MQXF shell fracture modeling

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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


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

Eelis Takala 13

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?

Eelis Takala 14

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


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)

Eelis Takala 19

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

Eelis Takala 25

Eelis Takala 26


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

Eelis Takala 29

Mechanical properties at cryogenic

temperature

Eelis Takala 30

Fitting to elastic solution?

Eelis Takala 31

S5 0.1 mm fillet (Sth 181 MPa)

Eelis Takala 32

Path 2Path 1

BP1 case: 2 mm hole (Sth 130 MPa)

Eelis Takala 33

Path 2Path 1

Eelis Takala 34


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

MQXF shell fracture modeling

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