520○ 600
Temperature : 548 K
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Crack velocity versus yield stress
23
Temperature : 548 K
0
2
4
6
200 400 600 800
0.2% offset yield stress (MPa)
Cra
ck v
eloc
ity (
x108 m
/s)
Yield stress (Mpa)600 520 310● ▲ ■ Experiment● ▲ ■ Calculation
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Summary
●The crack velocity was obtained as a function of KI, temperature,hydride distribution and material strength.
●The steady state crack velocity, Vs, tended to increase with anincrease in the 0.2 % offset yield stress.
●Effects of hydride orientation on DHC velocity was small●There was a qualitative agreement in crack velocity between FEM
analyses and experiment●FEM analyses showed that the increase in the 0.2 % offset yield
stress would accelerate the crack propagation by increasing thehydrostatic pressure at the crack tip.
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Fracture surface
25
Crack propagation
20µmTest temp. ; 523 K
DHCPre-crack
100µm
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-1500
-1000
-500
0
0 1 2 3 4 5 60.0
0.5
1.0
1.5
200 MPa300 MPa400 MPa
mm)
Hyd
roge
n flu
x ra
te (w
tppm
/mm
/s)
Distance from crack tip (µm)
Hyd
roge
n flu
x ra
te (p
pm/m
m/s
)H
ydro
stat
ic p
ress
ure
(MPa
)
□ 20○ 50△ 100▽ 200◇ 300
Applied stress (MPa)
Distributions of hydrostatic pressureand hydrogen flux rate
Temperature : 523K, Crack length:100µm
Contour lines ofHydrostatic pressure
Hydrogen diffusion
26
Hydrostatic pressure, p, is defined as
P = −Σσii /3
Hydrogen diffusion to the crack tip
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Hydrogen flux rate versus KⅠ
27
0.01
0.1
1
10
0 5 10 15 20
KⅠ (MPam1/2)
Hyd
roge
n flu
x ra
te (p
pm/m
m/s)
Ave
rage
hyd
roge
n flu
x ra
te (p
pm/m
m/s
)
Hydrogen flux to crack tip Carck velocity
1.E-10
1.E-09
1.E-08
1.E-07
0 5 10 15 20
KⅠ (MPam1/2)C
rack
vel
ocity
(m/s)
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V-KⅠ curvesCalculations and measurements
28
Temperature : 523 K
0.16μm
Hydride
Thickness of the hydride at the crack tip:0.1 – 0.2μm ( from the observation)
1.E-10
1.E-09
1.E-08
1.E-07
0 10 20 30
KⅠ (MPam1/2)
Cra
ck v
eloc
ity (m
/s)
■ Calculation