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 MeetingUniversity of California Los Angeles

Los Angeles, CAFeb. 23-25, 2004

University of California Los Angeles

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)

Produce True Stress-Strain Curves

Input True Stress-Strain Curves as material property in FEM or as a subroutine

Calibrate True Stress-Strain Curves with Experimental data

•Obtain material properties (σ-ε curves)

•Study material behaviors

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

Purely Empirical Models•Based purely on empirical testing and curve fitting•Continuum scale: material properties are considered homogeneous

Ludvik-Holloman

Johnson-Cook

Semi-empirical Models•Based partially on testing and includes certain physical phenomenon•Continuum scale: material properties are considered homogeneous

Klepaczko

Bodner-Partom

Materials Modeling Overview

)1)(ln1)(( **m

n TCBA

nK

mTnd

d

T

TDTB

TTG

TG

)]log(1[**,))(,(

)],(*),,([)(

max

110

),(0

0

)exp()(

),)(2

1exp()(

3

2

00101

20

Z

dmDZZZZ

E

Z

n

nD

p

en

p

Materials Modeling Overview-Cont’d

Dislocation Density Based Models

•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

Kocks-Mecking

Ghoniem-Matthews-Amodeo (GMA)*

rrr

vNL

bd

d

TbTT

1

),(),(),;( 0

......,...,...,

dt

dR

ttt

vb

sbbsm

gm

•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

Strain

Str

ess

(MP

a)

0 0.025 0.05 0.075 0.10

100

200

300

400

500

600

700

800

900

TrueExpEng(FEA)

HT-9 450C 0DPA Stress Strain Curves

Exp.

FEA

TRUE(using model)

strain

stre

ss(M

Pa

)

0 0.05300

350

400

450

500

550

600

trueexpEng(FEA)

F82H 450C 0DPA Stress-Strain Curves

F82H Example Showing Hardening

Exp.FEA

TRUE(using model)

Sample Model Application to EU Blanket FEM

EU-HCPB Blanket FEA

Design criteria for allowable stress are based on rulesapplied to ITER. Accidental pressurization of the box is a

faulted condition corresponding to level D criteria, implyingthat the faulted component will have to be replaced. The

criteria are based on the min(0.7 Su, 2.4 Sm), which is 324 MPafor 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 lowervon Mises stresses and larger displacements

DisplacementVon Mises Stress

•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

9.1m

Flibe

Lead

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

Effective Thickness

Actual C/S Transformed C/S

x

y

z

L

w

Classical Beam Theory (h << L):

zEI

wbLu

384

5 4

max

zx I

ywbL

8max

2

max,

Same Displacement Same Stress

uac= utr

t1

b

t

z

y

b

t2

y

z

Iac= Itr

12

3bhI z h

b

y

z

t2

ac= tr

trac I

t

I

t 21

t2

Actual and transformed c/s can not give same results unless height remains same.

Estimated Solid-Wall Thicknesses

FW

Divider

Stiffeners

BW

True Preserve Displacement Preserve Stress

1.53.0

28.0

17.0

38.0

24.0

2.04.0

20.0

All dimensions in mm.

17.0

3.01.5

20.0

17.0

1.53.0

Td= 22.3

Td= 31.89

Td= 17.89

Td= 17.89

T= 21.7

T= 29.19

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~0.44m3): 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 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