1. E LASTO -P LASTIC -C REEP M ODELING FOR THE F IRST W ALL WITH W A RMOR X.R. Wang 1, S. Malang 2, M. S. Tillack 1 1 University of California, San Diego, CA 2 Fusion Nuclear Technology Consulting, Germany ARIES-Pathways Project Meeting Bethesda, Washington DC April 4-5, 2011

2. O UTLINE  A simple thermal creep model for comparing the ANSYS results to experimental creep data  Structural criteria in detailed inelastic analysis  Creep rupture data and Norton Law parameter  Elastic-plastic-creep modeling for the first wall with W armor

3. THERMAL CREEP TEST FOR ODS EUORFER 97 STEEL G. YU AT. ALL, FUSION ENGINEERING AND DESIGN, 75-79, 1071(2002)  Norton Creep Law : dε cr /dt=C1σ C2 e -C3/T C1,C2, C3 are temperature-dependent creep constants, σ is applied stress, T is temperature C3=0 Creep exponent C2: 4.9-5.5 Assuming C2=5.1, the creep constant C1=3.245E-49  Applied constant stress:160-200MPa  Applied temperature: 650 °C  Corresponding creep strain rate associated with the steady stage: ~2.25E-7 1/s at applied stress of 160 MPa  Creep strain in primary stage: 1.1%  Creep strain in secondary stage: 1.8%

4. COMPARISON OF ANSYS CREEP RESULTS TO CREEP TESTED DATA ANSYS modeling, ε cr =~1.788% Hand calculation, ε cr =~1.8% Exp. Data (Creep-time curve), ε cr =~1.8% ANSYS modeling, ε cr =~1.788% Hand calculation, ε cr =~1.8% Exp. Data (Creep-time curve), ε cr =~1.8% Stress Model (1/4 Specimen) Specimen) Creep strain after 80000 s Stress after 80000 s Axisymme -tric element behavior Symmetr y BC Deformed shape was exaggerated by a factor of 10

5. T HERMAL C REEP M ODELING OF THE FW A RMOR  Temperature of the W-pins is ~ 680 ºC, therefore, thermal creep is not important as a deformation mechanism. W thermal creep begins to become significant around 1500 ºC and above.  As there is not enough creep coefficients for ODS steel (12YWT), and the thermal creep of the ODS steel is not included. (Gu’s creep data only at T=650 C and σ=160 MPa)  However, experiments shown the creep strength of “normal” ODS steel is much higher than for the FS itself. “Advanced” ODS steels (12CrYWTi) have an even higher creep strength at high temperature of 800 ᵒ C. For this reason, the creep of the ODS steel is ignored considering the relatively low temperature (~650 ᵒ C) during operation.  Only F82H material will be considered in the creep model, and the creep data of Eourfer 97 steel will be used in analysis.  There are 13 built-in creep models, 8 for primary stage, 3 for secondary stage, and 2 for combined primary and secondary models. Primary stage is not included.  Norton model is used in ANSYS.  Irradiation induced creep is not considered at present because of difficulty to find the irradiation induced creep test data ( Arnold Lumsdaine is helping us to collect the creep data.)

6. S TRUCTURAL C RITERIA IN D ETAILED I NELASTIC A NALYSIS  Structural strain limits: At elevated temperatures where creep occurs, it is generally impossible to avoid strain accumulation. However, it is necessary to limit strain accumulation to avoid excessive structural distortion and fracture.  The calculated maximum accumulated positive principal inelastic ( plastic plus creep ) strain at the end of life must meet the three limits: 1.Membrane (strain averaged through the thickness) ≤ 1% 2.Local (maximum strain anywhere) ≤ 5% 3.Membrane + bending ≤ 2% *Alfred Snow, “US Elevated Temperature Structural Design Standards: Current Status and Future Direction,” Westinghouse Electric Corporation, 1976.  Need experts’ opinion on the structural criteria

7. C REEP R UPTURE C URVES OF E UROFER S TEEL (FZK, CIEMAT DATA )* FW 450 ᵒ C500 ᵒ C550 ᵒ C S r, MPa at 1000 h 328254185 S r, MPa at 10000 h 295221152 * F. Tavassoli, DEMO Interim Structural Design Criteria, Appendix: A Material Design Limit Data, CEA/DEN/SAC/DMN, Dec. 2002. *M. Rieth, et. al, “EOUOFER 97 Tensile, Charpy, Creep and Structural Tests” FZKA 6911, Oct. 2003. Creep Rupture Stress, Sr

8. C REEP C OEFFICIENTS OF EUOFER S TEEL (FZK, CIEMAT DATA )*  Only the secondary creep is considered.  The secondary creep is ignored at temperature less than 425 ᵒ C.  Norton creep equation is expressed by: dε cr /dt=C1 σ C2 e -C3/T  The creep constants are obtained from plots of stress versus the secondary rate ( creep rate in 1/h, σ in MPa) T C1C2C3 Stress, MPa Creep rate,1/h 450 º C 8.352E-5722.7180.0 300 1.57E-6 500 º C 1.376E-5021.190.0 220 5.95E-7 550 º C 4.566E-4017.7690.0 160 6.68E-7 600 º C 2.490E-199.50950.0 100 2.6E-6 650 º C 6.217E-126.74730.0 50 1.8E-6 Norton law parameters for Eurofer Steel  Only C1, C2 and C3 are inputted into ANSYS.

9. C ONVERTED U NIT OF C REEP R ATE TO “1/ S ” FOR ANSYS I NPUTS TC1C2C3 Stress, MPa Creep rate,1/s 450 º C 2.32E-6022.718 0.0 3004.4E-10 500 º C 3.82E-5421.19 0.0 2201.7E-10 550 º C 1.27E-4317.769 0.0 1601.9E-10  Using the Norton law parameter table of the experimental test  Using “MPa” as the unit of the ANSYS inputs for the material properties (Young’s Modulus, Tangent Modulus) and the pressure loads for the inelastic analysis  Converting the unit of creep rate to 1/s

10. A LTERNATIVE M ETHOD TO U SE THE N ORTON L AW P ARAMETER TC1C2C3 Stress, Pa Creep rate,1/s 450 º C 5.E-202 22.7180.0300E+6 4.4E-10 500 º C 2.E-186 21.190.0220E+6 1.7E-10 550 º C 3.E-155 17.7690.0160E+6 1.9E-10 T C1C2C3 Stress, Pa Creep rate,1/s 450 º C 3.80E-433.9 0.0300E+6 4.4E-10 500 º C 1.51E-454.2 0.0200E+6 1.7E-10 550 º C 1.48E-464.4 0.0160E+6 1.9E-10  Using the Norton law parameter table and converting the unit of creep rate to 1/s and stress to Pa  Using the same creep rate from the creep rate plots and make adjustments to the C1 and C2. C1 were found in the range 3.9-5.5 for ODS Eourfer steel tested between 500 and 750 ᵒ C. ** ** G. Yu et. al, Thermal creep behavior of the EUROFER 97 RAFM steel and two European ODS EUORFER 97 steels, Fusion Engineering and Design, 75-79 (2005), 1037-1041.  The alternative method can speed up the ANSYS program obtaining solution, and the results are the same. Need experts’ comments on the method to handle C1 and C2.

11. T HERMAL L OADS FOR THE E LASTO - P LASTIC -T HERMAL C REEP M ODEL  Nonlinear structural behaviors of the FW are simulated by a combined elastic, plastic and creep models.  Processes of the fabrication, heat treatment, reactor start- up and normal operation are included in plastic model.  There are no stress, no plastic strain and creep strain during the FW brazing process.  The FW is in the plastic range during braze cool-down.  At this moment, the creep strains are ignored during the heat treatment because of such a short time. P=10 MPa q=1MW/m 2 1050 ᵒ C 700 ᵒ C 20 ᵒ C 385 ᵒ C Temperature Contour Elasto- Plastic and Creep Elasto-Plastic and Creep

12. L OCAL C REEP S TRAIN OF THE F82H  The maximum local creep strain of the F82H plate is ~ 0.17% at the Node A where the local stress occurs at the temperature of 450 ᵒ C.  Ɛ cr =~0.07% at the Node B with maximum temperature of 525 ᵒ C.  Ɛ cr =~0.05% at the Node C with temperature of 500 ᵒ C  The maximum local creep strain of the F82H plate is ~ 0.17% at the Node A where the local stress occurs at the temperature of 450 ᵒ C.  Ɛ cr =~0.07% at the Node B with maximum temperature of 525 ᵒ C.  Ɛ cr =~0.05% at the Node C with temperature of 500 ᵒ C Node C 500 ᵒ C Creep strain at node A Node A 450 ᵒ C Node D 500 ᵒ C Node A Node B Node C Node D Node B 525 ᵒ C Node A Node B Node C Node D Fabrication

13. P LASTIC S TRAINS A FTER 1000 H OURS  The total local strain (plastic + creep) at node A is ~0.9%, and ~0.8% at the node B after 1000 hours.  The plastic strain mainly occurs in the processes of the FW fabrication, and there is no additional plastic strain during normal operation.  Thermal creep can help relax the total stresses of the F82H plate during the operation, but can not recover the deformation which occurs during the FW fabrication. Ɛ plasticity =~0.76% after 1,000 hours Local plastic strain Plastic strain Creep strain at node A Node B C D Node A 450 ᵒ C Node B 525 ᵒ C

14. S TRESS R ELAXATION BY C REEP D EFORMATION Total stress is reduced after stress relaxation of the creep strain Local σ primary+thermal =~316 MPa with stress relaxation of creep at t=1000 hours σ primary+thermal =397 MPa at t=5 hours (fabrication and reactor start-up) Node A Node B Node C Node A 450 ᵒ C Node B 525 ᵒ C Node C 500 ᵒ C

15. S UMMARY  Inelastic analysis is performed in a operating time of ~1000 hours, and a long operating time such as 10,000 h or longer time may need to be analyzed. Calculated local creep strain ~0.17% and the plastic strain is ~0.72% at the Node A after 1000 hours. The local plastic plus creep strain is ~0.9%. Expected local creep strain is roughly ~1.57% after 10,000 h and the total strain is ~2.4% (< 5% local strain limit), however it needs confirmation by analysis ( assuming the initial creep rate of 1.57 E-6 1/h )  Further assessments of the structural strains are needed to compare other two strain limits.  Possible design methods to reduce the local total stresses and local creep strain of the F82H Round the corner where causes local primary stress Increase the thickness of F82H plate from 2 mm to 3 mm to reduce primary stress Node A