LS-Dyna and ANSYS Calculations of Shocks in Solids

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LS-Dyna and ANSYS Calculations of Shocks in Solids

• Goran Skoro
• University of Sheffield

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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

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Implicit vs Explicit Time Integration

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

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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

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PART I

• Hydrocode (FGE) and ANSYS results

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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.

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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

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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

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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

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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.

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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....

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Wire receives an energy for the whole of the
pulse!
Pulse time profile
wire diameter 0.6 mm shock transit time 100
ns
slow heating!!! pulse length 10x shock transit
time
surface velocity
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Pulse time profile
pulse length 5x shock transit time
pulse length shock transit time
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Pulse time profile
Pulse time profile could be important...
stress
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Pulse time profile
...if pulse time is longer than shock transit
time.
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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
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Current pulse width (effect of additional heating)
surface velocity
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similar effect for NF target
shock transit time 3.5 micro-s
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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 n1
  -gt n10
• 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!!!
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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.