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FUEL PERFORMANCE FUEL SWELLING and PCI

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FUEL PERFORMANCE FUEL SWELLING and PCI Powered By Docstoc
					          FUEL PERFORMANCE
      #7 CLADDING DEFORMATION
Due to the accumulation of fission products dissolved in fuel
 Oxide Fuel
 ΔV 
     (%)  1.8 (BU)  0.3 (BU)           BU  3 M Wd/kgU
                                  2

 V  fp
           0.08 (BU)  2.1               BU  3 M Wd/kgU

                                Solid fp swelling
           radiation
           densification




                              Burnup, MWd/kgU                 1
Swelling of hydride fuel




        Slope = 0.08




0   4     8        12   16   20   24
        Burnup, MWd/kgU
                                       2
              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

                                                            3
              Stresses in cladding
 • forces acting on the cladding arise from:
         - fuel swelling (closed gap, or hard PCMI)

      p     R
   (i  p) C /  C
z   ( Memo #5)
                                                           pgas




   - fission-gas and system pressure                              RC
           gas pressure p
                     gas
                                                      C
      Open gap :
                                p       R
       thin - wall tubes,    (gas  p) C /  C ;
     •




                                 1
                            z  2 
                                                                       4
Open gap - gas pressure (He + fg)
                        R ni
              p gas   
                         Vi / Ti
   i = void region in fuel element
      - plenum
      - gap
                                     See Memo #3
      - cracks                       for details
   R = gas constant
   ni = moles gas in region i
   Vi = volume of region i
   Ti = temperature of gas in region i             5
                 Plastic behavior
 • Equivalent uniaxial stress:

          *    1
                 2
                     (
                      
                      
                                2           2
                            z )  (  r )  (z  r ) 1 / 2
                                                      2
                                                           
 •deformation is incompressible:

             er + e  + ez = 0

• Deviatoric stresses:
solid does not deform under hydrostatic stress

           , dev     3     r   z 
                           1

           z, dev   z  3     r   z 
                           1

           r, dev   r  3     r   z 
                           1
                                                                  6
 • Prandtl-Reuss Flow Rule

             e*                      e*                      e* 
   e ,pl       , dev   e z,pl       z, dev   e r,pl       r, dev
            *                      *                      *

      e/ is obtained from uniaxial tests

 • Constitutive relations (elastic + plastic + creep + thermal):
reversible:                                    
                  e , tot  E    (z  r ) e ,pl  e ,cr  T
                             1         
elastic and
thermal                                        
                  e z, tot  E  z  (  r ) e z,pl  e z,cr  T
                             1         
irreversible:
                                              
                  er, tot  E r  (   z ) er,pl  er,cr  T
                            1        
plastic and
creep
                                                                                 7
Uniaxial tensile tests

Irradiation effect



           K(en

      Plastic
      strain




                         8
            Plastic properties of Zry
                    (MATPRO p 4.9-9)
Strain-hardening exponent:
T<1100 K: n = -0.095 + 1.17x10-3T – 2x10-6 T2 +9.6x10-10 T3
1100<T<1600 K: n = -0.23 + 2.5x10-4 T
T>1600 K:         n = 0.17
Strength coefficient (in Pa):
T<750 K:          K = 1.18x109 + 4.5x105T – 3.3x103T2 + 1.7T3
750<T<1090 K: K = 2.52x106exp(2.85x106/T2)
1090<T<1250 K: K = 1.84x108 – 1.43x105T
T>1250 K:         K = 4.3x107-6.7x104T + 37.5T2 – 7.3x10-3 T
                                                           9
          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):

                          A  5.3 x10 3 ( / 14 .5)
                                                     2
                                           
  e ,cr  A 1 e Bt                                 2
                            B  7.6 x10  7 ( / 14 .5)
                                            
     hoop stress, MPa (positive in compression)
   t = time under stress, s                                   10
Application to open gap
(in FRAPCON only creep acts)

 Compressive            Cladding radius-
 loading (p - pgas)     to-thickness ratio

Azimuthal stress     Time increment

     creep strain: e,cr = (R/R)creepdown




                                             11
  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
                                            12
             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
                   1  V 
              fp         from plot on slide 1
                   3  V  fp

• the strains follow the                            z C z          ref
                                         e z,pl            fp  fp
rigid pellet approximation:                          zC   z
           R C R          ref
e ,pl            fp  fp              no-axial-slip condition
           RC    R
 • By volume conservation, the cladding becomes thinner:
            ε r ,pl   (ε θ,pl  ε z ,pl )  2ε θ,pl
                                                                           13
        Cladding deformation (con’t)
 • only plastic deformation is considered
 • From Prandtl-Reuss rules
     Deviatoric stresses:
      azimuthal:  , dev     3    r   z   2   (
                                  1                     1     tensile)
            axial :      z, dev   z  3    r   z   0
                                         1


                         e*                     e* 
               e ,pl       ,dev   e z,pl       z,dev
                        *                     *
• from previous slide, epl = ezpl, so dev = dev and:  = z

             (note difference from open-gap case:  = ½z)

                      pi = p + SC/R) S  3K (fp – ref n
                                                      fp
From Memo #5:
                        S  p            (K & n from slide 9)
                                                                    14
• Example: TC = 625 K, n = 0.1, K = 600 MPa
Suppose PCMI starts at 40 MWd/kgU when  ref  1%
                                         fp


At 60 MWd/kgU, fp = 2.5% so S  395 MPa
For p = 7 MPa and C/R = 0.14, pi = 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




                                                           15

				
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posted:7/20/2011
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