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```University of California Los Angeles
First Steps Towards Realistic 3-D
Thermo-mechanical Model
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 StressStrain Curves
Input True StressStrain Curves as
material property
in FEM or as a
subroutine
Calibrate True StressStrain 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
Semi-empirical Models
Klepaczko
•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 )
•Based partially on testing and includes certain physical phenomenon
•Continuum scale: material properties are considered homogeneous

G (T )
[ d ( , , T )   * (, T )]
G0
 d  B(, T )( 0   ) n ( ,T ) ,  *   *0 [1  D1
Bodner-Partom

T
log( max )]m
T1

2 
n  1 Z 2n

( ) D0 exp( 
( ) ), e 
2n 
E
3 
md p
Z  Z1  ( Z 0  Z1 ) D0 exp( 
)
Z0
 p 
Materials Modeling Overview-Cont’d
Dislocation
Density Based
Models
Kocks-Mecking
Ghoniem-MatthewsAmodeo (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
   (  ; , T )   (, T )  b    0 (, T )
d
1
v

 Lr N r r
d b

  b m v g
 m
 s
t
 ...,
t
 ...,
 b
dRsb
 ...,
 ...
t
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:
HT-9 450C 0DPA Stress Strain Curves
900
800
TRUE
700
(using model)
FEA
Stress(MPa)
600
500
400
Exp.
300
200
Fixed
True
Exp
Eng(FEA)
100
0
0
0.025
0.05
Strain
Displaced
0.075
0.1
F82H Example Showing Hardening
F82H 450C 0DPA Stress-Strain Curves
600
550
TRUE
stress(MPa)
500
(using model)
450
FEA
Exp.
400
350
true
exp
Eng(FEA)
300
0
0.05
strain
Sample Model Application to
EU Blanket FEM
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)
3-D Modeling of a
Dual-Coolant Blanket Sector
Dual-Coolant Concept
Flibe
9.1m
Lead
Dual-Coolant Concept He-Manifold
Dual-Coolant Concept FW-Section
Section of FW showing
25-coolant channels
Structured FW to “Solid” FW
• An equivalent “Solid” FW would have a
lot less elements (~1,000 Elements)
• Replace with equivalent SOLID FW
(for structural loads only).
Section of FW with 25-coolant
channels (~72,000 Elements)
• Develop equivalent “Solid(?)” FW
structure for 3-D THERMAL analysis
Effective Thickness
y
x
z
y
y
t
w
t1
z
L
Classical Beam Theory (h << L):
5wbL4
umax 
384 EI z
Iz 
bh
12
b
Actual C/S
Transformed C/S
Iac= Itr
t2
h
z
b
uac= utr
y
3
t2
b
Same Displacement
wbL2 ymax
 x, max 
8I z
z
Same Stress
ac= tr
t1
t2

I ac I tr
t2
Actual and transformed c/s can not give
same results unless height remains same.
Estimated Solid-Wall Thicknesses
True
All dimensions in mm.
28.0
17.0
FW
1.5
24.0
2.0
Preserve Stress
Td= 22.3
T= 21.7
Td= 31.89
T= 29.19
Td= 17.89
T= 16.94
3.0
38.0
Divider
Preserve Displacement
4.0
20.0
17.0
Stiffeners
1.5
3.0
20.0
17.0
BW
1.5
3.0
Td= 17.89
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~0.44m3):
11,340 kg/m3
FLiBe(V~7.44m3):
2,000 kg/m3
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 TrueStress-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 StrainHardening”, 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, 197219(1990)
• http://users.du.se/~kdo/kk-project/publications.htm
```
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