ASME design on SSR1 G3

1. Technical Division SRF Department ASME design on SSR1 G3 • 2010 ASME Boiler and Pressure Code section VIII, Division 2 – Part 5 • Design by analysis methodology • Material properties • Design Load parameter • Protection against plastic collapse • Protection against collapse from buckling • Protection against local failure • Protection against failure from cyclic loading D. Passarelli, M. Merio, L. Ristori, B. Wands March 29, 2012

2. Conceptual Design of dressed SSR1 SRF cavity with Tuner Transition ring (under developing) Helium VesselSS316L CavityNb Bellows Lever Tuner Brazed-joint: Beam pipesCoupler portSide ring http://www-bdnew.fnal.gov/pxie/SRF/Meetings/2012/SSR1%20Tuner%20concept.pdf

3. 2010 ASME Boiler and Pressure CodeVIII Division 2 – Part 5 According to the ES&H Fermilab manual, the Cavity and Helium Vessel can be considered a pressure vessel and it must comply with the “2010 ASME Boiler and Pressure Vessel Code”. Among the various options provided by the code, we decided to follow the Design-by-Analysis methodology described in the “2010 ASME Boiler and Pressure Vessel Code section VIII, Division 2 – Part 5”. Division 1: formulas, simple shape, typically thicker walls Division 2: complex shape, FEM analysis… Requirement: • achieve the desired Maximum Allowable Working Pressure (MAWP) • at room temperature (293K) • at cryogenic temperature (2K)

4. 2010 ASME Boiler and Pressure CodeVIII Division 2 – Part 5 The Design-by-Analysis methodologyutilizes the results from finite element analysis to assure: • Protection against plastic collapseavoid unbounded displacement in each cross-section of the structure due to the plastic hinge • Elastic stress analysis method • Elastic-plastic stress analysis method • Protection against collapse from buckling buckling is characterized by a sudden failure of a structural member subjected to high compressive stress, where the actual compressive stress at the point of failure is less than the ultimate compressive stresses that the material is capable of withstanding. • Elastic stress analysis (Linear buckling) • Protection against failure from cyclic loading • Elastic ratcheting analysis method • Protection against local failure (i.e. joints) • Elastic-plastic analysis under the achieved MAWP

5. Material propertiesNb & SS316L • Linear Elastic curve (used for elastic analysis) • Elastic perfectly plastic (used for limit load analysis) • Elastic-Plastic curve (by Ramberg-Osgood correlation)(used for elastic-plastic analysis) The main parts of the Helium Vessel and Cavity are made in SS316L and Niobium, respectively. To describe the material model required to perform the different kind of analysis, by finite element software, the following mechanical and thermal properties for both materials are needed. • Mechanical properties (at 293K and at 2K): • Young’s Modulus (E) • Poisson’s ratio (ν) • Yield strength (Ys) • (True) Ultimate stress (Yust) • ES&H Fermilab manual • Niobium data by St. Louis Laboratories report (experimental data) • SS316L data by “2010 ASME Boiler and Pressure Vessel Code section II, Part D” (only @ room temperature) • Thermal properties: coefficient thermal expansion (CTE) curve from 293K to 2K.

6. Material properties Under development To create a folder of material (Nb and SS316L) properties, in agreement with the ASME Code (for the SS316L) and the testing on Nb already done at St. Louis Lab and we are planning to do at the University of Pisa. We are using the material adopted for the SSR1-prototype Engineering Note (by Bob Wands). • Niobium @ 293K • Young’s Modulus 105 GPa • Poisson’s ratio 0.38 • Yield strength 64 MPa • (True) Ultimate stress 248 MPa • Niobium @ 2K (assumes that the 2K properties are the same as 77 K CONSERVATIVE) • Young’s Modulus 105 GPa • Poisson’s ratio 0.38 • Yield strength 557 MPa • (True) Ultimate stress 710 MPa • SS316L @ 293K (the same props are used @ 2K (conservative approach)) • Young’s Modulus 193 GPa • Poisson’s ratio 0.3 • Yield strength 172 MPa • (True) Ultimate stress 758 MPa

7. Design Load parameterSSR1 load conditions The relevant loads acting on the SSR1 dressed cavity are: “P” pressure in the helium space under fault condition “Ps“ static head from liquid Helium (negligible) “D”dead weight of the system “T” cooldown from 293K to 2K “T” controlled axial displacement of 0.25mm at the Beam Pipe (“tuning” operation) For each analysis the code provides the load combination and factored load cases: Elastic stress analysis methodLoad combination: P+Ps+D Elastic plastic stress analysis methodGlobal Criteria_12.4(P+Ps+D) Global Criteria_22.1(P+Ps+D+T)

8. Design-by-AnalysisScheme of things to do Protection against plastic collapse Elastic stress analysis method Elastic plastic stress analysis method • MAWP • at 293K • at 2K Protection against collapse from buckling Protection against local failure Elastic stress analysis method Elastic plastic stress analysis method Protection against failure from ratcheting Elastic stress analysis method

9. Protection against plastic collapseElastic plastic stress analysis - @ 293K Elastic plastic material property @ T=293KLoad combination applied: 2.4(P+D) Refined mesh The elastic plastic stress analysis at 293K shows that the plastic collapse occurs on the area of the Endwall (bellows side), connected to the Daisy ribs, under a pressure of 5.35 bar (77.6 psi) Pressure of last solution………5.35bar

10. Protection against plastic collapseElastic plastic stress analysis - @ 2K Elastic plastic material property @ T=2KLoad combination applied: 2.4(P+D+T) (no tuning effect)Refined mesh Two-steps: Cooldown (ramped) + Dead weight (constant) Pressure (ramped) + Dead weight (constant) The elastic plastic stress analysis at 2K shows that the plastic collapse occurs under a pressure greater than 15 bar which gives a MAWP greater than 6.25 bar (90.6 psi)

11. Protection against collapse from BucklingLinear Buckling analysis - @ 293K Material properties @ T=293 K The cavity is the component with the lowest buckling load • Buckling pressure 33.6 bar • Capacity reduction factor for cylinders under external pressure • Design factor

12. Protection against collapse from BucklingLinear Bucklinganalysis - @ 2K Material properties @ T=2K The cavity is the component that buckles first • Buckling pressure 37 bar • Capacity reduction factor for cylinders under external pressure • Design factor

13. Design-by-AnalysisScheme Elastic plastic stress analysis methodGlobal Criteria_12.4(P+Ps+D) → material prop @ 293K Global Criteria_22.1(P+Ps+D+T) → material prop @ 2KCondition to satisfy: Convergence of the analysis Elastic stress analysis methodLoad combination P+Ps+D → material prop @ 293K Condition to satisfy: ResultMap of critical zones on the model ResultsMAWP@ 293K: 2.2 bar@ 2K: 6 bar (TbC) Protection against plastic collapse Elastic stress analysis method • MAWP • at 293K • at 2K Protection against collapse from buckling Protection against local failure ResultsMAWP@ 293K: 13 bar@ 2K: 14 bar Elastic plastic stress analysis method Elastic plastic stress analysis method Protection against failure from ratcheting Elastic stress analysis method

14. Conclusion We have defined a procedure to check the mechanical performances of the dressed SSR1 cavity in agreement with “ES&H Fermilabmanual” and “2010 ASME Boiler and Pressure Vessel Code”. The analyses performed so far meet the requirements The cavity is the weakest link of the system cavity/HV (plastic collapse on the endwall – buckling on the shell-part) Things to do: Perform the remaining analysis (Protection against Failure from Ratcheting) Check the local stresses (i.e. welds) using the criteria shown by the code (Protection against local failure) Proceed with the experimental tests, in collaboration with University of Pisa, to investigate the material properties of the Nb (at least @ RT) THANKS!