1. LS-Dyna and ANSYS Calculations of Shocks in Solids Goran Skoro University of Sheffield

2. Contents: Intro PART I Some history ANSYS results PART II LS-Dyna results NF Target Test measurements (current pulse; tantalum wire) Summary C. J. Densham (RAL), UKNF Meeting, January 2005.

3. Introduction The target is bombarded at up 50 Hz by a proton beam consisting of ~1ns long bunches in a pulse of a few micro-s length. The target material exposed to the beam will be ~ 20cm long and ~2cm in diameter. Energy density per pulse ~ 300 J/cc. Thermally induced shock (stress) in target material (tantalum). Knowledge of material properties and stress effects: measurements and simulations! NF R&D Proposal

4. Codes used for study of shock waves Specialist codes eg used by Fluid Gravity Engineering Limited – Arbitrary Lagrangian-Eulerian (ALE) codes (developed for military)  Developed for dynamic e.g. impact problems  ALE not relevant? – Useful for large deformations where mesh would become highly distorted  Expensive and specialised LS-Dyna  Uses Explicit Time Integration (ALE method is included) – suitable for dynamic e.g. Impact problems  Should be similar to Fluid Gravity code ANSYS  Uses Implicit Time Integration  Suitable for ‘Quasi static’ problems

5. Implicit vs Explicit Time Integration Explicit Time Integration (used by LS Dyna) Central Difference method used Accelerations (and stresses) evaluated Accelerations -> velocities -> displacements Small time steps required to maintain stability Can solve non-linear problems for non-linear materials Best for dynamic problems

6. Implicit vs Explicit Time Integration Implicit Time Integration (used by ANSYS) - Finite Element method used Average acceleration calculated Displacements evaluated Always stable – but small time steps needed to capture transient response Non-linear materials can be used to solve static problems Can solve non-linear (transient) problems… …but only for linear material properties Best for static or ‘quasi’ static problems

7. PART I Hydrocode (FGE) and ANSYS results

8. The y axis is radius (metres) Study by Alec Milne, Fluid Gravity Engineering Limited from 300K to 2300K and left to expand” “Cylindrical bar 1cm in radius is heated instantaneously

9. Study by Alec Milne Fluid Gravity Engineering Limited Alec Milne: “We find that these models predict there is the potential for a problem […]. These results use 4 different material models. All of these show that the material expands and then oscillates about an equilibrium position. The oscillations damp down but the new equilibrium radius is 1.015cm. i.e. an irreversible expansion of 150 microns has taken place. The damping differs from model to model. The key point is all predict damage.”

10. ANSYS benchmark study: same conditions as Alec Milne/FGES study i.e.ΔT = 2000 K The y axis is radial deflection (metres) C. J. Densham (RAL)

11. Comparison between Alec Milne/FGES and ANSYS results 160 microns150 micronsMean expansion 8.3 micro-s7.5 micro-sRadial oscillation period 120 microns100 micronsAmplitude of initial radial oscillation ANSYSAlec Milne/ FGES

12. Elastic shock waves in a candidate solid Ta neutrino factory target 10 mm diameter tantalum cylinder 10 mm diameter proton beam (parabolic distribution for simplicity) 300 J/cc/pulse peak power (Typ. for 4 MW proton beam depositing 1 MW in target) Pulse length = 1 ns

13. Elastic shock waves in a candidate solid Ta neutrino factory target Temperature jump after 1 ns pulse (Initial temperature = 2000K ) C. J. Densham (RAL)

14. Elastic shock waves in a candidate solid Ta neutrino factory target Elastic stress waves in 1 cm diameter Ta cylinder over 10 μs after ‘instantaneous’ (1ns) pulse Stress (Pa) at :centre (purple) and outer radius (blue) C. J. Densham (RAL)

15. PART II LS-Dyna results General purpose explicit dynamic finite element program Used to solve highly nonlinear transient dynamics problems  Advanced material modeling capabilities  Robust for very large deformation analyses LS-Dyna solver  Fastest explicit solver in marketplace  More features than any other explicit code

16. Material model used in the analysis Temperature Dependent Bilinear Isotropic Model  'Classical' inelastic model  Nonlinear – Uses 2 slopes (elastic, plastic) for representing of the stress-strain curve – Inputs: density, Young's modulus, CTE, Poisson's ratio, temperature dependent yield stress,... Element type: LS-Dyna Explicit Solid Material: TANTALUM

17. Study by Alec Milne, Fluid Gravity Engineering Limited ANSYS LS-Dyna ~190 microns [m] [s] “Cylindrical bar 1cm in radius is heated instantaneously from 300K to 2300K and left to expand”

18. First studies Because the target will be bombarded at up 50 Hz by a proton beam consisting of ~1ns long bunches in a pulse of a few micro-s length we have studied: The effect of having different number of bunches in a pulse; The effect of having longer bunches (2 or 3 ns); The effect of different length of a pulse.

19. Geometry: NF target 2cm 20cm Boundary conditions: freeUniform thermal load of 100K(equivalent energy density of ~ 300 J/cc) T initial = 2000K

20. ~10-20% effect < 3% effect

21. Characteristic time = radius / speed of sound in the tantalum

22. < 1% effect

23. longer macro-pulse

24. ~ RAL proton driver

25. BUT, -At high temperatures material data is scarce… -Hence, need for experiments to determine material model data (J.R.J. Bennett talk): -Current pulse through wire (equivalent to ~ 300 J/cc); -Use VISAR to measure surface velocity; -Use results to 'extract' material properties at high temperatures... -and test material 'strength' under extreme conditions....

26. to vacuum pump heater test wire insulators to pulsed power supply water cooled vacuum chamber Schematic diagram of the test chamber and heater oven.

27. Radial displacement of tantalum wire after 2 micro-s ms [mm] Temperature rise: 100K in 1 micro-s Tinitial : 2000K (wire diameter = 0.6 mm)

29. heat input stops

32. Doing the Test - J. R. J. Bennet The ISIS Extraction Kicker Pulsed Power Supply Time, 100 ns intervals Voltage waveform Rise time: ~100 ns Flat Top: ~500 ns Exponential with 20 ns risetime fitted to the waveform

33. Pulse time profile surface velocity wire diameter = 0.6 mm; shock transit time ~ 100 ns slow heating!!! pulse length ~ 10x shock transit time Wire receives an energy for the whole of the pulse!

34. Pulse time profile pulse length ~ 5x shock transit time pulse length ~ shock transit time

35. Pulse time profile stress Pulse time profile could be important...

36. ...if pulse time is longer than shock transit time. Pulse time profile

37. Current pulse width (effect of additional heating) ~ shock transit time for 0.6 mm wire wire continues to receive energy at the same rate after the characteristic time stress

38. Current pulse width (effect of additional heating) surface velocity

39. similar effect for NF target shock transit time ~ 3.5 micro-s

40. Summary of results so far: NF: The effect of having different number of bunches (n) in a pulse: at the level of 10-20% when n=1 -> n=10 The effect of having longer bunches (2 or 3 ns): No The effect of different length of a pulse: Yes test, wire: Estimate of surface velocities needed for VISAR measurements Estimate of effects of pulse time profile Estimate of effects of current pulse width (additional heating) Important parameters: Energy deposition rate and shock transit time!!!

41. Plans Investigate the effect of rise time, flat top duration and fall time for the current pulse into the wire. Calculate for the wire with the real current profile from the ISIS extract kicker magnet power supply and using the calculated radial current penetration/time formula. Investigate the effects of different numbers of 1 ns micro-pulses in a macro- pulse of 1micro-s. Investigate the axial shock and do 3D calculations. Calculate for the target (individual bars and toroid) with a realistic beam profile. Calculate the pbar target situation. Investigate other models in LS-DYNA. Investigate other programmes than LS-DYNA.