cladding deformation

8/3/2019 Cladding Deformation

1/15


2/15

2

Swelling of hydride fuel

0 4 8 12 16 20 24

Burnup, MWd/kgU

Slope = 0.08


3/15

3

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


4/15

4

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


5/15

5

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


6/15

6

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,


7/15

7

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


8/15


9/15

9

Plastic properties of Zry(MATPRO p 4.9-9)

Strain-hardening exponent:T


10/15

10

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):

27

23

)5.14/(10x6.7B

)5.14/(10x3.5 A

hoop stress, MPa (positive in compression)

t = time under stress, s


11/15

11

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


12/15

12

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


13/15

13

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:


14/15

14

Cladding deformation (cont) only plastic deformation is considered

From Prandtl-Reuss rules

0:axial

)tensile(:azimuthal

zr 3

1zdev,z

21

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)


15/15

15

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

cladding deformation

Documents