1. D. Passarelli, M. Merio, L. Ristori, B. Wands March 29, 2012
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)
Bellows
Helium Vessel SS316L
Cavity Nb
Lever Tuner
𝑘 𝑐𝑎𝑣 =25 𝑘𝑁 𝑚𝑚
𝑑𝑓 𝑑𝑙 =540 𝑘𝐻𝑧 𝑚𝑚
𝑑𝑓 𝑑𝑝 ≈0 ±10 𝐻𝑧 𝑡𝑜𝑟𝑟
𝑑𝑓 𝑑𝑝 =−0.7 𝑑 𝐵𝑃 +4.9
Brazed-joint:
Beam pipes Coupler port Side ring

3. 2010 ASME Boiler and Pressure Code VIII 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)
𝑀𝐴𝑊𝑃≥2 𝑏𝑎𝑟 at room temperature (293K)
𝑀𝐴𝑊𝑃≥4 𝑏𝑎𝑟 at cryogenic temperature (2K)

4. 2010 ASME Boiler and Pressure Code VIII Division 2 – Part 5
The Design-by-Analysis methodology utilizes the results from finite element analysis to assure:
Protection against plastic collapse avoid 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 properties Nb & SS316L
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” room temperature)
Thermal properties: coefficient thermal expansion (CTE) curve from 293K to 2K.
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)

6. Material properties
We are using the material adopted for the SSR1-prototype Engineering Note (by Bob Wands).
293K
Young’s Modulus 105 GPa
Poisson’s ratio 0.38
Yield strength 64 MPa
(True) Ultimate stress 248 MPa
2K (assumes that the 2K properties are the same as 77 K CONSERVATIVE)
Yield strength MPa
(True) Ultimate stress 710 MPa
293K (the same props are 2K (conservative approach))
Young’s Modulus 193 GPa
Poisson’s ratio 0.3
Yield strength MPa
(True) Ultimate stress 758 MPa
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.

7. Design Load parameter SSR1 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 method Load combination: P+Ps+D
Elastic plastic stress analysis method Global Criteria_1 2.4(P+Ps+D)
Global Criteria_2 2.1(P+Ps+D+T)

8. Design-by-Analysis Scheme of things to do
MAWP
≥2 𝑏𝑎𝑟 at 293K
≥4 𝑏𝑎𝑟 at 2K
Protection against collapse from buckling
Elastic stress analysis method
Protection against failure from ratcheting
Elastic stress analysis method
Protection against plastic collapse
Elastic plastic stress analysis method
Protection against local failure

9. Protection against plastic collapse Elastic stress analysis - @ 293K and 2bar
Elastic material T=293K Load combination applied: P+D
P = 2 bar
Refined mesh Condition to satisfy:
𝜎 𝑒𝑞 ≤S
𝑆 𝑁𝑏 =25 𝑀𝑃𝑎
𝑆 𝑆𝑆316𝐿 =100 𝑀𝑃𝑎
150 MPa
The elastic stress analysis at 293K and under MAWP required - shows that the area of the Endwall (bellows side), connected to the Daisy ribs, is potentially critical for the plastic collapse.

10. Protection against plastic collapse Elastic stress analysis - @ 2K and 4 bar
Elastic material T=2K Load combination applied: P+D+T (no tuning effect) P = 4 bar
Refined mesh Condition to satisfy:
𝜎 𝑒𝑞 ≤S
𝑆 𝑁𝑏 =200 𝑀𝑃𝑎
𝑆 𝑆𝑆316𝐿 =390 𝑀𝑃𝑎
200 MPa
350 MPa
Away from the point of singularities the stresses are under the limit

11. Protection against plastic collapse Elastic plastic stress analysis - @ 293K
Elastic plastic material T=293K Load 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 𝑀𝐴𝑊𝑃 𝑅𝑇 = =2.23𝑏𝑎𝑟 (32.3 𝑝𝑠𝑖)

12. Protection against plastic collapse Elastic plastic stress analysis - @ 2K
Two-steps:
Cooldown (ramped) + Dead weight (constant)
Pressure (ramped) + Dead weight (constant)
Elastic plastic material T=2K Load combination applied: 2.4(P+D+T) (no tuning effect) Refined mesh
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)
𝑀𝐴𝑊𝑃 𝐶𝑇 = ≥6.25𝑏𝑎𝑟 (90.6 𝑝𝑠𝑖)

13. Protection against collapse from Buckling Linear Buckling analysis - @ 293K
Material 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 𝛽=0.8
Design factor φ= 2 𝛽 =2.5
𝑀𝐴𝑊𝑃 𝑅𝑇 = ≅𝟏𝟑 𝑏𝑎𝑟 (188.5 𝑝𝑠𝑖)

14. Protection against collapse from Buckling Linear Buckling analysis - @ 2K
Material T=2K
The cavity is the component that buckles first
Buckling pressure 37 bar
Capacity reduction factor for cylinders under external pressure 𝛽=0.8
Design factor φ= 2 𝛽 =2.5
𝑀𝐴𝑊𝑃 2𝐾 = ≅𝟏𝟒𝑏𝑎𝑟 (203 𝑝𝑠𝑖)

15. Design-by-Analysis Scheme
MAWP
≥2 𝑏𝑎𝑟 at 293K
≥4 𝑏𝑎𝑟 at 2K
Protection against collapse from buckling
Elastic plastic stress analysis method
Protection against failure from ratcheting
Elastic stress analysis method
Protection against plastic collapse
Elastic stress analysis method Load combination P+Ps+D → material 293K
Condition to satisfy:
𝜎 𝑒𝑞 ≤S
Elastic plastic stress analysis method Global Criteria_1 2.4(P+Ps+D) → material 293K
Global Criteria_2 2.1(P+Ps+D+T) → material 2K Condition to satisfy:
Convergence of the analysis
Result Map of critical zones on the model
Results 293K: 2.2 2K: 6 bar (TbC)
Protection against local failure
Results 293K: 13 2K: 14 bar

16. Conclusion
We have defined a procedure to check the mechanical performances of the dressed SSR1 cavity in agreement with “ES&H Fermilab manual” 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 RT)
THANKS!