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Published by marybaguhin, 2019-06-28 17:20:08

The Effect of Hydrogen and Hydrides - ebook first test

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

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



α



































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

α

























































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

 























































































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












































































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




















































































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

Figure 2-1: Inverse pole figure characterization of texture in tubing (from [Kearns & Woods, 1966]). Numbers on contour lines
indicate orientation densities (times random) with respect to reference direction. Histograms show corresponding
(calculated) volume distributions of basal poles.







(1 1 2 ̅ 0) α−  (1 0 1 ̅ 0) α−Zr




















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

 














































































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

Figure 2-2: Correlation of hydride orientations with basal pole textures in samples cooled under 138 MPa uniaxial tensile stress.
The solid line, labelled as average curve from Fig. 5 of the paper by Kearns and Woods [Kearns & Woods, 1966] is the
correlation in unstressed samples (from [Kearns & Woods, 1966]).










 


















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









 




































Figure 2-3: One of the earliest micrographs [Parry, 1966] showing the composite structure of a hydride cluster (transverse section
of a Zr-2.5Nb pressure tube cooled under no external stress).


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










































16 2


















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

 




















 
 
 
̅
{1 0 1 7} αZr  


















































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

















Fe N 2
16


























































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
































































∆ ∗

= ∗ (− ) (− )


∗ = 





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

=  10 −2 10 −1

∗ =
=

=

  

∆ ∗ =

=

=
=



























∗ 2 −1
= (2 )






(− ) → 1 ∗




∆ ∗

= ∗ (− )





∆ ∗







2
1 (∆ ) −1 2
= [ ∙ ( ) ]
2 2 ∗

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

=

∗ =
∆ =















=
4
∗ =


=
=

=













∗2
= 2

∗ =

=






=

=

= 
















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




{0 0 0 2} −  ∥ (1 1 1) δ
[1 1 2 ̅ 0] α−Zr ∥ (1 1 ̅ 0)







 
 




 
2
ℎ ℎ = (4/3)


4
2
2
∆ = (∆ ℎ + ∆ ℎ + ∆ ℎ ) + 2 + 4
3 ℎ

∆ ℎ =





∆ ℎ =


∆ ℎ =





=
=


∆ ℎ 












∆ ∗ 









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

2 ̅ 3

∆ =
3 [ (−∆ ′ℎ − Δ ℎ ( ) − Δ ℎ ( ) − ∆ ℎ + ∆ )] 2




̅


̅ = + 2





̅

=





(−∆ ′ − Δ ( ) − Δ ℎ ( ) − ∆ + ∆ )









= =

∆ ′ℎ

, ( )

∆ ℎ = V ̅ ( )




=

 
=
=

̅ −
V =
, () = 




= 
= / ℎ






≪ 1


1
2
2
∆ ℎ = 1 − ∆ + 1 − 2 [Δ ∙ + 4(1 + ) ]

=




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

=

Δ =
=












Δ ℎ ( ) = (1 − ) Δ 2




1 1 (2 − )
2
2
Δ ℎ ( ) = (1 − ) 2 [Δ ∙ + 4(1 + ) + 8 (1 + ) ]


Δ ( )







Δ ( ) = Δ ℎ ( ) + Δ ( )

∆ ℎ ∆




∆ ℎ = −





Δ = −

=
=

= (α + )/


(α + ) 
= lambda = ⁄









|−∆ + ∆ | ≪ |−∆ ℎ − Δ ( ) − Δ ( )| ∆ ∗







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

2 ̅ 3

∆ =
3 ℎ ℎ 2



[ (−∆ ℎ − Δ ( ) − Δ ( ))]


4 [−∆ ℎ + ∆ ] ̅ 3
− { }
3 3



[ (−∆ ′ − Δ ( ) − Δ ℎ ( ))]






4
= 3 ( )


∗ 3


∗ ∗

̅

=



(−∆ ℎ − Δ ℎ ( ) − Δ ( ))




=







∆ = ∆ − [−∆ + ∆ ]






∆ ∗
2 ̅ 3

∆ = 2

3



[ (−∆ ℎ − Δ ℎ ( ) − Δ ℎ ( ))]


∆ ∗



[−∆ ℎ + ∆ ]

, = ∗ , { }


,




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

∆ ∗
∗ = ∗ (− )
,









∗2

= 2














−∆ = ( )



|∆ | > | ∆ |





̅ −

− V ̅ − ℎ ∆





̅
̅
̅ −
  −ℎ −ℎ























∆ = ∆ − [( ) − ]












[( ) − ]


, = ∗ , { }

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





















 (α + )/















1.66 ≡ = 1.5




















 








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

α



















































































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


 
α

3 −1
≈ 1 × 10 17 m s







=


5.253  10 −27 m 3  =

−3 −1
8.602 × 10 16 m s


̇ = 1.66  5.253 × 10 −27 × 8.602 × 10 16 = 7.501 × 10 −10 s −1

̇ 8.223 × 10 −6 s −1
3.333 × 10 −2  s −1  min −1 ̇
2.467 × 10 −4 
10 4

−3 −1
≈ 10 20 m s


















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













 














































 1/ (K)








∆ 2 ∆
∆ = −√∆ 2 ∙ ∆ ∆ =


−1
−1
−29 953 J K mol H





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



2
−∆ ℎ = 1.584 × 10 J m −3

∆ ∗
∆ ∗



 
̅






−∆ ℎ

Table 3-1: Enthalpies of dissolution and formation for TSSD, TSSP1 and TSSP2 derived from a fit of the experimental
data of Pan and co-workers [Pan et al., 1996] assuming a common value for the pre-exponential term,
4
= 3.9153 × 10 wppm. The corresponding value for TSSE was derived assuming ∆ =

−√∆ 2 ∙ ∆ .

Hydride Solubility Expressions (wppm) Enthalpies in Solubility Expressions (J mol H)
 1



( ) = ∙ exp(∆ ) ∆ = −31 000



( 1) = ∙ exp(∆ ⁄ ) ∆ 1 = −27 7040
1


( 2) = ∙ exp(∆ ⁄ ) ∆ 2 = −28 942
2

( ) = ∙ exp(∆ ⁄ ) ∆ = −29 953




© ANT International 2018
−3 −1
20
≈ 10 nuclei m s
−3
= 5.85 × 10 J m −2


1 × 10 −6
−3
3.8 × 10 J m −2
20
−3 −1
≈ 10 nuclei m s

















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











 = 0.0760 77.23 J m 3
−ℎ
̅
−1
J mol H  −ℎ = ̅ = 11.354 ×
−1
10 m mol H 
−6
3
876.9 J mol −1
−1
−29 306 + 876.9 = −28 429 J mol H



2.32 ×
20
10 nuclei m s ∆ = 572.6 − 558.1 = 14.5 K
−3 −1

590.4 − 558.1 K





2.008 × 10 −27 m 3














































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

Table 3-2: Calculation of critical nucleation parameters and nucleation rate at zero internal and externally applied
stress. Case of finite energy barrier model of solvus hysteresis - equilibrium solvus assumed to be given
midway between TSSD and TSSP2 solvi [Pan et al., 1996].

Critical nucleus dimensions
Note: Axis of rotation of ellipsoid is about x1:
3
Values of some Tn(K) = 558.1 VZr(m /(mol Zr)) = e11 = 0.172 rH(H/Zr) = 1.48
parameters 1.40110
-5
4
 = 0.3121 (MPa) = 3.031 10 e22 = 0 β = 1.5
δ
E(MPa) = 7.9510 ‘kB(J/(K atom)) = e33 = 0 cH (rH/β ) =
δ
4
δ
-23
1.380 10 0.98667
o
c(J/m ) = 0.0038 Ao(g/mol) = 6.025 Z = 0.1 cH (at. fn) =
2
10 0.008969331
23
2
p(J/m )= c+2i= R(J/(K∙mol)) = 8.3144 cH (wppm) = 100 d(m) = 4.5010
-10
o
0.0114
TSS equations- H(TSSD; J/mol H) Nnucl(sites/m ) =
3
Pan et al; constant A: = 31000 4.3010
22
H(TSSP1; J/mol H) Heter.nucl.red.factor =
= 27704 110
-6
H(TSSP2; J/mol H)
= 28942
A(wppm) = 3.9210
4
Solvus temperatures(at TD(K) = 624.5 TD(C) = 351.5 DH(m s ) = 1.1410
8
2 -1
given CH (wppm)):
0
TP1(K) = 558.1 TP1(C) = 285.1 d(m) = 4.5010
8
TP2(K) = 583.1 TP2(C) = 310.1
Estimated equilibrium Teq(K) = 603.4 H(Teq; J/mol H) =
solvus values: 29953
Teq(C) = 330.4 cH s, eq (wppm) = 49.2
Chemical energy: g , nucl (chem., J/m )
3
= -2.321 10
8
Strain energy reduction factor: 1
Critical nucleus dimensions when  depends only on the ratio of surface energies:



























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

Table 3-2 cont’d: Calculation of critical nucleation parameters and nucleation rate at zero internal and externally applied
stress. Case of finite energy barrier model of solvus hysteresis - equilibrium solvus assumed to be given
midway between TSSD and TSSP2 solvi [Pan et al., 1996].

gstrain( gstrain(re ao*(m) co*(m) Vo*(nu i(J/ =c/ Go* exp(- *(s - no*( nu Jo(nucl
3
3 -1
3
2
exact) duced) =∙a* cl,m ) m ) i Go*/kBT 1 ) cl/m ) /m s )
n)
1.94E+ 1.94E+07 4.317 8.203E 6.405E 0.2 0.01 4.451 8.11728E 1.14E 3.54E- 4.04E+
07 E-09 -11 -27 90 E-19 -26 +04 03 00
2.59E+ 2.59E+07 3.396 8.604E 4.157E 0.15 0.02 2.754 2.98249E 7.07E 1.30E 9.19E+
07 E-09 -11 -27 53 E-19 -16 +03 +07 09
3.88E+ 3.88E+07 2.509 9.533E 2.513E 0.1 0.03 1.503 3.38214E 3.86E 1.47E 5.69E+
07 E-09 -11 -27 80 E-19 -09 +03 +14 16
4.85E+ 4.85E+07 2.183 1.037E 2.070E 0.08 0.04 1.138 3.84287E 2.92E 1.68E 4.89E+
07 E-09 -10 -27 75 E-19 -07 +03 +16 18

5.54E+ 5.54E+07 2.038 1.106E 1.924E 0.07 0.05 9.914 2.57559E 2.55E 1.12E 2.86E+
07 E-09 -10 -27 43 E-20 -06 +03 +17 19
5.96E+ 5.96E+07 1.973 1.153E 1.881E 0.06 0.05 9.294 5.75676E 2.39E 2.51E 5.99E+
07 E-09 -10 -27 5 85 E-20 -06 +03 +17 19
6.45E+ 6.45E+07 1.917 1.214E 1.868E 0.06 0.06 8.771 1.13632E 2.25E 4.95E 1.12E+
07 E-09 -10 -27 33 E-20 -05 +03 +17 20
7.03E+ 7.03E+07 1.872 1.294E 1.900E 0.05 0.06 8.372 1.90763E 2.15E 8.32E 1.79E+
07 E-09 -10 -27 5 91 E-20 -05 +03 +17 20

7.72E+ 7.72E+07 1.848 1.404E 2.008E 0.05 0.07 8.152 2.53804E 2.09E 1.11E 2.32E+
07 E-09 -10 -27 60 E-20 -05 +03 +18 20
8.57E+ 8.57E+07 1.856 1.567E 2.262E 0.04 0.08 8.225 2.30658E 2.11E 1.01E 2.12E+
07 E-09 -10 -27 5 44 E-20 -05 +03 +18 20
1.27E+ 1.27E+08 2.891 3.663E 1.283E 0.03 0.12 1.996 5.57495E 5.13E 2.43E 1.25E+
08 E-09 -10 -26 67 E-19 -12 +03 +11 14
1.36E+ 1.36E+08 3.757 5.098E 3.014E 0.02 0.13 3.370 1.0074E- 8.65E 4.39E 3.80E+
08 E-09 -10 -26 8 57 E-19 19 +03 +03 06
1.41E+ 1.41E+08 4.625 6.509E 5.831E 0.02 0.14 5.107 1.62364E 1.31E 7.08E- 9.28E-
08 E-09 -10 -26 7 07 E-19 -29 +04 07 04
© ANT International 2018





























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

,




̅ ( )
,
( ℎ ) = , [ ℎ ]








̅
∆ ( )

,
( ′ ) = ( ) [− ]

, =
̅
( ) =


( )


̅
∆ ( ), ( ) =



=
and =
( )

̅
∆ ( )






̅
∆ ( )



̅
∆ ( )


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

̅
( )






̅
̅
∆ ( ) + ( )
,
( ) = ( ) [− ℎ ]


̅
( )


̅
( )


̅
∆ ( )



∆ ℎ
, ( ) ≅ , ( ′ )



8

−∆ ℎ = 2.321 × 10 J m −3
−3 −1
20
≈ 2.84 × 10 nuclei m s
−1
−3
6.2 × 10 J m −2 1 291 J mol H
J/m 3
−1
J mol H 31 000 +
−1
1 291 = 29 709 J mol H
≈ 2.84 × 10 nuclei m s
20
−3 −1
598.4 − 558.1 = 40.3 K





  






= 1.276 × 10 −27 m 3




















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

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

Table 3-3: Calculation of critical nucleation parameters and nucleation rate at zero internal and externally applied
stress. Case of accommodation energy model of solvus hysteresis - equilibrium solvus assumed to be
given by TSSD solvus [Pan et al., 1996].

Critical nucleus dimensions

Note: Axis of rotation of ellipsoid is
about x1:
Values of some Tn(K) = 558.1 VZr(m /(mol Zr)) = e11 = 0.172 rH(H/Zr) = 1.48 Nnud(sites/m ) = 4.30
3
3
parameters 1.401 10 10
5
22
 = 0.3121 (MPa) = 3.031 e22 = 0 β = 1.5 Heter.nucl.red.factor
δ
-6
10 = 1.00 10
4
E(MPa) = 7.95 kB(J/(K atom)) = e33 = 0 cH (rH/β ) =
δ
δ
10 1.380 10 0.98667
4
-23
O
c(J/m ) = 0.0062 Ao(g/mol) = 6.025 Z = 0.1 cH (at. fn) =
2
23
10 0.008969331
O
2
p(J/m ) = R(J/(K∙mol)) = cH (wppm) = d(m) = 4.50
-10
c+2i= 0.0186 8.3144 100 10
TSS equations- H(TSSD; J/mol A(wppm) = 3.92
Pan et al; H) = 31000 10
4
constant A:
H(TSSP1;
J/mol H) = 27704
H(TSSP2;
J/mol H) = 28942
Solvus TD(K) = 624.5 TD(C) = 351.5 DH(m s ) =
2 -1
temperatures 1.14 10
-10
(at given
CH (wppm)): TP1(K) = 558.1 TP1(C) = 285.1 d(m) = 4.50
o
10
-10
TP2(K) = 583.1 TP2(C) = 310.1
Estimated Teq(K) = 624.5 H(Teq;J/mol H) =
equilibrium 29953
solvus values:
Teq(C) = 351.5 cH s, eq (wppm) =
49.2
Chemical g , nucl (chem., J/m ) = -2.321 10
8
3
energy:
Strain energy reduction factor: 1
Critical nucleus dimensions when  depends only on the ratio of surface energies:





















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

Table 3-3 cont’d: Calculation of critical nucleation parameters and nucleation rate at zero internal and externally applied
stress. Case of accommodation energy model of solvus hysteresis - equilibrium solvus assumed to be
given by TSSD solvus [Pan et al., 1996].

gstrain( gstrain(re ao*(m) co*(m) Vo*(nu i(J/ =c/ Go* exp(- *(s ) no*(nu Jo(nucl/
-1
3 -1
2
3
exact) duced) =∙a* cl,m ) m ) i Go*/kBT cl/m ) m s )
3
n)
3.17E+ 3.17E+07 2.994 9.280E 3.483E 0.2 0.03 3.491 2.0821E- 5.49E 9.08E 4.98E+
07 E-09 -11 -27 10 E-19 20 +03 +02 05
4.22E+ 4.22E+07 2.370 9.794E 2.304E 0.15 0.04 2.187 4.6596E- 3.44E 2.03E 6.99E+
07 E-09 -11 -27 13 E-19 13 +03 +10 12
6.32E+ 6.32E+07 1.775 1.101E 1.453E 0.1 0.06 1.228 1.1938E- 1.93E 5.20E 1.01E+
07 E-09 -10 -27 20 E-19 07 +03 +15 18
7.87E+ 7.87E+07 1.565 1.213E 1.244E 0.08 0.07 9.537 4.1996E- 1.50E 1.83E 2.75E+
07 E-09 -10 -27 75 E-20 06 +03 +17 19

8.98E+ 8.98E+07 1.475 1.307E 1.192E 0.07 0.08 8.480 1.6555E- 1.33E 7.22E 9.63E+
07 E-09 -10 -27 86 E-20 05 +03 +17 19
9.66E+ 9.66E+07 1.438 1.372E 1.189E 0.06 0.09 8.061 2.854E- 1.27E 1.24E 1.58E+
07 E-09 -10 -27 5 54 E-20 05 +03 +18 20
1.04E+ 1.04E+08 1.410 1.457E 1.212E 0.06 0.10 7.741 4.3253E- 1.22E 1.89E 2.30E+
08 E-09 -10 -27 33 E-20 05 +03 +18 20
1.1367 1.14E+08 1.393 1.570E 1.276E 0.05 0.11 7.559 5.4734E- 1.19E 2.39E 2.84E+
E+08 E-09 -10 -27 5 27 E-20 05 +03 +18 20

1.25E+ 1.25E+08 1.396 1.731E 1.414E 0.05 0.12 7.595 5.2271E- 1.19E 2.28E 2.72E+
08 E-09 -10 -27 40 E-20 05 +03 +18 20
1.38E+ 1.38E+08 1.435 1.977E 1.705E 0.04 0.13 8.022 3.0023E- 1.26E 1.31E 1.65E+
08 E-09 -10 -27 5 78 E-20 05 +03 +18 20
1.55E+ 1.55E+08 1.547 2.398E 2.403E 0.04 0.15 9.321 5.5568E- 1.47E 2.42E 3.55E+
08 E-09 -10 -27 50 E-20 06 +03 +17 19
1.75E+ 1.75E+08 1.852 3.281E 4.716E 0.03 0.17 1.337 2.9145E- 2.10E 1.27E 2.67E+
08 E-09 -10 -27 5 71 E-19 08 +03 +15 17
2.03E+ 2.03E+08 3.058 6.320E 2.476E 0.03 0.20 3.643 2.8785E- 5.73E 1.25E 7.19E+
08 E-09 -10 -26 67 E-19 21 +03 +02 04
© ANT International 2018




























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




































  





































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








<0 0 0 1> ≡ = 0.0542



<1 1 ̅ 0 0> = <1 1 2 ̅ 0> ≡ = 0.0329







<1 0 1 ̅ 7>



 <1 1 2 ̅ 0> = <1 1 ̅ 0 0> ≡ ∥
≡ ⊥
<1 0 1 ̅ 7>









<1 0 1 ̅ 7> ≡ = 0.172




















 














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







=

= 



=







=
+









= 1 +











( = 0) ≡ (0)

∆ ℎ ∆


() (0)




∗ [−∆ ℎ + ∆ ]

() = (0)exp { }

() ( )

 = 0°









()



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

( )


(0) (0)






[−∆ ℎ , + ∆ , ] ∙

() = (0) { } = (0) { }








[−∆ ℎ , + ∆ , ] ∙
( ) = (0) { } = (0) { }




ℎ ,


= −∆ + ∆ ,


,


= −∆ ℎ , + ∆


( ) 





() (0) ∆ ∆


( ) = ( ) = (0) [ ∗ ] ≡ (0) [ ∗ ]






(0) = (0) (0)






∆ = −




(0) [ ∗ ∆ ]

( , %) = 100

1 + (0) [ ∗ ∆ ]


 ( , %)





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

100
( , %) =

1 + 1 [− ∗ ∆ ]
(0)


(0) = 1


  (0, %) = 50%


0.3/0.6 = ½ (0) = ½ ( , %) = 33%



í í























(0) (∆ ( ) + ∆ ( ))
( ) = (0) [ ∗ ]


∆ ( ) ∆ ( )
≡ (0) [ ∗ ] [ ∗ ]



∆ ( ) ∆ ( )













 













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



( ) = ⊥ − ⋅ ∙









( ) = ∥ − ⋅ ∙ = − ⋅ ∙




= 0

∆ ( )





∆ ( ) = ( ) − ( ) = ⋅ ( ⊥ − ⋅ [ − ])






≈ 1 − = 0.0213





= 0.172 = 0.9867



= 1.5


− = 0.0213 ∆ ( ) = 0.0936



= 2.008 ×

10 −27 m 3 = 558.1 K

Table 3-4: Effect of external circumferential (hoop) tensile stress on % radial hydride fraction, . (Starting from 2%

radial hydride for the externally unstressed tube material.)
Circumferential (Hoop) Tensile Stress,  (MPa) ( , %), % Radial Hydrides

0 2
40 5
80 13
120 27
160 50
200 73

240 88
280 95
320 98
360 99

400 100
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Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.

















 (0) 


















































Figure 3-1: Plot of the theoretical predictions given in Table 3-4 showing the sigmoidal variation of the % radial hydrides ( ) as a
function of stress.







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









[ − ]

∆ ( ) = ⋅ ( ⊥ ∥ − ⋅ [ − ])





= 1.5 = 0.072




= 0.0458 ∆ ( ) = −0.00355

































( ) = − ⋅ ⋅




( ) = − ⋅ ⋅













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


= [ ∗ ∆ ( ) ]












∆ ( ) = ⋅ ⋅ [ − ]





















 
















































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Figure 3-2: Blister grown on a pressurized loop tube on the circumferential (horizontal)-radial (vertical) section of the tube wall
(from [Leger et al., 1989]). The pressure applied inside the tube resulted in  133 MPa uniaxial tensile stress in the
circumferential direction




































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

( )






( ) = ( )

=

=


( , %)




( ) 100

( , %) = 100 1 + ( ) ≡ 1

1 +

(− )
( , %)





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

Figure 4-1: Plots of the % radial hydrides ( ( , %)) in a Zr-2.5Nb flattened tube specimen containing 100 wppm H for two
different maximum temperatures from which the specimens were cooled as a function of uniaxial tensile stress applied
2
in the tube circumferential direction (MN/m  MPa) (Series C specimen). Maximum temperatures from which the
specimens were cooled are indicated in the figure (from [Hardie & Shanahan, 1975]).





























Figure 4-2: Curve fits to data of % radial hydrides ( ( , %)) versus uniaxial externally applied tensile stress in the tube’s
circumferential direction for different maximum temperatures from which the specimens were cooled (from [Hardie &
Shanahan, 1975]). The data used in these fits were of specimens from the ID stringer zone of flattened Zr-2.5Nb
pressure tube material, all with hydrogen content of 100 wppm. The ID stringer zone is a region of maximum
macroscopic residual compressive stress in the material. The number beside each curve corresponds to the specimen
number in Table 2 of [Hardie & Shanahan, 1975] and to the number given in the legend showing the maximum
temperature from which each of the specimens was cooled.










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

Figure 4-3: Curve fits to data of % radial hydrides ( ( . %)) versus uniaxial externally applied tensile stress in the tube’s
circumferential direction for different maximum temperatures from which the specimens were cooled (from [Hardie &
Shanahan, 1975]). The data used in these fits were of specimens from the OD mixed zone of flattened Zr-2.5Nb
pressure tube material, all with hydrogen content of 100 wppm. The OD zone is a region of maximum macroscopic
residual tensile stress. The number beside each curve corresponds to the specimen number in Table 1 of [Hardie &
Shanahan, 1975] and to the number given in the legend showing the maximum temperature from which each of the
specimens was cooled.







  





















 





(%)











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


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