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UNIVERSITY OF CALIFORNIA. MQXF Shell Analysis. H. Pan, G. Vallone, E. Anderssen , S. Prestemon 1 P. Ferracin , E. T. Takala 2 1 LBNL, 2 CERN MQXFBP1 Al shells Meeting 03/07/2019. Index. Introduction Plastic Deformation FAD Conclusion. Index. Introduction Plastic Deformation FAD
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UNIVERSITY OF CALIFORNIA
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
Index • Introduction • Plastic Deformation • FAD • Conclusion G. Vallone
Index • Introduction • Plastic Deformation • FAD • Conclusion G. Vallone
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
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
Magnet Summary G. Vallone
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
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
Index • Introduction • Plastic Deformation • FAD • Conclusion G. Vallone
Results (1) • Highly refined mesh around the corner • Plastic strainlocalized around the corner • Total strain is mostly azimuthal G. Vallone
Material Model • Bilinear plastic strain model • Data from CERN measurements G. Vallone
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
Index • Introduction • Plastic Deformation • FAD • Conclusion G. Vallone
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
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
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
FAD – MQXFBP1 (3) – Yield Stress Plastic zone • , • Yield stress instead of flow stress – more conservative • The 130 MPa case is still safe G. Vallone
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
Thanks for your attention! G. Vallone
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
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
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
Structural Discontinues • The BSI 7910:2005 suggests to integrate the effect of sharpcorners in the stressintensity magnification factor ~ KI G. Vallone