UNIVERSITY OF CALIFORNIA

1. UNIVERSITY OF CALIFORNIA

2. MQXF Shell Analysis H. Pan, G. Vallone, E. Anderssen, S. Prestemon1 P. Ferracin, E. T. Takala2 1LBNL, 2CERN MQXFBP1 Al shells Meeting 03/07/2019

3. Index • Introduction • Plastic Deformation • FAD • Conclusion G. Vallone

4. Index • Introduction • Plastic Deformation • FAD • Conclusion G. Vallone

5. Introduction (1) • Same cross-section, different magnet length: • MQXFS: 387 mm, 774 mm • MQXFA: 326 mm, 651 mm • MQXFB: 342 mm, 683 mm G. Vallone

6. Introduction (2) • One MQXFAP2 shell failed during cooldown or powering, preventing the magnet to achieve the desired performances • The same structure design did not fail in numerous magnets (mechanical models, short models, first prototype) • Cooling from the bottom (vertical cryostat): differential thermal contraction stress? G. Vallone

7. Magnet Summary G. Vallone

8. Measured Material Properties at 4.2 K (1) • Measurementsperformed at CERN. Two samples in each direction • Measurements are consistent. But would need more samples for statistics • Would be interesting to compare with roomtemperature data • Limit elongation for T74 higher in the circumferential direction • T6 (MQXFAP1, AP2) data: work in progress G. Vallone

9. Measured Material Properties at 4.2 K (2) (*): Crack deviation was observed for these specimens (**): From published data • AA7175 T74 > • AA7075 T652: in R-C direction but similar to T74 in the C-R direction • R-C direction is not a relevant failure mode • We miss relevant data for the C-L direction for T652 • R-C behaviour of the T74? G. Vallone

10. Index • Introduction • Plastic Deformation • FAD • Conclusion G. Vallone

11. Results (1) • Highly refined mesh around the corner • Plastic strainlocalized around the corner • Total strain is mostly azimuthal G. Vallone

12. Material Model • Bilinear plastic strain model • Data from CERN measurements G. Vallone

13. Results – Plastic Zone Depth • The plastic zone depth is ~insensitive to radius • Plastic zone smaller than 350 µm for MQXFBP1 • Stress approaches the elastic solution outside the plastic zone G. Vallone

14. Index • Introduction • Plastic Deformation • FAD • Conclusion G. Vallone

15. Introduction - FAD • R6FailureAssessment Diagram: • Limit curve fits failure points and b.c. at the axis (fracture and plastic failure) • Load points inside the curve are considered safe • A load margin can be computed projecting the loading point onto the curve G. Vallone

16. FAD – MQXFBP1 (1) 0°path 0°path Plastic zone • LEFM: plastic regions should not be considered • Plasticdepth: • 130 MPa membrane stress 0.4 mm • 170 MPa membrane stress 0.9 mm • Less refined mesh is more conservative • Loadfactor plot suggests that a crack should not propagate G. Vallone

17. FAD – MQXFBP1 (2) Plastic zone • , • FAD solution is valid only if the crack is smaller than the plastic depth • The 130 MPa solution is below the failure curve for the range of crack size studied (0.4 to 2.5 mm) • Low margin for the 170 MPa case G. Vallone

18. FAD – MQXFBP1 (3) – Yield Stress Plastic zone • , • Yield stress instead of flow stress – more conservative • The 130 MPa case is still safe G. Vallone

19. Discussion • The plasticanalysis and the comparison with previous magnets suggests that the BP1 shell should not fail locally – no crack initiation due to plastic strain • The FAD was used for structural assessment • For a shell prestress of 130 MPa cracks smaller than 2.5 mm will not propagate • This is true also with conservative assumptions on the material properties G. Vallone

20. Thanks for your attention! G. Vallone

21. Convergence Analysis • A convergence analysis was performed to ensure that the mesh is accurate enough to evaluate the solution on the small corner: • Minimumelementsize after which results variations are negligible (<3%) • Max plastic strain but also total plastic energy to verify that there is no further accumulation of strain ‘behind’ the corner • The study was repeated for each corner radius, but: • As the radius becomes smaller, more elements are required to obtain a converged solution – modelsize becomes prohibitive G. Vallone

22. Results – Summary • Above the elongation limit (10.9 %) the solution is not valid: the material will fail in these corners and redistribute the stress • The BP1 strain is below the limit and lower than other tested magnets G. Vallone

23. Ultrasonic Testing • Class 3 of EN 4050-4 or Class B according to ASTM B594-13 • ASTM is slightly less conservative • We are accepting shells with (potential) cracks as large as 2/3 mm (response) G. Vallone

24. Structural Discontinues • The BSI 7910:2005 suggests to integrate the effect of sharpcorners in the stressintensity magnification factor ~ KI G. Vallone