1. Preliminary analysis for the dressed LHC RF cavity (2) April 28th 2016 – EDMS 1605583
L. Dassa, L. Mettler

2. Mechanical properties of copper (as per CERN Store): E = 115 GPa
G = 44 GPa (→ ν = 0.307)
Source: Copper & copper alloys, ASM international, p. 453
σY = 200 MPa (Rp0.2)
σR = 240 MPa (Rm)
Source: Technical Specification N° Ed. 8 EDMS No: Oxygen-Free Electronic copper sheets Cu-OFE
Mechanical properties of copper (annealed)
σY = 50 MPa (Rp0.2)
σR = 226 MPa (Rm)
Source: EDMS No: Guillaume Maîtrejean “Mechanical properties of OFE Copper, Niobium and Stainless Steel 316L/LN” Oxygen-Free Electronic copper sheets Cu-OFE
Dressed cavity
Material properties
Mechanical properties of stainless steel 316LN:
E = 196 GPa
ν = 0.27 (→ G = 77.2 GPa)
σY = 280 MPa (Rp0.2)
σR = 580 MPa (Rm)
Source: EN :2008
For ≤ 3 mm sheets, the steel shall be cold-rolled and solution annealed.
For > 3 mm sheets/plates, the steel shall be hot-rolled and solution annealed.

3. Dressed cavity (p=1.5 atm)
Top box added to tank: Solid / solid shell elements
Point mass of coupler added to the top flange (163 kg)
Gravity loads for all modelled components taken into account
Geometry and Mesh (2)

4. Dressed cavity (p=1.5 atm)
Geometry and Mesh
Biphasic vessel included!
Coupler weight not included!

5. Dressed cavity (p=1.5 atm)
Submodel created for parts of the tank to investigate stress concentrations
Geometry and Mesh (2)

6. 4 checks for each component
Dressed cavity
Strenght Assessement
4 checks for each component 1 2 4 3

7. CAVITY

8. Cavity (p=1.5 atm)
Primary local
Primary membrane + primary bending P
Limit: 1.5 f (= 200 MPa)
Results with pressure only
linearization required

9. PL = primary local membrane = 41 MPa < 1.5 f (= 200 MPa)
Cavity (p=1.5 atm)
CAVITY: (f = σY/1.5 = 133 MPa)
PL = primary local membrane = 41 MPa < 1.5 f (= 200 MPa)
Stress linearization
Shell model, presented in the previous meeting, is not representative (ratio radius/thickness not acceptable)

10. Primary local
Primary membrane + primary bending P
Limit: 1.5 f (= 50 MPa)
Brazed components (p=1.5 atm)
BRAZED C.: (f = σY/1.5 = 33 MPa)
PL = primary general membrane <> 1.5f (= 50 MPa)
-> linearization required
Warning -> close to flange

11. VESSEL

12. detailed study required
TANK: (f = σY/1.5 = 187 MPa)
Cavity (p=1.5 atm)
Tank: linear elastic analysis
detailed study required

13. Cavity (p=1.5 atm)

14. Cavity (p=1.5 atm)

15. Primary local
Primary membrane + bending P
Results with pressure only (primary PL)
Vessel (p=1.5 atm)
Some spot is in presence of not compliant welded joint
TANK: > 1.5 f (=280 MPa) (f = σY/1.5 = 187 MPa)

16. Linear elastic analysis summary: CAVITY: (f = σY/1.5 = 133 MPa)
Pm = primary general membrane < f (= 133 MPa)
PL = primary local membrane = 41 MPa < 1.5 f (= 200 MPa)
P = primary general membrane + bending = 171 MPa < 1.5 f (= 200 MPa)
P + Q = primary + secondary local membrane + bending = 226 MPa < 3 f (= 400 MPa)
Brazed components: (f = σY/1.5 = 33 MPa)
Pm = primary general membrane < f (= 33 MPa) NOT VERIFIED
PL = primary local membrane < 1.5 f (= 50 MPa) NOT VERIFIED
P = primary general membrane + bending < 1.5 f (= 50 MPa) NOT VERIFIED
P + Q = primary + secondary local membrane + bending = 54 MPa < 3 f (= 100 MPa)
Cavity (p=1.5 atm)
Linear elastic analysis
Summary
TANK: (f = σY/1.5 = 187 MPa)
Pm = < f (=187 MPa)
PL = <1.5 f (=280 MPa) NOT VERIFIED
P = < 1.5 f (=280 MPa) NOT VERIFIED
P + Q < 3 f (=560 MPa)

17. Conclusions
Cavity (not brazed)
Acceptable
Cavity (brazed)
not acceptable according to standard -> Acceptable with particular statement
Tank
not acceptable according to standard ->Verification ongoing with nonlinear analysis (some issue in the application of the standard) -> level of plasticization to verify
Biphasic vessel to study
Not compliant welded joints
Total
Redo analysis with new Cu limits (see E. Cantergiani report)?
Assessment report

18. Back-up slides

19. From EN 13445
From EN 13458

20. From EN 13445