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MQXF shell fracture modeling

P. Ferracin, E. Takala

22. February 2019

CERN

E. Anderssen, H. Pan, G. Vallone

Outline

• Overview of 3D models

• Shell length comparison (MQXFS/A/B)

• Why sub-modeling is needed?

• Submodel

• Mesh size

• Plastic deformation

• Linear elastic fracture mechanics (LEFM)

• 2D Fracture propagation modeling

• Study case: MQXFBP1 hole in the corner axis

• Conclusion

Eelis Takala 2

Eelis Takala 3

Introduction (1)

3

Different shell sizes:

Short Long

S 387 774

AP1 325.6 651.3

BP1 341.5 683

3D Mechanical Ansys Models

• Short model 1.5 m• MQXFS series

• Fully working 3D mechanical model

• Long model 4 m• MQXFBA pair

• Long model 7 m• MQXFBP pair

• Cutout features missing

Eelis Takala 4

Can we use the short

model in place of the

long when cutouts are

studied?

Al shell in simple BP1 vs S4 models

Eelis Takala 5

BP1 no cutoutsS4 with cutout featuresSeqv

Stress components simple BP1 vs S4

Stress is at similar level

in the middle of the shell

=> short model is a

common representative

Comparison models LBNL/CERN

Paolo Ferracin 7

665 MPa max

AP1 S4

Why sub-modeling?

• Graded approach for structural analysis [1]

• I Basic stress analysis

• II Basic FEA 2D/3D

• III Advanced FEA:

• Sharp corners -> stress concentration factor infinite

-> elasto-plastic FEM analysis required

• IV LEFM (brittle materials 𝐾Ic ≤ 100MPa√m)

• Elasto-plastic model with details

• Refinement of mesh until “converged solution”

Eelis Takala 8

[1] E. Anderssen, S. Prestemon, “US HL-LHC Accelerator Upgrade Project Structural Design Criteria”, US-HiLumi-Doc-909

Eelis Takala 9

[1] E. Anderssen, S. Prestemon, “US HL-LHC Accelerator Upgrade Project Structural Design Criteria”, US-HiLumi-Doc-909

Eelis Takala

Submodelling Strategy

• Detailed model of the failed region

• Shell modelled with elastoplastic properties (isotropic hardening)

• A yoke piece was added to stay sufficiently far from the modified region• The impact of local features is negligible sufficiently far from them

• Displacements after cooldown: powering impact on shell stress is negligible

10

Submodel validation

11Eelis Takala

• St. Venant principle

should be respected

• In ANSYS classic the

convention is comparison

along paths

|| ⋅ || = න𝐶

⋅2d𝐶

• Problem: which paths

should be checked?

𝛽 =

Solution comparison in Bmiddle

Eelis Takala 12

Ƹ𝑒𝜃Ƹ𝑒𝑟

Ƹ𝑒𝑧

Mesh Density

• Mesh density study

• Refinement around

the detail (fillet)

• Max plastic strain

• Plastic energy

• Convergence

• detail mesh size

≤50um

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Sub-modeling

• Elastic analysis & LEFM

• Failure Assesment Diagram (FAD)

• If there is a crack (fabrication defect or plastic

collapse)

• Does it propagate?

• Plastic analysis

• Which is the extension of the plastic region?

• Do we have plastic collapse?

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Failure assessment diagram paths

• Path 1• 45 degree wrt z-axis

• Radially in the middle of the shell

• Path 2• Along z-axis

• Radially in the middle of the shell

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30°

70°

FAD diagram (LEFM)

Eelis Takala

𝐿

𝐿′≥ 1 ⇔ No Failure

𝐿

𝐿′< 1 ⇔ Failure

[1] E. Anderssen, S. Prestemon, “US HL-LHC Accelerator Upgrade Project Structural Design Criteria”, US-HiLumi-Doc-909

BP1 case: 0.2 mm fillet (Sth 130 MPa)

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Path 2Path 1

BP1 High stress: 0.2 mm fillet (Sth 170 MPa)

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Path 2Path 1

S4 case: 0.1 mm fillet (Sth 130 MPa)

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Path 2Path 1

Summary of maximum strain

• Based on inter-/extrapolation of LBNL model results

• Agreement for BP1 and S4 cases between LBNL and CERN models

• Higher strain obtained for S5 CERN model

• BP1 should not exceed the limit elongation

• The solution obtained for AP1 and AP2 is not valid: the material fails

Eelis Takala 20

Crack Propagation

• Simple 2D model simulating the crack propagation

• Crack direction is assumed from the experimental evidence

• The initial direction is in agreement with the minimum stress gradient direction

• 2 way symmetry, model loaded with horizontal displacements

• This would approximate a trough-thickness crack

G. Vallone 21

usym

Crack

Line

Results (1)

G. Vallone 22

• Magnified displacements

• The model was loaded up to failure

Proposed Design for the Weld Cutout

23

Proposed 15 mm cutout

path

• Stress level at the concentration location is expected

significant reduction if the fillet radius is as large as 15 mm.

• No plastic deformation in the results.

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2 mm hole (Sth 130 MPa) 0.2 mm fillet (Sth 130 MPa)

BP1 case comparison

BP1 case: 2 mm hole at the axis

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Eelis Takala 26

2 mm hole (Sth 130 MPa) 0.2 mm fillet (Sth 130 MPa)

BP1 case comparison

Path 1 Path 1

Path 2 Path 2

MQXFBP1 safety margin

• LBNL model

• Shell stress vs total strain

more or less linear

• CERN model

• 5% @ 130 MPa

• 7.5% @ 170 MPa

• 10% @ 210 Mpa?

=> Safety factor 1.6 in

terms of average shell

stress

Eelis Takala 27

LBNL models

Conclusions

• Analysis of the corner performed with elastic

and plastic sub-modeling

• General agreement between CERN and LBNL

models (S5 under inspection)

• According to the model BP1 has large margin

with respect to elongation to break and load

factor more than 1

• Lower strain and higher load factor than tested short

models

• Strain safety factor 1.6 in terms of average shell

stress

Eelis Takala 28

APPENDIX

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Mechanical properties at cryogenic

temperature

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Fitting to elastic solution?

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S5 0.1 mm fillet (Sth 181 MPa)

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Path 2Path 1

BP1 case: 2 mm hole (Sth 130 MPa)

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Path 2Path 1

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2 mm hole (Sth 130 MPa) 0.2 mm fillet (Sth 130 MPa)

BP1 case comparison: path 1

Elastic solution was

possible here

Introduction - Structural Discontinues (2)

• The BSI 7910:2005 suggests to integrate the effect of sharp corners in the stress

intensity magnification factor

G. Vallone 35