The Effect of Hydrogen and Hydrides - ebook first test

Table 4-1: Experimentally and theoretically determined parameters in Equation 4-2 for specimens containing
100 wppm H.

Source Stressing (Nucleation) Temperature 10 B (10 Pa)
3
 6

(C)
Experimental – Mixed Zone 400 148 0.038
Experimental – Stringer Zone 400 0.49 0.037

Theoretical† (285) 204 0.030
∗
†Calculated using Equation 3-42 to Equation 3-44 with Eint = 0.115circ and the data for and given in Table 3-2


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 
































 










 ′ ℎ
 ′′
ℎ











Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.

Figure 4-4: Schematic of comparison of hydride orientation correspondences and orientation of the “natural" (zero external stress)
hydrides in tube versus sheet material. The latter material was used to study hydride orientation with and without
external stress (from [Bai et al., 1994]).






( )

( ) = 0.30 ( )


( )


( ) = 0.43 1 ( ) = 2.33
⁄
















()

∗
∗
, ,



() = (0)exp ( )




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(0.7 × ∗ +0.3 × ∗ ) ∙
= [ , , ]

( )




( ) = (0)exp ( )




1 − ( ∗ + ∗ ) ∙
= ( ) [ , , ]
2

= ( ) − (0)


(0) =

∗
, = 4.3 × 10 −27 m 3
∗
, = 15 × 10 −27 m 3

= 400C  

⁄
( ) = () ( (), + ( ))


1
( ) = 1 + 2.33 ∙ ( − )




−8


− ≈ [−1.8 × 10 ( )( + )]

( )

( )

( )




= +

 




1
( ) = 1 + 2.33 ∙ [−1.8 × 10 ( ) ∙ ( − 25)]


−8


⁄
1 (0)





Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.

⁄
1 (0)







( )






































Figure 4-5: Plot showing comparison between model predictions and experimental results (from [Bai et al., 1994]). The solid line,
marked equation (12) in the plot, is the model prediction based on Equation 4-9. The ‘n values’ given by the vertical
axis are equivalent to ( ) as defined in this text.









⁄
(0) (0)










 








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































































Table 4-2: Kearns parameters, faxial, fcirc, frad, for the RD, WD and TD, respectively, of the plate. The designation of
these Kearns factors as corresponding to the axial, circumferential and radial directions of fuel cladding
tubes was made by Sakamoto and Nakatsuka [Sakamoto & Nakatsuka, 2006] on the basis that these
factors have closely similar magnitudes in the indicated plate directions.

faxial (RD) fcirc (WD) frad (TD)

Sheet A 0.074 0.210 0.718
Sheet B 0.050 0.237 0.718
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Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.






( ) ≡ ( 
40




























Figure 4-6: Direction of tapered specimens cut from Zircaloy-2 rolled plate (from [Sakamoto & Nakatsuko, 2006]). TD, RD and WD
in the figure refer to the transverse, rolling and width directions, respectively.


( )







 




( )

( )

( )














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Figure 4-7: Texture dependence of ( ) (denoted by Fn in the figure) (fraction of radial hydrides) of specimens oriented as
indicated in Figure 4-6, containing 60 to 90 wppm hydrogen, loaded at 160 MPa and cycled through the temperature
range from 355 to 160C five times (from [Sakamoto & Nakatsuko, 2006]).








































Figure 4-8: Applied stress dependence of ′( ) (fraction of ‘radial’ hydrides relative to the value of (0) at zero load with the
former denoted by Fn in the figure) cycled five times between 355 to 160C with an externally applied tensile stress of
160 MPa for specimens containing 61, 130 and 251 wppm hydrogen and with an externally applied tensile stress of
130 MPa for specimens containing 135, 239 and 668 wppm hydrogen. All tests were done with specimens oriented in
the WD (from [Sakamoto & Nakatsuko, 2006]).











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2
( ) = ∙ ( ∙ ∙ )  





2
( ) = (0) + ∙ [ ∙ ( − ) ∙ ]


ℎ
 = 0.007 = 0.5 MPa −1 ℎ =
76 ℎ = 79
2
= 0.0981
(0)

= 79
ℎ

(0) ≅ 0.021




































Figure 4-9: Applied stress dependence of  (ratio of fraction of ‘radial’ to ‘circumferential’ hydrides; denoted by R in the figure) for
specimens cut in the WD from two different sheets (A and B). The solid and dashed lines represent fits to the data
using the general expression derived from the Ells model given by Equation 4-10 in which account was also taken of
presumed residual compressive stresses acting in the tensile loading direction of these WD-oriented specimens.
Residual compressive stresses of 76 and 79 MPa were assumed for specimens taken from sheets A and B,
respectively (from [Sakamoto & Nakatsuko, 2006]).





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( ) ( )


⁄
( ) = ( ) (1 + ( ))


(0) ≅ 0.021
( )

( )

( ) = 0.97

( ) ≅ 0.03







(0) ≅ 0.03











































Figure 4-10: Plot of ( ) versus External Stress, , using the fit to the experimental data given by Equation 4-10 assuming an
internal residual stress of 79 MPa in the direction of the externally applied tensile stress.















Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.


  


















100
( , %) = ∗

1 + 1 ∙ [− ∆ ]
( )
∗ =
∆ =




 =


 



⁄
1 ( )


1 ( ) 98
( ) = ( ) = 2 = 49


∆ = ∙





100
( , %) =

∙
1 + 49 ∙ [− ∗ ]
∗





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∆
= ′ (∆ )⁄ 3
∗





100
(%) =

1 + 49 ∙ [− ∙ ]
(∆ ) 3








 = 24 000





= 24 × 10 5






























Figure 4-11: Effect of hoop stress on stress orienting behaviour of hydrides in SRA Zircaloy-4 tubing solution annealed at various
temperatures assuming that the undercooling from the incoherent solvus, T, is the same for all solution temperatures.
(Note that the corresponding figure in [Desquines et al., 2014] (from [Chu et al, 2008]) has the [H] labels erroneously
reversed; i.e., the 450C line should have the highest [H] value.).






  








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
















( , %) = 98%

 ( , %) ≈ 98%


































Figure 4-12: Plots of % radial hydrides, ( , %), versus tensile hoop stress calculated using Equation 4-14 for SRA Zircaloy-4
tubing material solution annealed at the indicated temperatures. T in Equation 4-14 is the solution temperature minus
T; i.e., the temperature at which hydride nucleation occurs. The indicated hydrogen contents, [H], corresponding to
the solution temperatures are calculated based on the TSSD data of [Pan et al., 1996].












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

( , %) = 98%

( , %) = 3%




























Figure 4-13: Effect of hoop stress on stress orienting behaviour of hydrides in SRA Zircaloy-4 tubing solution annealed at various
temperatures assuming that the undercooling from the incoherent solvus, T , is the same for all solution
temperatures. (Note that the corresponding figure in [Desquines et al., 2014] (Figure 4-14) has the [H] labels
erroneously reversed; i.e., the 450C line should have the highest [H] value.)






( , %) ( , %)


( , %)


































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Figure 4-14: Comparison of % radial hydrides, n ( ( , %) in the notation of this text), versus solution temperature for an applied
hoop stress of 160 MPa (from [Chu et al., 2008]).
















































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




 











+ 1 ( − ) = 0


=
=






−

= −



=
=










⁄
( ) = [1 − ( ) − ]



= 0

⁄
> 0 






−


= , > 0
ℎ








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−
= −


⁄
⁄
1 − (1 − ) −


≡



= − ( − )





= = 0
= ℎ

2
 ∝ ℓ ⁄ = ℓ


ℓ =
= 

= 1 − 1
2

 






1
( , ) = ∗


1 + [ Ω ∆ ]


⁄



= (1 − ) ≡ 1/ = (0) 1/ = ( ) ≡ = (0) = (0) = (0)



= 1 = 2
( , ), = 1 ≡ = 2 ≡  = 90° 1/ (0) =
=

= =90° (0)/ = (0) (0)

 = 90° (0)

⁄
≡ (0) = (0) ( (0) +  (0))



Ω ∗ ∆
 
Ω ∗
∗








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∗
⁄
=



4 9 2
∗
∗
Ω ≡ =


3 (−∆ ℎ − ∆ ) 3
18 2

∗
∗
≡ ∆ = (−∆ ℎ − ∆ ) 2


Ω ∗
∗ ∗
Ω ∗


∆


∗
 Ω = 15.79 ×

10 −27 3 = 1041

Ω ∗












−

= 1 −

ℎ

















2
= 0.065 J/m = 0.28 J/m 2 ∆ = 100 MJ/m 3




Ω ∗ Ω ∗
∗ ∗
∆ ∆



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









−3 −1
20
≈ 10 nuclei m s 




























































Figure 4-15: Results of calculations of hydride volume fraction, , and orientation parameter, , (where ‘r’ refers to radial hydrides)
as a function of time at a constant applied tensile stress of 150 MPa in Zr-2.5Nb material containing 100 wppm H. The
inset figure shows the cooling history during reorientation (from [Massih & Jernkvist, 2009]).


Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.









































 ZrH 1.66
 

δ
(1 1 1) ≈ ‖ (0 0 0 1) −



























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Figure 4-16: Experimental results showing EBSD pattern of hydrogenated Zircaloy-4 plate material with intergranular hydrides in
yellow boxed regions and intragranular hydrides in pink boxed regions (from [Qin et al., 2011]).







 










































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Figure 4-17: Possible shapes of intergranular hydride nuclei, described under (a) to (c) in the following (from [Qin et al., 2011]). (The
symbol, σ, in this figure refers to surface energies denoted by  in this text.)







16 3

∗
Δ ( ) = 3(−∆ ℎ + ∆ ) 2 ( )





3
( ) = 1 − 1.5 + 0.5




16 3

∗
Δ ( ) = 3(−∆ ℎ + ∆ ) 2 ( )





1
( ) = (2 − 6 + 2 + 3 − )
3
3
4








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16 3

∗
Δ ( ) = 3(−∆ ℎ + ∆ ) 2 ( )




1
3
3
( ) = (−3 + + 3 − )
2
 





= −1 ( )
2




= −1 ( )


α
α 




































 











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∗
,( ) / ∗



,( )
∗
∗
,( ) ,( ) ,( ) (−∆ ,( ) ⁄ )



∗
∗ = (−∆ ⁄ )




⁄
,( ) ⁄ = 3 Λ 






,( ) ⁄ =

exp [2 ⁄ ]
2




∗
∗
2
,( ) 3 Λ ∆ ,( ) − 2 − ∆ ∗

∗ = ( )exp [− ( )]

= 10 μm = 0.5146 nm Λ = 10 −2 ,( ) ⁄
1.54 × 10 −6





= 0.05 J/m 2 = 0.5 J/m 2


(0 0 0 1) −

= = 0.3231


 

Δ = Δ = 2.724 × 10 J/m 3
8

> 0.16 J/m 2

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 
















∆




16 3

∗
Δ ( ) = 3(−Δ ℎ + ∆ + ∆ ) 2 ( ) ( = , , )






∆ = −( )



= 


 =


 =



∆
ℎ











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̅


∆ ℎ = Δg ℎ − ̅ ℎ [ 3 ( )]
̅
ℎ
̅ −

∗
Δ ( )







, = + ( )

 
























Figure 4-18: Schematic showing the relationship between the orientation of the intergranular hydride, the grain boundary orientation
and the tensile strength ( in this text) direction (from [Qin et al., 2011]).


∗
Δ ( )

=

























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̅
[1 1 0] ∥

̅
[1 2 1 0] − (1 1 1) ≈∥ (0 0 0 1) −

̅
(0 0 0 1) − (1 0 1 7) −
(0 0 0 1) −

δ






 




 









̅
̅
[1 1 0] ∥ [1 2 1 0] − (1 1 1) ≈∥ (0 0 0 1) −





























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




































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Figure 4-19: Micrograph of specimen J-10-B-1 showing the boundary along the length of the taper between mostly radially and non-
radially oriented hydrides. The horizontal scale indicates the tensile stress acting at a particular location along the
length of the specimen (from [Leger & Donner, 1985]).































































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Figure 4-20: Illustration of analysis Method 1 used to determine hydride reorientation threshold in route 2 Zr-2.5Nb flattened
pressure tube material containing regions of tensile (positive) and compressive (negative) macroscopic residual
stresses (from [Leger & Donner, 1985]).
















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Figure 4-21: Illustration of the 50%-wall-thickness method (Method 2) to determine the threshold stress for 100% radial hydride
formation in a standard Zr-2.5Nb pressure tube material (from [Leger & Donner, 1985]).






















 







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Figure 4-22: Correlation of threshold stress for 100% radial hydride formation versus ultimate tensile strength in the axial direction
of Zr-2.5Nb pressure tubes produced by different manufacturing routes and for a standard cold-worked Zircaloy-2
pressure tube (from [Leger & Donner, 1985]).































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

















































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Figure 4-23: Dependence of threshold stress, ℎ , to achieve 100% radial hydride orientation with loading temperature in a
Zr-2.5Nb pressure tube alloy used in Indian 500 MWe PHWRs (from [Singh et al., 2004]).






















































Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.




 


















 

 

 
 
 








 

  































Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.

Figure 4-24: Dependence of threshold stress to achieve 100% radial hydride orientation with loading temperature in a Zr-2-5Nb
pressure tube alloy used in Indian 500 MWe PHWRs (from [Singh et al., 2006]).
































  




















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   

 















  















































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Table 4-3: Comparison of hydrogen terminal solubility (in wppm) from different authors and different materials.

T







(C) [Pan et al., [Kearns, 1967], [Une & [Vizcaíno et [Pan et al., [Pan et al., [Une & Ishimoto,
1996], Zircaloy-2 Ishimoto, al., 2002], 1996], 1996], 2003],
Zr-2.5Nb and -4 2003], Zircaloy-2 Zr-2.5Nb Zr-2.5Nb Zircaloy-2
Zircaloy-2
400 169.3 206.1 187.0 234.2 244.4 212.0 349.1
300 57.7 70.2 59.9 68.8 109.2 88.6 145.5
200 12.5 15.2 11.8 12.0 34.7 25.6 41.9
100 1.2 1.4 1.0 0.80 6.0 3.8 6.2
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

 
























  



























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






















































Figure 4-25: Hydride distributions in the radial-circumferential plane of a hydrogenated Zircaloy-4 fuel cladding tube: (a) before and
(b) to (d) after hydride reorientation tests on specimens R21AC, R32AC and R43AC corresponding to: (a) 400C to
room temperature, no load and (b) 200 to 100C, (c) 300 to 200C and (d) 400 to 300C, all under load (from [Hong &
Lee, 2005]).




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

 




















 












































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Figure 4-26: Distribution and orientation of hydrides in the wall of specimen R47H7 cooled under load from 400C to 300C; then
held there for 7 h before cooling to room temperature with the load removed: (a) radial-circumferential and (b) axial-
radial sections (from [Hong & Lee, 2005]).




















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Figure 4-27: Ring tensile test specimen and test configuration (from [Min et al., 2013]).






























Figure 4-28: Temperature and stress histories applied to ring specimens (from [Min et al., 2013]).










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


























Figure 4-29: Results of hydride reorientation tests showing (left plot) the percent radial hydride fraction and (right plot) average
radial hydride length as a function of cooling rate; the plots are for specimens with different total hydrogen contents
(from [Min et al., 2013]).




















































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 























 






















  
 



Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.

Figure 4-30: Thermo-mechanical treatments to study radial hydride precipitation for two different maximum temperatures: (a)
350C, (b) 450C (from [Desquines et al., 2014]).





,



Table 4-4: RHT test matrix for maximum temperature of 450C

CCT [H] content Sample length Maximum stress - ,A(MPa)
(#) (wppm) (mm)

1 67±10 16.8 200
2 77±10 15.1 200
3 96±10 17.3 200

4 105±25 18.3 230
5 192±17 20.2 200
6 194±17 19.3 200
7 325±28 10.3 200

8 497±61 17.8 200
9 552±46 15.0 230
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Table 4-5: RHT test matrix for maximum temperature of 350C.

CCT [H] content Sample length Maximum stress -,A(MPa)
(#) (wppm) (mm)
10 53±6 20.2 200
11 63±11 16.7 230

12 69±6 17.2 230
13 74±7 19.9 200
14 127±36 17.5 200
15 141±40 18.0 230

16 177±17 19.3 230
17 217±33 20.0 200
18 309±26 9.1 200
19 322±27 10.5 200

20 525±44 19.2 200
21 540±47 18.5 230

© ANT International 2018















































Figure 4-31: Metallographic cross-section, edged to reveal the hydride distribution in specimen CCT-6 after RHT with maximum
temperature of 450C (from [Desquines et al., 2014]).


Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.

Figure 4-32: Plot of limits of radially and circumferentially oriented hydrides determined in specimen CCT-6 from the metallographic
section shown in Figure 4-31, superimposed on the normalized circumferential tensile stress map (from
[Desquines et al., 2014]).



,0% ,100% ,0%
,100%








,100%



[H](wppm)
,100% (MPa) = 110 + 65 (1 − 65 ) ± 20






Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.

,0%





,0% (MPa) = [H](wppm) + (℃) +







,0% (MPa) = [H](wppm) + { ( (℃); (℃))} +

= 0.0200 =
0.3862 = 186.9  =
350°C = 450°C





































Figure 4-33: Plot showing the relationship between applied hoop (circumferential) stress and hydrogen content for all specimens
tested. As indicated, simple equations were fitted to the data (from [Desquines et al., 2014]).





















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





























 
































[H](wppm)
( ) = ,0% + ( ,100% − ,0% {[H](wppm); ( )} )


,100%
,0% ( )











Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.

Figure 4-34: Contour lines determined from the interpolation expression derived by Desquines and co-workers
[Desquines et al., 2014] given by Equation 4-42 representing fractions of radial hydrides (in 10% intervals) after an
RHT with = 350℃. Superimposed on this are the results from pressurization tests with = 350℃ by
Bouffioux [Bouffioux, 2002] (black dots; identified in the figure as ‘EDF  350C’). The numbers beside the dots give
the values of corresponding to each datum (from [Desquines et al., 2014]).




































Figure 4-35: Contour lines determined from the interpolation expression derived by [Desquines et al., 2014] given by Equation 4-42
representing fractions of radial hydrides (in 10% intervals) after an RHT with close to 400C. Superimposed on
this are the results from pressurization tests by various authors. The legend for the dots refers to the following
references: All circles (EDF) [Bouffioux, 2002]; diamonds ([Racine, 2005]; hexagonal (ANL-M5), [Billone et al., 2012].
The numbers beside the dots give the values of corresponding to each datum (from [Desquines et al., 2014]).


Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.

 












= 0.59

= 0.05 = 0.31




















































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