International Conference of Fracture 2017: A procedure to determine the fracture properties of nuclear cladding from ring compression tests. A parametric study

1. Determination of Fracture Toughness of Nuclear
Fuel Cladding from Ring Compression Tests
F.J. Gomez(1), M.A. Martin-Rengel(2), J. Ruiz-Hervias(2)
• (1) ADVANCED MATERIAL SIMULATION, Bilbao Spain
• (2) Universidad Politecnica de Madrid, Spain
www.amsimulation.com
E-mail: javier.gomez@amsimulation.com

2. Introduction
Westinghouse, “Descripción del SNGV Westinghouse”, Westinghouse Nuclear Española, I.S.B.N. .84-300-8592-0

3. Introduction
DESPLAZAMIENTO (mm)
CARGA(KN)
1
2
3
4
5
6
LOAD,kN
Displacement, mm

4. Introduction
• Iterative material characterization
Fracture energy
Optimization techniques

5. Experimental programme
20 ºC 135 ºC 300 ºC
0.5mm/min100mm/min
0
0.5
1
1.5
0 1 2 3 4 5 6 7 8
P(kN)
0 ppm
150 ppm
250 ppm
500 ppm
1200 ppm
2000 ppm
0
0.5
1
1.5
0 1 2 3 4 5 6 7 8
0 ppm
150 ppm
250 ppm
500 ppm
1200 ppm
2000 ppm
0
0.5
1
1.5
0 1 2 3 4 5 6 7 8
0 ppm
150 ppm
250 ppm
500 ppm
1200 ppm
2000 ppm
0
0.5
1
1.5
0 1 2 3 4 5 6 7 8
P(kN)
d (mm)
0 ppm
150 ppm
250 ppm
500 ppm
1200 ppm
2000 ppm
0
0.5
1
1.5
0 1 2 3 4 5 6 7 8
d (mm)
0 ppm
150 ppm
250 ppm
500 ppm
1200 ppm
2000 ppm
0
0.5
1
1.5
0 1 2 3 4 5 6 7 8
d (mm)
0 ppm
150 ppm
250 ppm
500 ppm
1200 ppm
2000 ppm

6. Numerical modelling
Finite elements
• ABAQUS
• 6-8 node elements
• 5 mm size
• NLGEOM
• Contact at upper surface →rigid
surface
• Friction 0.125
• Cohesive zone model
• Linear softening curve
• User subroutine UEL
wc
ft
Displacement, w
Stress,σ
Gf
 dwwfG
cw
f 
0

7. Optimization algorithm
Fracture energy
Optimization techniques
(AMS algorithms)
0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4 5 6 7 8
P(kN)
d (mm)
Numerical
Experimental

8. Optimization algorithm
  duPPErr num
finu
u
2
exp
_
max_
 
1. Exhaustive search NxN matrix - coarse
2. Critical region analysis - coarse
3. Nelder-Mead Downhill Simplex – coarse
4. Nelder-Mead Downhill Simplex - fine
800
900
1000
1100
1200
0.04 0.06 0.08 0.1 0.12 0.14
Step 1 matrix
f
t
(MPa)
w
c
/2 (mm)

9. Optimization algorithm
  duPPErr num
finu
u
2
exp
_
max_
 
1. Exhaustive search NxN matrix - coarse
2. Critical region analysis - coarse
3. Nelder-Mead Downhill Simplex – coarse
4. Nelder-Mead Downhill Simplex - fine
800
900
1000
1100
1200
0.04 0.06 0.08 0.1 0.12 0.14
Step 1 matrix
Step 2 random search
Step 3 coarse minimum
Step 4 fine minimum
f
t
(MPa)
w
c
/2 (mm)

10. Optimization algorithm
  duPPErr num
finu
u
2
exp
_
max_
 
1. Exhaustive search NxN matrix - coarse
2. Critical region analysis - coarse
3. Nelder-Mead Downhill Simplex – coarse
4. Nelder-Mead Downhill Simplex - fine
0
0.2
0.4
0.6
0.8
1
0 1 2 3 4 5 6 7 8
Experimental
Numerical - step 3
Numerical - step 4
P(kN)
u (mm)
OUTPUT -> Fracture Toughness KIC = 69 MPam0.5

11. Results
0
0.5
1
1.5
0 4 8
P(kN)
20ºC
0 ppm
0
0.5
1
1.5
0 4 8
20ºC
150 ppm
0
0.5
1
1.5
0 4 8
20ºC
250 ppm
0
0.5
1
1.5
0 4 8
20ºC
500 ppm
P(kN)
d (mm)
0
0.5
1
1.5
0 4 8
20ºC
1200 ppm
d (mm)
0
0.5
1
1.5
0 4 8
20ºC
2000 ppm
d (mm)
20 ºC
0.5 mm/min

12. 0
0.5
1
1.5
0 4 8
135ºC
2000 ppm
d (mm)
0
0.5
1
1.5
0 4 8
135ºC
1200 ppm
d (mm)
0
0.5
1
1.5
0 4 8
P(kN)
135ºC
500 ppm
d (mm)
0
0.5
1
1.5
0 4 8
135ºC
250 ppm
0
0.5
1
1.5
0 4 8
135ºC
150 ppm
0
0.5
1
1.5
0 4 8
P(kN)
135ºC
0 ppm
Results
135 ºC
0.5 mm/min

13. 0
0.5
1
1.5
0 4 8
300ºC
2000 ppm
d (mm)
0
0.5
1
1.5
0 4 8
300ºC
1200 ppm
d (mm)
0
0.5
1
1.5
0 4 8
P(kN)
300ºC
500 ppm
d (mm)
0
0.5
1
1.5
0 4 8
300ºC
250 ppm
0
0.5
1
1.5
0 4 8
P(kN)
300ºC
150 ppm
Results
300 ºC
0.5 mm/min

14. 0
0.5
1
1.5
0 4 8
20ºC
2000 ppm
d (mm)
0
0.5
1
1.5
0 4 8
20ºC
1200 ppm
d (mm)
0
0.5
1
1.5
0 4 8
20ºC
500 ppm
P(kN)
d (mm)
0
0.5
1
1.5
0 4 8
20ºC
250 ppm
0
0.5
1
1.5
0 4 8
20ºC
150 ppm
0
0.5
1
1.5
0 4 8
P(kN)
20ºC
0 ppm
Results
20 ºC
100 mm/min

15. 0
0.5
1
1.5
0 4 8
135ºC
2000 ppm
d (mm)
0
0.5
1
1.5
0 4 8
135ºC
1200 ppm
d (mm)
0
0.5
1
1.5
0 4 8
P(kN)
135ºC
500 ppm
d (mm)
0
0.5
1
1.5
0 4 8
135ºC
250 ppm
0
0.5
1
1.5
0 4 8
135ºC
150 ppm
0
0.5
1
1.5
0 4 8
P(kN)
135ºC
0 ppm
Results
135 ºC
100 mm/min

16. 0
0.5
1
1.5
0 4 8
300ºC
2000 ppm
d (mm)
0
0.5
1
1.5
0 4 8
300ºC
1200 ppm
d (mm)
0
0.5
1
1.5
0 4 8
P(kN)
300ºC
500 ppm
d (mm)
0
0.5
1
1.5
0 4 8
300ºC
250 ppm
P(kN)
Results
300 ºC
100 mm/min

17. Error estimation
• The fitting procedure introduces an error.
• Similar P-d curves correspond a range of Fracture Toughness
• There exists a relationship between Err and Fracture Toughness error
• The final error in the Fracture Toughness depends on the quality of the adjustment
400
600
800
1000
1200
1400
0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11
f
t
(MPa)
w
c
/2 (mm)
K
IC
= 75 MPam
0.5
K
IC
= 61 MPam
0.5
  duPPErr num
finu
u
2
exp
_
max_
 

18. Error estimation
The relation Err – DKIC is determined numerically by using the optimum as the
reference curve
  duPPErr num
finu
u
2
exp
_
max_
 
0
5
10
15
0 0.0005 0.001 0.0015 0.002
DK/K
IC,ref
(%)
Error
Coarse mesh calculation + POD-BRF interpolation
400
600
800
1000
1200
1400
0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11
f
t
(MPa)
w
c
/2 (mm)
K
IC
= 75 MPam
0.5
K
IC
= 61 MPam
0.5

19. Error estimation
The relation Err – DKIC is determined numerically by using the optimum as the
reference curve
  duPPErr num
finu
u
2
exp
_
max_
 
1. Fixed a value for Err
2. Determine the set of points
(wc, ft) where the error is less or
equal tan Err* relative to the
reference curve
3. Calculate K*IC,max and K*IC,min,
4. DK* 400
600
800
1000
1200
1400
0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11
f
t
(MPa)
w
c
/2 (mm)
K
IC
= 75 MPam
0.5
K
IC
= 61 MPam
0.5

20. Error estimation
  duPPErr num
finu
u
2
exp
_
max_
 
0
5
10
15
0 0.0005 0.001 0.0015 0.002
DK/K
J,ref
(%)
Error
The relation Err – DKIC is determined numerically by using the optimum as the
reference curve

21. 0
20
40
60
80
100
120
0 500 1000 1500 2000 2500
FractureToughness,K
IC
(MPa.m
0.5
)
Hydrogen content (ppm)
20ºC
135ºC
300ºC
Error estimation
Final output: KIC ± DKIC
0
20
40
60
80
100
0 500 1000 1500 2000 2500
FractureToughness,K
IC
(MPa.m
0.5
)
Hydrogen content (ppm)
20ºC
135ºC
300ºC
0.5 mm/min 100 mm/min

22. Conclusions
• The proposed procedure combines experimental tests, finite
element simulations and an optimization algorithm to determine
the Fracture Toughness.
• The method has been applied successfully to zirlo tested at three
temperatures, two velocities and six hydride contents.
• Numerical calculations significally fit experimental data.
• The inverse method proposed introduced an error that has been
estimated numerically.
• The final output is KIC ± DKIC

23. Thank you for your attention.

24. Background
Material → ZIRLO
Ring compression tests
Cilinders: 10 mm height, 9.5 mm diameter (ext)
0.57 mm thickness
Hydrides
Cathodic charging in KOH aqueous solutions + thermal treatment
150 wppm of H
Hydrogen concentrations studied 0, 150, 250, 500, 1200 and 2000 ppm
500 wppm of H 1200 wppm of H

25. Background
0
0.2
0.4
0.6
0.8
1
0 1 2 3 4 5 6 7
P(kN)
d (mm)
Experimental
Numerical
135ºC20ºC
300ºC
0
200
400
600
800
1000
1200
0 0.05 0.1 0.15 0.2 0.25 0.3
Stress(MPa)
Plastic strain
300ºC
135ºC
20ºC
wc
ft
Displacement, w
Stress,σ
Gf
 dwwfG
cw
f 
0
• Linear softening
• User element subroutine UEL

26. Background
  duPPErr num
finu
u
2
exp
_
max_
 
1. Exhaustive search NxN matrix - coarse
2. Critical region analysis - coarse
3. Nelder-Mead Downhill Simplex – coarse
4. Nelder-Mead Downhill Simplex - fine