University of California Los Angeles
S. Sharafat, Y. Nosenko, J. Chiu, P. Pattamanush,
M. Andersen, S. Banerjee, and N. Ghoniem
Mechanical Engineering Department,
University of California Los Angeles
ITER-TBM Meeting
University of California Los Angeles
Los Angeles, CA
Feb. 23-25, 2004

Outline
• Phenomenological Materials
Modeling & its Applications to FEM
• Sample Model Application to EU
Blanket FEM
• 3-D Modeling of a Dual-Coolant
Blanket Sector

Phenomenological
Materials Modeling
And its Applications to FEM

Material Models to FEM Cycle
Solve Model for stress and strain
(LSODE)
•Obtain material properties ( σ-ε curves)
•Study material behaviors
Produce True Stress-
Input True Stress-
Strain Curves as material property in FEM or as a subroutine
Strain Curves
Calibrate True Stress-
Strain Curves with
Experimental data

Materials Modeling
Provide predictive relations between the nano- and micro-structure of the material and its macroscopic mechanical properties by computational modeling.
Typical Stress-Strain Curve Typical Creep Curve

Materials Modeling Overview
Purely Empirical Models
Ludvik-Holloman
Johnson-Cook
•Based purely on empirical testing and curve fitting
•Continuum scale: material properties are considered homogeneous
 
K
 n
 
( A

B
 n
)( 1

C ln
 
*
)( 1

T
* m
)
Semi-empirical Models
Klepaczko
Bodner-Partom
•Based partially on testing and includes certain physical phenomenon
•Continuum scale: material properties are considered homogeneous

 d


G ( T )
[
 d
G
0
(

,
  , T )
 
* (
  , T )]
B (
  , T )(

0
 
) n (
 
, T ) ,

*
 
*
0
[ 1

T
D
1
T
1 log(
 max
 
)] m
  p
Z

2
3
(


) D
0 exp(
 n

2 n
1
(
Z

)
2 n
),
  e

Z
1

( Z
0

Z
1
) D
0 exp(
 m
 d
  p
Z
0
)


E

Materials Modeling Overview-Cont’d
Dislocation
Density Based
Models
Kocks-Mecking
Ghoniem-Matthews-
Amodeo (GMA)*
• Based on microstructure parameters-dislocation density
(the main source of plastic deformation)
• Based on microstructural evolution-allows for time dependent phenomenon to be studied, i.e., creep
• It is phenomenological
• Continuum scale: material properties are considered homogeneous
 d
 d

 
(

;
  , T )
 
(
  , T )
  b

1
 b

L r
N r v r
 
  
0
(
  , T )

 
 
 t m b
 m v g

...,
 
 t s

...,
 
 t b

..., dR sb dt

...
•N. M. Ghoniem, J. R. Matthews, R. J. Amodeo, “A Dislocation Model for Creep in Engineering Materials”, Res Mechanica , 29 ,
197-219(1990)

Model Implementation-FEA Set up
Dislocation Based Material Model True Stress-Strain are used in FEA:
Fixed
Displaced
500
400
300
200
100
0
0
900
800
700
600
HT-9 450C 0DPA Stress Strain Curves
TRUE
(using model)
FEA
0.025
0.05
Strain
Exp.
0.075
True
Exp
Eng(FEA)
0.1

F82H Example Showing Hardening
F82H 450C 0DPA Stress-Strain Curves
600
550
500
TRUE
(using model)
Exp.
450
400
FEA
350
300
0.05
true exp
Eng(FEA)
0 strain

EU-HCPB Blanket FEA
Design criteria for allowable stress are based on rules applied to ITER. Accidental pressurization of the box is a faulted condition corresponding to level D criteria, implying that the faulted component will have to be replaced. The criteria are based on the min(0.7 Su, 2.4 Sm), which is 324 MPa for 400°C warm EUROFER steel.

EU-HCPB Blanket FEA
• Using FZK-boundary conditions the elastic ANSYS model results in very similar stress and deformation levels
Displacement
Von Mises Stress

Implementing Material Modeling
• Use GMA* dislocation-based creep model to analyze elasto-plastic response
• Input the true stress-strain curve into ANSYS FEM
• Perform elasto-plastic analysis
• Preliminary results indicate lower von Mises stresses and larger displacements
Von Mises Stress
Displacement
•N. M. Ghoniem, J. R. Matthews, R. J. Amodeo, “A Dislocation Model for Creep in Engineering Materials”, Res Mechanica , 29 ,
197-219(1990)

Lead
Dual-Coolant Concept
Flibe
9.1m

Dual-Coolant Concept He-Manifold

Dual-Coolant Concept FW-Section
Section of FW showing
25-coolant channels

Structured FW to “Solid” FW
Section of FW with 25-coolant channels (~72,000 Elements )
• An equivalent “Solid” FW would have a lot less elements (~1,000 Elements )
• Replace with equivalent SOLID FW
(for structural loads only).
• Develop equivalent “Solid(?)” FW structure for 3-D THERMAL analysis

y
Effective Thickness z x w y t y z z t
1
L b
Actual C/S b
Transformed C/S Classical Beam Theory (h << L):
5 wbL
4 u max

384 EI z
 x , max
I z

 bh
3
12 wbL
2 y max
8 I z y z b h
Same Displacement u ac
= u tr
Same Stress
 ac
=
 tr
I ac
= I tr
I t
1 ac
 t
2
I tr t
2 t
2
Actual and transformed c/s can not give same results unless height remains same.
t
2

FW
Estimated Solid-Wall Thicknesses
True
All dimensions in mm.
28.0
Preserve Displacement Preserve Stress
Td= 22.3
T

= 21.7
17.0
1.5
3.0
38.0
Td= 31.89
24.0
T

= 29.19
Divider
2.0
4.0
Stiffeners
1.5
3.0
20.0
17.0
1.5
3.0
20.0
17.0
BW
Td= 17.89
Td= 17.89
T

= 16.94
T

= 16.94

Self-Weight plus Hydrostatic Loads of
Full Dual-Coolant Blanket Model

Loading and Boundary Conditions
•Attachment of the blanket to the shield
•Only the back of the DC-Blanket interlocks with the shield:
•Four 2-cm wide stripes top-to-bottom
Elements: ~80,000 (solid tetrahedral)
Pb (V~0.44m
3 ): 11,340 kg/m 3
FLiBe(V~7.44m
3 ): 2,000 kg/m 3

Max. Displacement: ~0.3 mm

Total Displacement (x50)

Max. von Mises: ~115 MPa

Von Mises (x50)

Max. Von Mises: 128 Mpa Max. Displacement: 0.3 mm

Total Displacement (x1555)

Total Displacement (x1555)

Summary
• Dislocation-based creep models have been used to generate True-
Stress-Strain for ferritic steels (F82H, HT-9)
• FEM elasto-plastic analysis based on True-Stress-Strain curves were conducted.
• In collaboration with FZK accident-based loading case of EU-HCPB was analyzed.
• Elasto-Plastic analysis io EU-HCPB is ongoing.
• 3-Dimensional FEM of Dual-Coolant Blanket has been initiated:
• Hydrostatic pressures due to ~16,000 kg of Pb/Flibe results in deformations of~3mm and stresses of ~120MPa.
• Thermal analysis of 3-D full scale model is under development.

References
• Nasr M. Ghoniem and Kyeongjae Cho, "The Emerging Role of
Multiscale Modeling in Nano- and Micro-mechanics of Materials", J.
Comp. Meth. Engr. Science, CMES , 3(2) ,147-173 (2002).
• H. Mecking and U. F. Kocks, “Kinetics of Flow and Strain-
Hardening”, Acta Metallurgica , 29 , 1865-1875 (1981).
• Y. Estrin and H. Mecking, “A Unified Phenomenological Description of Work Hardening and Creep Based on One-Parameter Models”, Acta
Metallurgica , 32 , 57-70 (1984).
• N. M. Ghoniem, J. R. Matthews, R. J. Amodeo, “A Dislocation Model for Creep in Engineering Materials”, Res Mechanica , 29 , 197-
219(1990)
• http://users.du.se/~kdo/kk-project/publications.htm