LS-Dyna and ANSYS Calculations of Shocks in Solids

Goran Skoro

University of Sheffield

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.

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

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

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

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

PART I

Hydrocode (FGE) and ANSYS results

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

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.”

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)

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

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

Elastic shock waves in a candidate solid Ta neutrino factory target

Temperature jump after 1 ns pulse

(Initial temperature = 2000K )

C. J. Densham (RAL)

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)

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

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

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”

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.

Geometry: NF target

2cm

20cm

Boundary conditions: free

Uniform thermal load of 100K

(equivalent energy density of ~ 300 J/cc)

Tinitial = 2000K

~10-20% effect

< 3% effect

Characteristic time = radius / speed of sound in the tantalum

< 1% effect

longer macro-pulse

~ RAL proton driver

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....

to vacuum pump

heater

test wire

insulators

to pulsed power supply

to pulsed power supply

water cooled vacuum chamber

Schematic diagram of the test chamber and heater oven.

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)

heat input stops

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

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!

Pulse time profile

pulse length ~ 5x shock transit time

pulse length ~ shock transit time

Pulse time profile

stress

Pulse time profile could be important...

...if pulse time is longer than

shock transit time.

Pulse time profile

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

Current pulse width (effect of additional heating)

surface velocity

similar effect for NF target

shock transit time

~ 3.5 micro-s

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!!!

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.