LS-Dyna and ANSYS Calculations of Shocks in Solids

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

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!

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

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.?T = 2000 K

11. Comparison between Alec Milne/FGES and ANSYS results

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

14. Elastic shock waves in a candidate solid Ta neutrino factory target

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

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.

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....

44. 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)

45. 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.