1. 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 University of California Los Angeles

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

3. Phenomenological Materials Modeling And its Applications to FEM

4. 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

5. 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 CurveTypical Creep Curve

6. 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

7. 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)* N. M. Ghoniem, J. R. Matthews, R. J. Amodeo, “A Dislocation Model for Creep in Engineering Materials”, Res Mechanica, 29, 197-219(1990)

8. Model Implementation-FEA Set up Dislocation Based Material Model True Stress-Strain are used in FEA: Fixed Displaced Exp. FEA TRUE (using model)

9. F82H Example Showing Hardening Exp. FEA TRUE (using model)

10. Sample Model Application to EU Blanket FEM

11. 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.

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

13. 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 Displacement Von 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)

14. 3-D Modeling of a Dual-Coolant Blanket Sector

15. Dual-Coolant Concept 9.1m Flibe Lead

16. Dual-Coolant Concept He-Manifold

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

18. 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

19. Effective Thickness Actual C/STransformed C/S x y z L w Classical Beam Theory (h << L): Same DisplacementSame Stress u ac = u tr t1t1 b t z y b t2t2 y z I ac = I tr h b y z t2t2  ac =  tr t2t2 Actual and transformed c/s can not give same results unless height remains same.

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

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

22. 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

23. Max. Displacement: ~0.3 mm

24. Total Displacement (x50)

25. Max. von Mises: ~115 MPa

26. Von Mises (x50)

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

28. Total Displacement (x1555)

30. 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.

31. 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