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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 md 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