# LS Dyna Spec

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13-Dec-2015Category

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LS-Dyna and ANSYS Calculations of Shocks in SolidsGoran SkoroUniversity of Sheffield

Contents:IntroPART ISome historyANSYS resultsPART IILS-Dyna resultsNF TargetTest measurements (current pulse; tantalum wire)Summary

IntroductionThe 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!

Codes used for study of shock wavesSpecialist codes eg used by Fluid Gravity Engineering Limited Arbitrary Lagrangian-Eulerian (ALE) codes (developed for military) Developed for dynamic e.g. impact problemsALE 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 codeANSYSUses Implicit Time IntegrationSuitable for Quasi static problems

Implicit vs Explicit Time IntegrationExplicit Time Integration (used by LS Dyna)Central Difference method used Accelerations (and stresses) evaluated Accelerations -> velocities -> displacementsSmall time steps required to maintain stabilityCan solve non-linear problems for non-linear materialsBest for dynamic problems

Implicit vs Explicit Time IntegrationImplicit Time Integration (used by ANSYS) - Finite Element method used Average acceleration calculated Displacements evaluatedAlways stable but small time steps needed to capture transient responseNon-linear materials can be used to solve static problemsCan solve non-linear (transient) problemsbut only for linear material propertiesBest for static or quasi static problems

PART IHydrocode (FGE) and ANSYS results

The y axis is radius (metres) from 300K to 2300K and left to expandCylindrical bar 1cm in radius is heated instantaneously

Study by Alec Milne Fluid Gravity Engineering LimitedAlec 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.T = 2000 K The y axis is radial deflection (metres)

Comparison between Alec Milne/FGES and ANSYS results

Elastic shock waves in a candidate solid Ta neutrino factory target10 mm diameter tantalum cylinder10 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 targetTemperature jump after 1 ns pulse (Initial temperature = 2000K )

Elastic shock waves in a candidate solid Ta neutrino factory target

PART II LS-Dyna resultsGeneral purpose explicit dynamic finite element programUsed to solve highly nonlinear transient dynamics problemsAdvanced material modeling capabilitiesRobust for very large deformation analysesLS-Dyna solverFastest explicit solver in marketplaceMore features than any other explicit code

Material model used in the analysisTemperature Dependent Bilinear Isotropic Model'Classical' inelastic modelNonlinearUses 2 slopes (elastic, plastic) for representing of the stress-strain curveInputs: density, Young's modulus, CTE, Poisson's ratio, temperature dependent yield stress, ...Element type: LS-Dyna Explicit SolidMaterial: TANTALUM

Cylindrical bar 1cm in radius is heated instantaneously from 300K to 2300K and left to expand

First studiesBecause 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.

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....

Doing the Test - J. R. J. BennetThe ISIS Extraction Kicker Pulsed Power SupplyVoltage waveform Rise time: ~100 ns Flat Top: ~500 nsExponential with 20 ns risetime fitted to the waveform

SummaryResults (NF):The effect of having different number of bunches (n) in a pulse: at the level of 10-20% when n=1 -> n=10The effect of having longer bunches (2 or 3 ns): NoThe effect of different length of a pulse: YesResults (test, wire):Estimate of surface velocities needed for VISAR measurements