Figure 4-36: Specimen geometries showing directions with respect to working directions of original sheet material: (a) tapered
uniaxial tension; (b) “plane-strain" tension; (c) “near-equibiaxial" tension. Dimensions are in mm (from
[Cinbiz et al., 2016]).
⁄
= = 0.014
≅ 0.06
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
⁄
≈ 0.83 1
1
2
2
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
Figure 4-37: Stress distributions calculated from FE of the “near-equibiaxial" specimen at 400C for an average tensile stress
across the notch roots of 210 MPa: (a) and (b) major and minor principal stress distributions; (c) and (d) stress
biaxiality ratios. Gauge widths are indicated by double arrows in each figure (from [Cinbiz et al., 2016]).
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
Total length of (radial) hydrides oriented within 45° ≤ θ ≤ 135°
RHF =
Total length of hydrides at any orientation
Figure 4-38: Hydride microstructure shown in a cross section of the tapered uniaxial specimen viewed along the edge face (from
Cinbiz et al., 2016]).
= 0
⁄
1
2
⁄
= 0 . 8
2
1
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
> 0
⁄
2
1
⁄
> 0.57
1
2
= 0
⁄
1
2
⁄
= 0
2
1
⁄
> 0.57
2
1
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
Figure 4-39: Optical micrographs viewed along the specimens’ face normal direction of the out-of-plane (also called radial) hydrides
⁄
in a double-edged notched “plane-strain" specimen showing, (a) variation of stress biaxiality ratio ( 2 1 ) across the
gauge section; (b) out-of-plane hydrides visible in the uniaxial tensile region near the notch where the major principal
⁄
stress exceeds 155 MPa (c) transition from in-plane to out-of-plane hydrides at 2 1 > 0.5 occurring at major
principal stress of 110 MPa.The red arrows in (b) and (c) show the orientation of the major principal stress direction at
the locations indicated (from [Cinbiz et al., 2016]).
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
Figure 4-40: Optical micrographs giving the hydride microstructure in a “near-equibiaxial" tension specimen. Arrows indicate the
major and minor principal stress directions existing in the specimen after application of a far-field tensile load (from
[Cinbiz et al., 2016]).
⁄
> 0.57
2
1
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
Figure 4-41: Threshold stress (as given by major principal stress) for onset of out-of-plane hydride formation as a function of stress
biaxiality. Each datum point represents the average of three to five measurements (from [Cinbiz et al., 2016]).
> 0.83
⁄
2
1
1
⁄
> 0.57
1
2
= 0
⁄
1
2
⁄
= 0
2
1
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
> 0.57
⁄
1
2
⁄
> 0.5
1
2
⁄
⁄
= 0 = 0 . 8
1
2
1
2
2
1
⁄
= 1 3 ( + )
ℎ
2
1
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
Figure 4-42: Hoop stress distribution in F-ANP ring material calculated by FE for RHT at 400C corresponding to an applied load
generating a mid-plane hoop stress of 120 MPa (from [Daum et al., 2006]).
Figure 4-43: Composite micrograph of tube wall section showing hydride precipitates in an F-ANP ring with 250 wppm hydrogen
content under a 120 MPa mid-plane average stress exposed to an RHT at 400C. Insets provide better detail at mid-
plane (90; bottom middle) and 40 (centre, left) locations (from [Daum et al., 2006]).
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
Figure 4-44: Composite micrograph of tube wall section showing hydride precipitates in an HBR ring (corrosion layer removed
before RHT) with 650 wppm hydrogen content under a 120 MPa mid-plane average stress exposed to an RHT at
400C. Insets provide better detail at mid-plane (90; bottom middle) and 0 (centre, left) locations (from
[Daum et al., 2006]).
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
Table 4-6: Test matrix for BWR cladding:
(a) Irradiated BWR-50GWd/t-type Ziraloy-2 (with liner); (b) irradiated BWR-55GWd/t-type Zircaloy-2 (with liner); (c)
irradiated BWR-55GWd/t-type Zircaloy-2 (with liner); (d) irradiated BWR-40GWd/t-type Zircaloy-2 (no liner).
(e) Unirradiated BWR-50GWd/t-type Zircaloy-2 (with liner).
A: Hydride reorientation test (constant hoop stress); A': hydride reorientation test (gas was closed packed in the tube and
hoop stress decreased with temp.); B: ring compression test; C: longitudinal tensile test (low strain rate);
and D: ring tensile test, longitudinal tensile test (each test including high strain rate)
Temperature Cooling Hoop stress (MPa)
rate
(a) (C) (K) (C/h) 0 (heat treatment 16 28 40 70 85 100 As-irradiated (no heat
without stress) treatment)
400 673 A+B A+B A+B A+B A+B . . . . . . B
300 573 30 A+B+C A+B A+B A+B A+B+C A+B A+B
250 523 A+B . . . A+B A . . . . . . A+B
300 573 3 A+B . . . . . . . . . A+B . . . . . .
0.6 A+B . . . . . . . . . A+B . . . . . .
(b) Temperature Cooling Hoop stress (MPa)
rate
(C) (K) (C/h) 0 (heat treatment 40 70 85 100 As-irradiated (no heat
without stress) treatment)
340 613 30 A A A . . . A A
300 573 A . . . A A A
275 548 A . . . A . . . A
(c) Temperature Cooling Hoop stress (MPa)
rate
(C) (K) (C/h) 0 (heat treatment 100 As-irradiated (no heat
without stress) treatment)
300 573 3 Aˊ D
(d) Temperature Cooling Hoop stress (MPa)
rate
(C) (K) (C/h) 0 (heat treatment 70 As-irradiated (no heat
without stress) treatment)
300 573 3 A+B B
(e) Temperature Cooling Hoop stress (MPa)
rate
(C) (K) (C/h) 0 (heat treatment 70 100 As-irradiated (no heat
without stress) treatment)
400 673 30 A A+B A B
300 573 A A A
© ANT International 2018
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
Table 4-7: Test matrix for PWR cladding:
(a) Irradiated PWR-48GWd/t-type Zircaloy-4; (b) irradiated PWR-39GWd/t- type Zircaloy-4; (c) irradiated
PWR-55GWd/t-type MDA and ZIRLO.
A: hydride reorientation test (constant hoop stress) and B: ring compression test.
Temperature Cooling Hoop stress (MPa)
rate
(a) (C) (K) (C/h) 0 (heat treatment 85 100 115 130 As-irradiated (no heat
without stress) treatment)
340 613 30 . . . . . . A+B . . . A+B B
300 573 A+B A+B A+B A A+B
275 548 A . . . A+B A+B A+B
250 523 . . . . . . A+B . . . A+B
300 573 3 A+B . . . ___ A+B A
0.6 . . . . . . ___ A+B . . .
(b Temperature Cooling Hoop stress (MPa)
) rate
(C) (K) (C/h) 0 (heat treatment 80 100 115 130 As-irradiated (no heat
without stress) treatment)
300 573 30 . . . . . . . . . . . . A . . .
(c) Temperature Cooling Hoop stress (MPa)
rate
(C) (K) (C/h) 0 (heat treatment 80 100 115 130 As-irradiated (no heat
without stress) treatment)
300 573 30 . . . . . . . . . A A . . .
© ANT International 2018
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
Figure 4-45: Schematic of the variation of temperature and applied hoop stress during an HRT (from [Aomi et al., 2009]).
4.5.2.1
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
Figure 4-46: Micrographs, etched to reveal hydrides, of irradiated cladding specimens of Zircaloy-2 cladding tubes from a BWR
before and after HRT. All metallography is on cross sections of the radial-circumferential plane, except for (b), which
shows the longitudinal-radial plane (from [Aomi et al., 2009]).
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
(40) (45) (40)
= 40 (45)
Figure 4-47: Correlations between fractions of radial hydride formation and hoop stress for: (a) hydride number and (b) hydride
lengths for different Zircaloy-2 cladding, all having Zr liners and for different HRTs (from [Aomi et al., 2009]).
Figure 4-48: Effect of cooling rate of HRT on (a) radial hydride orientation in terms of ratios, Fl(45) and Fn(40), and (b) sum of the
lengths of all hydrides and only radial hydrides. Results are for Zircaloy-2 cladding with Zr liner used in BWRs (from
[Aomi et al., 2009]).
(40) (45)
(40) (45)
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
4.5.2.2
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
Figure 4-49: Micrographs showing the hydride distribution, morphology and orientations before and after HRT of PWR cladding
(from [Aomi et al., 2009]).
Figure 4-50: Correlation between the variation in fraction of radial hydride lengths (Fl(45)), with hoop stress during HRT for
irradiated type PWR-48GWd/t Zircaloy-4 cladding (from [Aomi et al., 2009]).
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
Figure 4-51: Plot of sum of all hydride lengths in the radial 45 directions versus TSSD (given as TSSd in the figure) concentration
(in wppm) for irradiated type PWR-48GWd/t Zircaloy-4 cladding (from [Aomi et al., 2009]). (The definition of the
ordinate (Sum of the lengths of hydrides per area (l/mm)) is given by the ratio of the sum of the lengths of hydrides
measured in the observed area (mm) divided by the area over which the hydride length measurements were counted
2
(l/mm )
(45)
(45)
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
Figure 4-52: Effects of cooling rate on radial hydride ratio Fl(45) and maximums of lengths of radial hydrides within included angle
45 from the radial direction for irradiated Zircaloy-4 type PWR 48-GWd/t cladding (from [Aomi et al., 2009]).
(45)
(45) (45)
(45)
Figure 4-53: Comparison of reorientation behaviour based on the Fl(45) radial hydride length ratios amongst different PWR cladding
materials for an HRT with 300C maximum temperature and cooling rate of 30C/h (0.5°Cmin); Fr in the legend
refers to the radial Kearns texture factor, denoted by in this text (from [Aomi et al., 2009]).
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
4.5.2.3
(40) (45)
(40) (45)
∙ (40) − { − ( , )} (40)
(40) = _ _ _ _
( _ , _ )
∙ (45) − { − ( , )} (45)
(45) = _ _ _ _ o
( _ , _ )
_ =
_ =
( _ , _ ) =
(40) , (45) o =
o
_ < _ ( _ , _ ) = _ (40) = (40) (45) =
(45)
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
Figure 4-54: Reorientation behaviour taking account only of the hydrogen in solution at Tmax of the HRT for irradiated BWR
Zircaloy-2 cladding with Zr liner at a cooling rate of 30C/h (0.5°C/min) (from Aomi et al., 2009]).
(40) (40)
(40)
(40) = 1 − (40)
(40)
(40)
(40) = ∙ ( )
(40)
(40)
(40)
(45)
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
Figure 4-55: Stress dependence for differently defined hydride reorientation ratios for irradiated BWR Zircaloy-2 cladding with liner
at a cooling rate of 30C/h (0.5°Cmin) (from [Aomi et al., 2009]).
⁄
log (40) 1 1
⁄
log (40)
⁄
1
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
Figure 4-56: Temperature dependence for BWR Zircaloy-2 cladding with liner for HRTs at different applied hoop stress values and
a cooling rate of 30C/h (0.5°C/min). The experimentally determined hydride reorientation ratios have been adjusted to
account only for dissolved hydrogen as contributing to hydride precipitation (from [Aomi et al., 2009]).
≥
⁄
log (40) 1
≥
≅
= 400℃ < 400℃
< 400℃
,
⁄
log (40) 1 1/
log (40) log (40) 1 1/
⁄
(40) (40)
1
(40) =
1 + 49 ∙ [− ∙ ]
3
(∆ )
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
∙
(40) = 0.02 ∙ [ (∆ ) ]
3
= 24 × 10 5 =
=
=
∆ =
∆
∆ = −
,
= − ∆ ≡
,
∆
⁄
(40) 1
⁄
1 ∆
(40) 1 1 (40)
⁄
⁄
Equation 4-49 for two different hoop stress values of 100 and 50 MPa as indicated in the legend. All (40) values were calculated
⁄
⁄
at whilst the results are plotted either versus 1 or the corresponding 1 . The data marked ‘cst
T’ used the same value of = 56 K for all values of , i.e., = − 56 K.. All other (40)
values were calculated with increasing with decrease in temperature.
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
Figure 4-58: (a) Cladding Tube Deformation Test (CTDT) setup; (b) specimen loading mechanism; (c) loading cycle used: RT, room
⁄
temperature, , maximum temperature of the cycle; , cooling rate and F(N), applied force (from [Alam &
Hellwig, 2008]).
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
Figure 4-59: Contour plot obtained from FE analysis of maximum principal stress in a CTDT specimen at = 450°C under a
load of 290 N (from [Alam & Hellwig, 2008]).
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
Figure 4-60: Procedure for determining the threshold stress for hydride reorientation obtained in CTDT specimens. The stress
occurring on the radial hydride band that is farthest from the wall edge of the digitized micrograph shown on the left is
determined through comparison with the across-the-wall maximum principal stress profile plot shown on the right (from
[Alam & Hellwig, 2008]).
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
Figure 4-61: Evolution of % of radial hydrides and of maximum hydride band length as a function of applied stress in an internal
pressurization test for a specimen containing 250 wppm of hydrogen (from [Alam & Hellwig, 2008]).
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
Figure 4-62: Fraction of radial hydride length as function of externally applied tensile hoop stress for a) one cycle and b) three
cycles. Note that the data cover hoop stress values ranging from compressive (negative) to tensile (positive) (from
[Valence et al., 2011]).
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
Figure 4-63: % Radial hydride length fraction as a function of interaction energy difference between radial and circumferential
hydrides (from [Valence et al., 2011]).
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
4.6.1.1
{0 0 0 2} −
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
Figure 4-64: Basal and prismatic pole figure, {0 0 0 2} − and {10 1 ̅ 1} − , respectively, for Zircaloy-2 plate material (from
[Colas et al., 2010]). RD and TD refer to the rolling and transverse directions of the plate, respectively. The intensity
scale is shown on the right hand side of the figure.
= 0.887 = 0.101 = 0.012
Figure 4-65: (a) Correspondence between tensile sample and plate material directions and (b) tensile sample geometry and
dimensions (from [Colas et al., 2010]).
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
Figure 4-66: Schematic of experimental set up for hydride reorientation tests at beamline 1-ID at Argonne National Laboratories
showing the idealized initial and reoriented orientations of the hydride precipitates in the sample (from
[Colas et al., 2010]).
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
Figure 4-67: Diffracted intensity (logarithmic scale) versus d-spacing (in Å) obtained by integration over the entire diffraction ring for
a Zircaloy-2 specimen containing 600 wppm hydrogen (from [Colas et al., 2010]).
4.6.1.2
(1 1 1) δ
δ
(1 1 1) δ
Figure 4-68: Evolution of the integrated intensity of the (1 1 1) peak taken from the RD angular section versus time and
δ
temperature for two thermo-cycles for two different Zircaloy-2 specimens containing 110 and 530 wppm hydrogen,
respectively, cycled under no external load showing the method used to determine TSSD and TSSP (from
[Colas et al., 2010]).
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
δ
δ
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
Figure 4-69: Loci of the terminal and onset temperatures, and (equivalent to TSSD and TSSP, respectively), for hydride
dissolution and precipitation, respectively, determined by synchrotron irradiation. These data are compared to the
correlation of similar data by Une and Ishimoto [Une & Ishimoto, 2003] derived with the DSC method (from
[Colas et al., 2014]).
(1 1 1) δ
(1 1 1) δ
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
Figure 4-70: Evolution of the intensity of the hydride (1 1 1) peak with time and temperature when full dissolution is not achieved
δ
(CWSR Zircaloy-4 sample with 246 wppm of hydrogen) (from [Colas et al., 2010]).
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
4.6.1.3
)
100 × (0.5 × + )
(%) =
(%)
(1 1 1) δ
(1 1 1) δ
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
Figure 4-71: Plot of the FWHM versus time of the (1 1 1) peaks in the TD and RD in a Zircaloy-4 specimen containing 530 wppm
δ
hydrogen. Only the cooling phase of the applied thermo-mechanical cycle is shown. The applied tensile stress of
85 MPa resulted in reoriented hydrides (from [Colas et al., 2010]).
(1 1 1) δ
(1 1 1) δ
(1 1 1)
(1 1 1)
(1 1 1)
(1 1 1) δ
(1 1 1) δ
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
4.6.2.1
α
Figure 4-72: (a) Schematic of the texture directions in the sheet material; (b) (0 0 0 2) − pole figure of the sheet material used
in the study of [Colas et al., 2013]; (c) schematic of the texture directions in typical fuel cladding material; (d)
(0 0 0 2) − pole figure for typical fuel cladding material (from [Colas et al., 2013]).
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
(1 1 1) δ
(0 0 0 2) −
4.6.2.2
(1 1 1) δ
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
(%)
Figure 4-73: Evolution of (%) (denoted by RHF (%) in the figure) and average hydride size versus thermal cycles for a sample
with hydrogen content of 192 wppm (in Colas’ thesis this is given as 200 wppm, which is the rounded up value of 192)
cooled at 1C/min from a maximum temperature of 410C under a 230 MPa external tensile stress applied at the
maximum temperature (from [Colas et al., 2013]).
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
Figure 4-74: Evolution of (%) (denoted by RHF (%) in the figure) and average hydride size versus hydrogen content for samples
cooled under a 230 MPa external tensile stress (from [Colas et al., 2013])).
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
(%)
(%) [H]
[H]
[H]
[H]
27 009
4
( , , ) = 4.010 × 10 exp (− )
28 068
4
( , & , ) = 45.26 × 10 exp (− )
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
4.6.2.3
{10.1} −
̅
{10.1} − {1 0 1 1} α−Zr
(1 1 1) δ
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
ℎ ℎ
2
2
2
ℎ = ℎ √(ℎ + + )
ℎ
̅
(1 0 1 1) α−Zr
α
α
Figure 4-75: Variations in strain in the TD derived from shifts in the zirconium (1 0 1 ̅ 1) αZr peak in a sample during heating and
cooling having a hydrogen content of 129 wppm under zero externally applied stress. The linear thermal expansion
strain in the nonhydrogenated material is represented as a solid purple line (from [Colas et al., 2014]).
α
(α + )/
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
α
α
α
α
(1 1 1) δ
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
Figure 4-76: Variations in relative strain in the TD as determined from shifts in the (1 1 1) peak during heating and cooling in a
δ
sample with hydrogen content of 294 wppm under zero applied stress. Note the significant jump in strain during
heating between and (from [Colas et al., 2014]).
= 4.7929 Å
α = 4.8140 Å
4.4 × 10 3
14.2 10 −6 /°C
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
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