2. Thermomechanical Simulations of the PS Internal Dump
Francois-Xavier Nuiry Giulia Romagnoli Tobias Polzin

3. Agenda
Material Choices
From Energies to Mechanical Stresses
Results

4. Increase of energy density per temperature increase
Material Choices
Various alloys available (2000 different metal alloys in CES Selector)
For evaluation of different alloys a performance factor was defined. It consists of the thermal robustness
in combination with the ability to absorb energy with a low temperature increase. This factor should be has high as possible.
Increase of energy density per temperature increase

5. Considered factors: Material performance factor
Material Choices
Considered factors:
Material performance factor
Availability of material and material data
Machinability
RP requirements (activation)
vacuum requirements (outgassing)

6. Material Choices Sorted with performance factor Titanium Alloys
Ti12Mo6Zr2Fe
Grade21 R58210 (Ti15Mo3Al3Nb0.2Si)
Ti6Al4V
Grade 4
Nickel Alloys
EP741NP
Rene 41
UDIMET 500
Nimonic 81
Nimonic 90
Nichrome 70/30
UDIMET 700
Nimonic 80A
Hastelloy S
Inconel 718
Haynes 230
Nimonic 75
Inconel 625
Inconel 600
Tungsten Alloys
INERMET 180
Tungsten-25Rhenium
Sorted with performance factor

7. Sliced core reduces the axial stresses
Material Choices
Resulting Geometry
Beam direction
Ti6Al4V
Rene41
Sliced core reduces the axial stresses

8. From Particles to Mechanical Stresses
ANSYS thermal
Import of energy distribution and application as internal heat generation
Beam parameters
FLUKA
Monte Carlo Simulation of particle interactions
ANSYS mechanical
Import of temperature distribution and application as load
Energy distribution
Temperature distribution

9. FE model construction Quality Assurance for Simulation Setup
Model geometry represents reality
Material models are valid for load case (temperature dependency, …)
Material data clearly referenced
FLUKA import to ANSYS carefully cross-checked
Mesh quality studied and mesh convergence achieved
Assumptions for simulation setup (timing, damping) are not influencing the result

10. Thermal Results ACCIDENTAL LHC25 SFTPRO
ACCIDENTAL SCENARIO
26 GeV
5×1013
σ = 1.8 mm x 4.7 mm
Pulse time 2.1 µs
Pulse period 2.4 s
3 consecutive pulses
LHC 25ns BEAM
26 GeV
2.3×1013
σ = 1 mm x 4.7 mm
Pulse time 2.1 µs
Pulse period 3.6 s
5 consecutive pulses then cooling down time of 20 s
STFPRO BEAM
14 GeV
2×1013
σ = 2 mm x 3.7 mm
Pulse time 2.1 µs
Pulse period 1.2 s
2 consecutive pulses then cooldown time of 15 s
ACCIDENTAL
LHC25
SFTPRO
Average heating power over pulse period / kW -
2.5
1.0
Material
Ti6Al4V
Rene 41
Maximum Temperature over maximum number of continous pulses spec. in EDMS / ⁰C
185
260
132
178 72 64
MST* / ⁰C
350
877
*Source: GRANTA, CES Selector 2015

11. Thermal Results ACCIDENTAL scenario: 5E13 p+ @ 26 GeV/c in 2.1E-6s
after third impact
185⁰C
260⁰C

12. Results LHC25ns scenario: 2.4E13 p+ @ 26 GeV/c in 2.1E-6s Thermal
after fifth impact
132⁰C
178⁰C
Before next cycle
56⁰C
83⁰C
Still 83⁰C in the Rene 41 without cooling

13. Results SFTPRO scenario: 2E13 p+ @ 14 GeV/c in 2.1E-6s Thermal
After second impact
72⁰C
64⁰C
Before next cycle
34⁰C
31⁰C
Still 34⁰C in the Rene 41 without cooling

14. ACCIDENTAL after third impact
Results
Mechanical – Eq. v. Mises Stress
ACCIDENTAL after third impact
122 MPa
445 MPa
ACCIDENTAL scenario occurs about 1500 times over lifetime  no fatigue calculation
Ti6Al4V
Rene41
Eq. v Mises Stress / MPa
122
445
Yield Strength / MPa
880 (at 200⁰C)
827 (at 370⁰C)
Safety Factor
7.2
1.8
Source: Metallic Materials and Elements for Aerospace Vehicle Structures, Military Handbook - MIL-HDBK-5J
Department of defense, Federal Aviation Administration, 2003

15. Results Mechanical – Eq. v. Mises Stress LHC25 after fifth impact
Ti6Al4V
Rene41
Eq. v Mises Stress / MPa 73
253
Yield Strength / MPa
950 (at 132⁰C)
825 (at 204⁰C)
Safety Factor 13
3.2
Source: Metallic Materials and Elements for Aerospace Vehicle Structures, Military Handbook - MIL-HDBK-5J
Department of defense, Federal Aviation Administration, 2003
Appears frequently (expected about 3 million times over lifetime), fatigue is studied.
Maximum v. Mises Stress occurs in the second block of Rene 41 after five continuous impacts

16. Results Mechanical – Fatigue studies
To evaluate the fatigue of the materials, isothermal fatigue tests are considered as source for the fatigue strengths.
The load cycles are assumed to happen all at the maximum temperature
For Ti6Al4V the stresses stay always under the fatigue limit of 300 MPa (3E6 cycles with stress ratio=0 at 480⁰C, unnotched specimen, solution treated and aged)*
Rene41 needs closer fatigue investigation
*Source: Metallic Materials and Elements for Aerospace Vehicle Structures, Military Handbook - MIL-HDBK-5J
Department of defense, Federal Aviation Administration, 2003

17. Fatigue curves for Rene 41 at 371⁰C
Fatigue curve for Rene 41
Fatigue curves for Rene 41 at 371⁰C
STILL STUDIED!!!!
200 MPa
(220 MPa at RT)
530 MPa
(582 MPa at RT)
3 million cycles
Source:
FATIGUE OF RENE 41 UNDER CONSTANT AND RANDOM-AMPLITUDE LOADING AT ROOM
AND ELEVATED TEMPERATURES, NASA Technical Note TN D-3075

18. Pressure in second Rene41 block after first LHC25 impact
Results
Mechanical
Two dominant stress states in the cores:
Internal stresses in the core caused by concentrated heat in the center
(compressive stresses in the center surrounded by tensile stresses)
Reflections of mechanical waves at the surface in the center of each core after each impact
(high tensile stress peaks)
Pressure in second Rene41 block after first LHC25 impact

19. Results Mechanical – Fatigue Studies
Stress state on Surface of second Block of Rene41
Normal Stress in x-Direction
Normal Stress in z-Direction
Normal Stress in y-Direction
The Material in the surface is able to deform in axial direction  plane stress

20. Each value is lower than 530MPa for a lifetime of 3E6 cycles
Results
Mechanical – Fatigue Studies
Stress state on Surface of second Block of Rene41
The maximum stress intensity (TRESCA) is 157 Mpa.
The maximum von Mises eq. stress is 140 Mpa.
The maximum principle stress is 156 Mpa.
Each value is lower than 530MPa for a lifetime of 3E6 cycles
Source:
FATIGUE OF RENE 41 UNDER CONSTANT AND RANDOM-AMPLITUDE LOADING AT ROOM
AND ELEVATED TEMPERATURES, NASA Technical Note TN D-3075

21. Each value is lower than 530MPa for a lifetime of 3E6 cycles,
Results
Mechanical – Fatigue Studies
Stress state in Center of second Block of Rene41
The maximum stress intensity (TRESCA) is 261 Mpa.
The maximum von Mises eq. stress is 252 Mpa.
The maximum principle stress is 122 Mpa.
Each value is lower than 530MPa for a lifetime of 3E6 cycles,
Source:
FATIGUE OF RENE 41 UNDER CONSTANT AND RANDOM-AMPLITUDE LOADING AT ROOM
AND ELEVATED TEMPERATURES, NASA Technical Note TN D-3075

22. Results Mechanical – Fatigue Studies
Stress state in the second Block of Rene41
The stress state in the center is complex
The fatigue data is received in a different load case
The data looks promising but has to be closer checked
v. Mises eq. Stress

23. Following Post-Processing
Reviewing the fatigue data of Rene41, including radiation damage
Evaluation of the Stresses in the Ti6Al4V housing
Evaluation of the Stresses in the brazed surfaces
Stresses during long term use with an implemented cooling system, so far there is no steady state considered

25. Material Choices Combination of materials necessary
Increasing density to absorb gradually more energy
Titanium as first material seems feasible
Tungsten as last material may be possible
Preliminary studies done by W. Kozlowska
Combination of three materials
Nickel alloy seems promising in between
Follow up by D. Morgan
Source:
“LHC Injectors Upgrade: Technical Design Report – Volume 1 – Protons” (EDMS: /4)
“Preliminary Thermo-Mechanical Simulations Applied to the New PS Internal Dump” (EDMS: )

26. From Particles to Mechanical Stresses
FLUKA
Based on chemical composition and density a deposed energy distribution is calculated via FLUKA (Thanks to ES-STI-FDA)
The energy is then assumed to be focused in the center of the bin

27. From Particles to Mechanical Stresses
Quality Assurance for Import
ACCIDENTAL
LHC25
SFTPRO
FLUKA
ANSYS
Error
Maximum of deposed Energy / J/cm3/pulse
321
317.0
1.2%
176
178.06
1.0% 80 79
1.3%
Overall deposed Energy / kJ/pulse
40.7
39.1
4.0%
18.75
18.27
3.0%
8.3
8.1
2.4%

28. From Energies to Mechanical Stresses
Used Material Properties
density
sp. heat
therm. conduct.
CTE
Young’s mod.
poiss. ratio
Kg/m3
J/kg/C
W/m/C
1E-6/C
GPa
Temperature region / C
20-750
20-700
20-500
20-430
Ti6Al4V
4430 -
4331
557
824
7.23
12.93
8.75
10.3
116 84
0.31
Rene 41
8250
280
694 10
17.26 12
14.4
189
147
0.29
Source: Metallic Materials and Elements for Aerospace Vehicle Structures, Military Handbook - MIL-HDBK-5J
Department of defense, Federal Aviation Administration, 2003

29. From Energies to Mechanical Stresses
Geometric Simulation Model
Symmetry
(geometry and boundary conditions)
Symmetry planes

30. From Energies to Mechanical Stresses
Meshing
Bonded Contact
Side view
Characteristics of the
full model mesh
Number of Elements
248k
Kemax/Kemin
1.2E3
Average skewness (standard deviation)
0.76 (0.13)
Front view

31. From Energies to Mechanical Stresses
Mesh Size
horizontal
coarse
vertical
fine

32. From Energies to Mechanical Stresses
Mesh Size: Submodelling needed for one core of each material
Finer meshing for the core with the highest stresses per material.
Mesh size 0.3 x 0.3 x 0.5 mm
Mesh characteristics with submodelled core for Rene 41
Number of Elements
128k
Kemax/Kemin
2.2E10
Average skewness (standard deviation)
0.06 (0.13)
Beam
Beam

33. From Energies to Mechanical Stresses
Simulation Setup (timing)
Thermal conduction takes place in a larger time scale than the load application
Division of each pulse in three loadsteps (duration):
First step is to apply the beam energy (few microseconds)
Second step is for simulating mechanical waves (100 microseconds)
Third step allows to apply the temperature distribution corresponding to the end of the pulse period (0.01 seconds)

34. Backup Temperature distribution is calculated in a discrete way.
For each time step in the thermal simulation there is a Temperature field.
These fields have to be applied in the mechanical simulation at a fixed time step
In general the next mechanical time to apply the load is defined by
In the first two load steps per pulse the mechanical and the thermal time steps are equal so we say:
For the last load step we define for the mechanical time step

35. From Energies to Mechanical Stresses
Maximum temperature
Thermal simulation
time
Start of next impact
Maximum temperature
Mechanical simulation
time
Start of next impact after 0.01s

36. From Energies to Mechanical Stresses
Simulation Setup (damping)
For faster convergence damping is necessary
Also more realistic, because each material has natural damping
After 1E-4s there is no peak in the stresses expected (observed in past STI experience)
After this time, damping should take effect.
Assumption: a conservative damping ratio is selected:
Eigen frequencies taken from FFT
With Rayleigh damping we damp in the stiffness matrix with 1E-8

37. Fatigue Data for Rene41
For the Rene 41 there is one source for the fatigue strength, even for random loading.
The data was received by bending of a thin notched probe
The notch is designed to cause a stress intensity factor of around 7
Source:
FATIGUE OF RENE 41 UNDER CONSTANT AND RANDOM-AMPLITUDE LOADING AT ROOM
AND ELEVATED TEMPERATURES, NASA Technical Note TN D-3075

38. Fatigue Data for Rene41
Stress is calculated for a bar with the width of the notched region
To get the fatigue strength for a unnotched part, this stress has to be corrected
The stress intensity factor is only valid for a stress over the bigger width

39. Fatigue Data for Rene41

40. Backup
Explaining that scaling to 0.01s is possible