Title: FUEL PERFORMANCE
1FUEL PERFORMANCE 7 CLADDING DEFORMATION
Due to the accumulation of fission products
dissolved in fuel
Oxide Fuel
Solid fp swelling
Burnup, MWd/kgU
2Swelling of hydride fuel
Slope 0.08
8
Burnup, MWd/kgU
3Cladding properties
- Type (Zry-2, Zry-4, ZIRLO, M5)
- Fabrication cold-worked or stress-relieved-anneal
ed - Surface roughness
- Texture factor (fraction of grains of hcp Zr with
basal planes parallel to the tube axis usually
small) - Fill-gas type and pressure (usually He at 10
atm) - or liquid-metal bond
- Plastic and thermal creep properties
- Irradiation hardening and irradiation creep
4Stresses in cladding
- forces acting on the cladding arise from
- - fuel swelling (closed gap, or hard PCMI)
pgas
- fission-gas and system pressure
?C
gas pressure pgas
5Open gap - gas pressure (He fg)
- i void region in fuel element
- plenum
- gap
- - cracks
- R gas constant
- ni moles gas in region i
- Vi volume of region i
- Ti temperature of gas in region i
See Memo 3 for details
6Plastic behavior
- Equivalent uniaxial stress
- deformation is incompressible
- er ?? ?z 0
- Deviatoric stresses
- solid does not deform under hydrostatic stress
7e/s is obtained from uniaxial tests
- Constitutive relations (elastic plastic
creep thermal)
reversible elastic and thermal irreversible
plastic and creep
8Plastic strain
Uniaxial tensile tests
9Plastic properties of Zry(MATPRO p 4.9-9)
Strain-hardening exponent Tlt1100 K n -0.095
1.17x10-3T 2x10-6 T2 9.6x10-10
T3 1100ltTlt1600 K n -0.23 2.5x10-4 T Tgt1600
K n 0.17 Strength coefficient (in
Pa) Tlt750 K K 1.18x109 4.5x105T
3.3x103T2 1.7T3 750ltTlt1090 K K
2.52x106exp(2.85x106/T2) 1090ltTlt1250 K K
1.84x108 1.43x105T Tgt1250 K K
4.3x107-6.7x104T 37.5T2 7.3x10-3 T
10Compressive creep of Zry (from MATRPO, Vol. IV,
p. 4.8-14)
- Nearly all creep data are from tensile tests,
very little compressive creep data available - creep is slow deformation due to applied stress
below or above the yield stress - In reactor, the system pressure causes cladding
creepdown while gap is open - Compressive thermal creep (positive for
creepdown)
sq hoop stress, MPa (positive in compression) t
time under stress, s
11Application to open gap(in FRAPCON only creep
acts)
Compressive loading (p - pgas)
Cladding radius-to-thickness ratio
Time increment
Azimuthal stress (sq)
creep strain ??,cr (DR/R)creepdown
12Gap closure PCMI
- Open gap - hot but intact pellet
- Initial cracking relocation
a fraction x 0.5 of initial hot gap is
converted to void volume inside cracks
- Soft PCMI fuel first contacts cladding no
interfacial pressure
- Hard PCMI void volume eliminated from fuel
high interfacial pressure
13Post-PCMI cladding strain
- At hard PCMI, the stress in the cladding changes
from compressive to tensile it passes through
a state of zero stress, which is the reference
state - Creepdown is replace by outward plastic
deformation driven by fission-product swelling of
fuel
- the strains follow the rigid pellet
approximation
no-axial-slip condition
- By volume conservation, the cladding becomes
thinner
14Cladding deformation (cont)
- only plastic deformation is considered
- From Prandtl-Reuss rules
Deviatoric stresses
- from previous slide, eq,pl ez,pl, so sq,dev
sq,dev and
sq sz
(note difference from open-gap case sq ½sz)
pi p S(dC/R) sq S - p
S 3K (Gfp G )n
From Memo 5
(K n from slide 9)
15- Example TC 625 K, n 0.1, K 600 MPa
- Suppose PCMI starts at 40 MWd/kgU when G 1
At 60 MWd/kgU, Gfp 2.5 so S 395 MPa For p
7 MPa and dC/R 0.14, pi 62 MPa sq 387
MPa
What to compare this to? MATPRO suggests the
burst strength sburst 1.36K 820 MPa Since
sq lt sburst by a good margin, the cladding is safe