FUEL PERFORMANCE

1
FUEL PERFORMANCE 7 CLADDING DEFORMATION
Due to the accumulation of fission products
dissolved in fuel
Oxide Fuel
Solid fp swelling
Burnup, MWd/kgU
2
Swelling of hydride fuel
Slope 0.08
8
Burnup, MWd/kgU
3
Cladding 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

4
Stresses 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
5
Open 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
6
Plastic behavior

• Equivalent uniaxial stress

• deformation is incompressible
• er ?? ?z 0

• Deviatoric stresses
• solid does not deform under hydrostatic stress

7

• Prandtl-Reuss Flow Rule

e/s is obtained from uniaxial tests

• Constitutive relations (elastic plastic
  creep thermal)

reversible elastic and thermal irreversible
plastic and creep
8
Plastic strain
Uniaxial tensile tests
9
Plastic 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
10
Compressive 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
11
Application 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
12
Gap 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

13
Post-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

14
Cladding 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