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

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° 2000 - Ed. 8 EDMS No: 790780 Oxygen-Free Electronic copper sheets Cu-OFE Mechanical properties of copper (annealed) σY = 50 MPa (Rp0.2) σR = 226 MPa (Rm) Source: EDMS No: 1331848 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 10028-7:2008 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.

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)

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

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

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

CAVITY

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

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)

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

VESSEL

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

Cavity (p=1.5 atm)

Cavity (p=1.5 atm)

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)

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)

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

Back-up slides

From EN 13445 From EN 13458

From EN 13445