This document summarizes research on modeling crack growth in nuclear fuel pellets using peridynamics. Peridynamics is a nonlocal continuum theory that allows cracks to initiate and propagate in unguided locations and paths. The model represents the fuel pellet material as a network of bonds between material points. Forces on each point are calculated based on its relative displacement from neighboring points. The model is used to simulate crack growth under increasing loads by damaging bonds that exceed a critical stretch threshold. Simulations show cracks initiating and propagating through the pellet material in complex patterns as the load increases. Temperature and displacement distributions within the pellet are also mapped at different load levels.

1. Department of Aerospace and Mechanical Engineering
Crack Growth in Nuclear
Fuel Pellet
Y.L. Hu and E. Madenci
University of Arizona, Tucson, AZ

2. Peridynamics
Peridynamics is a nonlocal continuum theory - “Peri”
comes from a Greek root for “near”.
Silling SA. Reformulation of elasticity theory for discontinuities and long-range forces[J]. Journal of the
Mechanics and Physics of Solids, 2000, 48:175-209.
• Allows for crack initiation in
unguided locations;
• Allows for crack propagation
along unguided paths;
• Allows for multi-crack emergence
and their interaction.
Force density
function
2

3. Peridynamic Equilibrium Equation
Classical Continuum Mechanics:
PD Equilibrium Equation:
     ', , ', , ', ,
x
xH
t t dV t  u x f u u x x b x&&
   '
1
, ', , ', , , , ,
i
x
N
x ij i j i j jH
j
t dV t dV

  f u u x x f u u x x
Silling S.A., Askari E. A meshfree method based on the peridynamic model of solid mechanics. Computers and
Structures, 2005, Vol.83, 1526-1535.
Askari E. Xu JF. Peridynamic Analysis of Damage and Failure in Composites,44th AIAAAerospace Sciences
Meeting and Exhibition,No.2006-88,Reno,Nevada,2006.
     , , , ,t t t   u x σ u x b x&&
Reference
Configuration
Deformed
Configurationi
j j
i
3

4. Bond-based Peridynamics
Force density function:
 
'
, ', , '
'
c s



y y
f u u x x
y y
0
0
1, intact bond,
0, damaged bond,
s s
s s


 

Micromodulus c
' '
Stretch
'
s
  


y y x x
x x
'
Direction of force density
'


y y
y y
Bond
Stretch
Bond
Force
S0
c
Critical Stretch
Micromodulus
Status variable - 
4

5. 3. Nuclear Fuel Pellet
(a)
Computational model:
6
4.1 , , 1
200.0 , 0.345, 1.0 / /
Mesh Spacing varies from 0.0082 to 0.041
R mm b x t mm
E GPa v mm mm T
x mm mm
 
   
  
 

6. 3. Nuclear Fuel Pellet
Coupled thermal-mechanical equation is solved fully implicitly.
 
1
, , , ,
0
iN
PD ij i j i j j i
j
Thermal v
t dV
k d Q


  

     


R f u u x x b 0
R T A
T
PD PD
Thermal Thermal
  
  
  
  
   
R R
u T
K
R R
u T
Tangent Stiffness (PTS) matrix
Randomized critical stretch is
distributed under Gaussian
distribution.

7. 3. Nuclear Fuel Pellet
Temperature distribution contour
Diameter 300N  Diameter 800N 

8. 3. Nuclear Fuel Pellet
Displacement distribution contour
Diameter 300N  Diameter 800N 

9. 3. Nuclear Fuel Pellet
Damage pattern
Diameter 800N  Diameter 1000N 