![patrick.heighway@physics.ox.ac.uk
Summary
•We have performed large-scale molecular dynamics simulations of shock and release in micron-
scale tantalum single crystals loaded along their [011] axis
•By tracking the temperature evolution of Lagrangian material elements, we have shown that the
shock-release of these simulated crystals is markedly non-isentropic
•The temperature evolution of the releasing material elements was interpreted with moderate
success using a heat equation accounting for thermoelastic cooling, plastic-work heating and
exchange of energy with the microstructure
•The heat equation showed the heating on release is dominated by plastic-work owing to the
substantial material strength exhibited by the crystals
•The simulations were consistent with experiments where the thermally-induced strains of laser-
shocked targets were recorded by means of femtosecond x-ray diffraction](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
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APS March Meeting 2020 - Nonisentropic Release of a Shocked Solid
- 1. Nonisentropic release of a shocked solid patrick.heighway@physics.ox.ac.uk Patrick Heighway, Marcin Sliwa, David McGonegle, Matthew Suggit, Justin Wark University of Oxford, UK Christopher Wehrenberg, Jon Eggert, Amy Lazicki, Hye-Sook Park, Rob Rudd, Ray Smith, Damian Swift, Bruce Remington Lawrence Livermore National Laboratory, USA Cindy Bolme Las Alamos National Laboratory, USA Andrew Higginbotham University of York, UK Hae Ja Lee, Bob Nagler, Franz Tavella SLAC National Accelerator Laboratory, USA
- 2. patrick.heighway@physics.ox.ac.uk Summary •We have performed large-scale molecular dynamics simulations of shock and release in micron- scale tantalum single crystals loaded along their [011] axis •By tracking the temperature evolution of Lagrangian material elements, we have shown that the shock-release of these simulated crystals is markedly non-isentropic •The temperature evolution of the releasing material elements was interpreted with moderate success using a heat equation accounting for thermoelastic cooling, plastic-work heating and exchange of energy with the microstructure •The heat equation showed the heating on release is dominated by plastic-work owing to the substantial material strength exhibited by the crystals •The simulations were consistent with experiments where the thermally-induced strains of laser- shocked targets were recorded by means of femtosecond x-ray diffraction
- 3. patrick.heighway@physics.ox.ac.uk Introduction: release from the shock state
- 4. patrick.heighway@physics.ox.ac.uk Introduction: release from the shock state
- 5. patrick.heighway@physics.ox.ac.uk Introduction: release from the shock state •Close to the surface the ultra-high strain rate can cause the flow stress to be extreme (~ GPa) • Causes substantial heating via plastic work plastic flow
- 6. patrick.heighway@physics.ox.ac.uk Introduction: release from the shock state •Close to the surface the ultra-high strain rate can cause the flow stress to be extreme (~ GPa) • Causes substantial heating via plastic work •Moreover, the huge defect densities created during compression can partially annihilate on release† • Stored energy is recovered and released as heat dislocation annihilation Dislocations visualised using the dislocation extraction algorithm (DXA): A. Stukowski, V. V. Bulatov, A. Arsenlis, Model. Simul. Mater. Sci. 20, 085007 (2012). plastic flow † See M. Sliwa et. al., Phys. Rev. Lett. 120, 265502 (2018).
- 7. patrick.heighway@physics.ox.ac.uk Setup of molecular dynamics shock-release simulations •We used LAMMPS [1] to simulate shock and release in tantalum single crystals •Modelled using the Ravelo “Ta2” potential [2] •We tracked the evolution of Lagrangian material elements • Here we focus on an element 200 nm from the rear surface 011 100 011 [1] S. Plimpton, J. Comput. Phys. 117, 1 (1995) [2] R. Ravelo, T. C. Germann, O. Guerrero, Q. An,B. L. Holian, Phys. Rev. B 88, 134101 (2013)
- 8. patrick.heighway@physics.ox.ac.uk Evolution of elastic strains and temperature shock plastic release elastic release
- 9. patrick.heighway@physics.ox.ac.uk Evolution of elastic strains and temperature shock plastic release elastic release
- 10. patrick.heighway@physics.ox.ac.uk Interpretation of temperature evolution with heat equation •Temperature evolution is governed by thermoelastic cooling, plastic-work heating, and exchange of energy with the microstructure: 𝑑𝑇 𝑑𝑡 = 𝑇TE + 𝑇PW + 𝑇MS = 𝑇𝛾 ∶ 𝑑𝜀 𝑒 𝑑𝑡 + 1 𝑐 𝑉 𝜎 ∶ 𝑑𝜀 𝑝 𝑑𝑡 − 1 𝑉 𝑑𝐸 𝑠 𝑑𝑡 •Thermal conduction is negligible over the timescales of interest (~ 1 nanosecond) •Prediction is reasonably convincing – discrepancy due to non-equilibrium nature of dense dislocation network 𝑑𝑡 𝑇TE
- 11. patrick.heighway@physics.ox.ac.uk Interpretation of temperature evolution with heat equation 𝑑𝑡 𝑇TE 𝑑𝑡 𝑇TE + 𝑇PW •Temperature evolution is governed by thermoelastic cooling, plastic-work heating, and exchange of energy with the microstructure: 𝑑𝑇 𝑑𝑡 = 𝑇TE + 𝑇PW + 𝑇MS = 𝑇𝛾 ∶ 𝑑𝜀 𝑒 𝑑𝑡 + 1 𝑐 𝑉 𝜎 ∶ 𝑑𝜀 𝑝 𝑑𝑡 − 1 𝑉 𝑑𝐸 𝑠 𝑑𝑡 •Thermal conduction is negligible over the timescales of interest (~ 1 nanosecond) •Prediction is reasonably convincing – discrepancy due to non-equilibrium nature of dense dislocation network
- 12. patrick.heighway@physics.ox.ac.uk Interpretation of temperature evolution with heat equation 𝑑𝑡 𝑇TE 𝑑𝑡 𝑇TE + 𝑇PW 𝑑𝑡 𝑇TE + 𝑇PW + 𝑇MS •Temperature evolution is governed by thermoelastic cooling, plastic-work heating, and exchange of energy with the microstructure: 𝑑𝑇 𝑑𝑡 = 𝑇TE + 𝑇PW + 𝑇MS = 𝑇𝛾 ∶ 𝑑𝜀 𝑒 𝑑𝑡 + 1 𝑐 𝑉 𝜎 ∶ 𝑑𝜀 𝑝 𝑑𝑡 − 1 𝑉 𝑑𝐸 𝑠 𝑑𝑡 •Thermal conduction is negligible over the timescales of interest (~ 1 nanosecond) •Prediction is reasonably convincing – discrepancy due to non-equilibrium nature of dense dislocation network
- 13. patrick.heighway@physics.ox.ac.uk Setup of experiment performed at Matter in Extreme Conditions instrument (9.6 keV, 50 fs pulse) (6-μm thick [011] fiber- textured tantalum + 50 μm polyimide) (5 to 25 J, 5 to 10 ns pulse) Figure adapted from Wehrenberg et. al., Nature 550, 496-499 (2017)
- 14. patrick.heighway@physics.ox.ac.uk Setup of experiment performed at Matter in Extreme Conditions instrument shocked ambient released 2θ φ (9.6 keV, 50 fs pulse) (6-μm thick [011] fiber- textured tantalum + 50 μm polyimide) (5 to 25 J, 5 to 10 ns pulse)
- 15. patrick.heighway@physics.ox.ac.uk Locus of shock-release states in phase space * Equation of state used was SESAME 3520 *
- 16. patrick.heighway@physics.ox.ac.uk Locus of shock-release states in phase space * Equation of state used was SESAME 3520 *
- 17. patrick.heighway@physics.ox.ac.uk Summary •We have performed large-scale molecular dynamics simulations of shock and release in micron- scale tantalum single crystals loaded along their [011] axis •By tracking the temperature evolution of Lagrangian material elements, we have shown that the shock-release of these simulated crystals is markedly non-isentropic •The temperature evolution of the releasing material elements was interpreted with moderate success using a heat equation accounting for thermoelastic cooling, plastic-work heating and exchange of energy with the microstructure •The heat equation showed the heating on release is dominated by plastic-work owing to the substantial material strength exhibited by the crystals •The simulations were consistent with experiments where the thermally-induced strains of laser- shocked targets were recorded by means of femtosecond x-ray diffraction
- 18. Thank you for your attention patrick.heighway@physics.ox.ac.uk Patrick Heighway, Marcin Sliwa, David McGonegle, Matthew Suggit, Justin Wark University of Oxford, UK Christopher Wehrenberg, Jon Eggert, Amy Lazicki, Hye-Sook Park, Rob Rudd, Ray Smith, Damian Swift, Bruce Remington Lawrence Livermore National Laboratory, USA Cindy Bolme Las Alamos National Laboratory, USA Andrew Higginbotham University of York, UK Hae Ja Lee, Bob Nagler, Franz Tavella SLAC National Accelerator Laboratory, USA Full article available at: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.123.245501
- 19. patrick.heighway@physics.ox.ac.uk Additional slides: Tests of heat equation (I) •Thermoelastic cooling term was assessed by taking a fully- periodic, defect-free crystal at 100 GPa and 1750 K, and ‘manually’ evolving its elastic strains so as to simulate release back to ambient conditions •Atomic coordinates were remapped under an adiabatic integration scheme to emulate release without artificially heating the system •Elastic strain profiles 𝜀 𝑒 𝑡 were those of a material element undergoing shock release from 100 GPa •Shear stresses induced in the crystal are never large enough to precipitate plastic flow, so the release is entirely reversible and the only mechanism changing the temperature of the crystal is thermoelastic cooling •Heat equation predicts the temperature evolution very well: discrepancy between measured and predicted curves is at most 10 K
- 20. patrick.heighway@physics.ox.ac.uk Additional slides: Tests of heat equation (II) •Plastic heating terms were assessed by isochorically deforming a fully-periodic crystal containing a pre-existing dislocation network in such a way that dislocations are made to flow •Computational cell was expanded by 25% along 𝑧 over the course of 100 ps and compressed along 𝑥 and 𝑦 in such a way that the volume of the cell was conserved •Adiabatic integration scheme used as before •Absence of any volume change means the thermoelastic term is negligible and only plastic work terms influence the temperature of the crystal •Agreement between the predicted and measured temperature evolution is extremely good: profiles differ by no more than 5 K over the course of the deformation
- 21. patrick.heighway@physics.ox.ac.uk Additional slides: Depth dependence of release temperature
- 22. patrick.heighway@physics.ox.ac.uk Additional slides: Grüneisen parameter for Ta2 potential
- 23. patrick.heighway@physics.ox.ac.uk Additional slides: Will my crystal heat? •Instantaneous ratio of plastic-work heating 𝑇PW to thermoelastic cooling 𝑇TE for a uniaxially releasing material element for which both 𝛾 and 𝜀 𝑒 are scalar reads 𝑅 = 4 3 𝜏 𝑐 𝑉 𝑇 1 𝛾 , where • 𝜏 is the flow stress • 𝑐 𝑉 is the volumetric heat capacity • 𝑇 is the instantaneous temperature • 𝛾 is the Grüneisen parameter