Cladding Deformation
Transcript of Cladding Deformation
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Swelling of hydride fuel
0 4 8 12 16 20 24
Burnup, MWd/kgU
Slope = 0.08
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Cladding properties Type (Zry-2, Zry-4, ZIRLO, M5) Fabrication: cold-worked or stress-relieved-annealed 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
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Stresses in cladding forces acting on the cladding arise from:
- fuel swelling (closed gap, or hard PCMI)
gas pressure p gas
21
z
CCgas
;/R)pp( tubes,wall-thin
:gapOpenC
RC
)5#Memo(/R)pp(
z
CCi
- fission-
gas and system pressure
p gas
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Open gap - gas pressure (He + fg)
ii
igas T/V
nRp
i = void region in fuel element
- plenum- gap
- cracks
R = gas constantn i = moles gas in region i
Vi = volume of region i
Ti = temperature of gas in region i
See Memo #3for details
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Plastic behavior
deformation is incompressible:
er + e + ez = 0
2/12r z
2r
2z2
1 )()()(*
Equivalent uniaxial stress:
Deviatoric stresses:solid does not deform under hydrostatic stress
zr 31r dev,r
zr 31
zdev,z
zr 31
dev,
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Prandtl-Reuss Flow Rule
dev,r pl,r dev,zpl,zdev,pl, **
**
** ee ee ee
T)( cr ,pl,r zE1tot, eee
T)(cr ,zpl,zr zE
1
tot,zeee
Constitutive relations (elastic + plastic + creep + thermal):
reversible:elastic andthermal
irreversible:
plastic andcreep
e / is obtained from uniaxial tests
T)( cr ,r pl,r zr E1tot,r eee
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Plastic properties of Zry(MATPRO p 4.9-9)
Strain-hardening exponent:T
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Compressive creep of Zry(from MATRPO, Vol. IV, p. 4.8-14)
Btcr , e1 Ae
Nearly all creep data are from tensile tests, very littlecompressive creep data available
creep is slow deformation due to applied stress below orabove the yield stress In reactor, the system pressure causes cladding creepdown while gap is open Compressive thermal creep (positive for creepdown):
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)5.14/(10x6.7B
)5.14/(10x3.5 A
hoop stress, MPa (positive in compression)
t = time under stress, s
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Application to open gap(in FRAPCON only creep acts)
Compressiveloading (p - p gas )
Azimuthal stress
creep strain: e ,cr = ( R/R) creepdown
Time increment
Cladding radius-to-thickness ratio
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Gap closure & PCMI
Open gap - hot but intact pellet
Initial cracking & relocationa fraction x ~ 0.5 of initial hot gap isconverted to void volume inside cracks
Soft PCMI fuel first contactscladding no interfacial pressure
Hard PCMI void volume eliminatedfrom fuel high interfacial pressure
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Post-PCMI cladding strain At hard PCMI, the stress in the cladding changes from
compressive to tensile; it passes through a state of zerostress, which is the reference state
Creepdown is replace by outward plastic deformationdriven by fission-product swelling of fuel
ref fpfp
C
Cpl,z z
z
zze
no-axial-slip conditionref fpfpCCpl, R
R
RRe
By volume conservation, the cladding becomes thinner:
pl,pl,zpl,pl,r 2)(
1slideonplotfromVV
31
fpfp
the strains follow therigid pellet approximation:
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Cladding deformation (cont) only plastic deformation is considered
From Prandtl-Reuss rules
0:axial
)tensile(:azimuthal
zr 3
1zdev,z
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zr 31
dev,
dev,zpl,zdev,pl, **
**
ee
ee
Deviatoric stresses:
from previous slide, e pl = ez pl, so dev = dev and: = z
(note difference from open-gap case: = z)
From Memo #5:p i = p + S C/R)
S p
S 3K ( fp n ref fp
(K & n from slide 9)
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Example: T C = 625 K, n = 0.1, K = 600 MPa
Suppose PCMI starts at 40 MWd/kgU when 1% ref fp
At 60 MWd/kgU, fp = 2.5% so S 395 MPa
For p = 7 MPa and C/R = 0.14, p i = 62 MPa & 387 MPa
What to compare this to? MATPRO suggests the
burst strength : burst ~ 1.36K = 820 MPa
Since < burst by a good margin, the cladding is safe