1. Dynamics of twinning dislocations in Tantalum 02/28/2012 L. Sandoval, M. Surh, A. Chernov and D. Richards Lawrence Livermore National LaboratoryLLNL-PRES-531393This work was performed under the auspices of the U.S. Departmentof Energy by Lawrence Livermore National Laboratory under ContractDE-AC52-07NA27344, Lawrence Livermore National Security, LLC LLNL-PRES-531393 1
2. Results from HE loading on Ta show twinning EBSD maps showing twins in Ta as a function of position relative to the HE initiation site for the side interface initiated sample. Figures taken from Gray III et al. (2009).Lawrence Livermore National Laboratory LLNL-PRES-531393 2
3. Qualitative comparison with experimental results Although simulation results do not correspond to the stress history of the shock- loaded experiment, this is a successful qualitative comparison.Lawrence Livermore National Laboratory LLNL-PRES-531393 3
4. LLNL Multi-scale strength model for Ta1 Starting from the Orowan’s relation It gives material strength as a function temperature, pressure, strain rate and dislocation density. It is based on plastic deformation by thermally activated dislocation motion. Connects simulation results from atomistic to continuum length scales. The model gives a reasonable agreement with experiments for some conditions. 1 N. Barton et al. J. Appl. Phys. 109, 073501 (2011).Lawrence Livermore National Laboratory LLNL-PRES-531393 4
5. LLNL Multi-scale strength model for Ta1 Starting from the Orowan’s relation It gives material strength as a function temperature, pressure, strain rate and dislocation density. It is based on plastic deformation by thermally activated dislocation motion. Connects simulation results from atomistic to continuum length scales. The model gives a reasonable agreement with experiments for some conditions. 1 N. Barton et al. J. Appl. Phys. 109, 073501 (2011).Lawrence Livermore National Laboratory LLNL-PRES-531393 4
6. LLNL Multi-scale strength model for Ta1 Starting from the Orowan’s relation Twinning: Thresholds, nucleation and growth rates It gives material strength as a function temperature, pressure, strain rate and dislocation density. It is based on plastic deformation by thermally activated dislocation motion. Connects simulation results from atomistic to continuum length scales. The model gives a reasonable agreement with experiments for some conditions. 1 N. Barton et al. J. Appl. Phys. 109, 073501 (2011).Lawrence Livermore National Laboratory LLNL-PRES-531393 4
7. Nucleation rates of twinning dislocation loops in Ta We study the twin boundary energetics and structure in a bilayered system in order to determine twinning nucleation rates. Within KJMA theory, the normal growth rate, vn , is given by 1 vn ∼ h(J2d vf ) 3 , (1) where h is the step’s height, J2d is the nucleation rate, and vf is the front velocity of twinning dislocations.Lawrence Livermore National Laboratory LLNL-PRES-531393 5
8. Nucleation rates of twinning dislocation loops in Ta We study the twin boundary energetics and structure in a bilayered system in order to determine twinning nucleation rates. Within KJMA theory, the normal growth rate, vn , is given by 1 vn ∼ h(J2d vf ) 3 , (1) where h is the step’s height, J2d is the nucleation rate, and vf is the front velocity of twinning dislocations.Lawrence Livermore National Laboratory LLNL-PRES-531393 5
9. Nucleation rates of twinning dislocation loops in Ta 10 Jxz =11.4 τ =93 ps 1025 τ =133 ps 8 τ =193 ps 6 Jxz(1/(m2 s)) ∆µ (meV) Jxz =12.3 4 1024 Jxz =14.5 τ =2092 ps 2 Jxz =7.6 Jxz =16.5 200 205 210 215 220 00 200 400 600 800 1000 1/∆µ(1/eV) T (K) (a) (b) Nucleation rates of twinning dislocation loops in Ta under a hydrostatic pressure of ∼ 0.4 GPa. (a) Nucleation rate Jxz as a function of the inverse driving force, ∆µ = ωσ , for 300 K (ω : atomic volume, σ : shear stress, : shear strain). (b) Nucleation rates obtained via md simulations. Values are given in units of 1024 m−2 s−1 .Lawrence Livermore National Laboratory LLNL-PRES-531393 6
10. Velocity of twinning dislocations in Ta: simulation setup • EAM potential for Tantalum from Ackland-Thetford (Phil. Mag. A 56, 15 (1987)). 50nm • N ∼ 2.5 × 106 atoms. EDGE • Constant strain-rate simulations. • Constant shear stress simulations. • NVE ensemble. SCREW 50nm • We use the LLNL award-winning 20nm molecular dynamics code ddcMD.Lawrence Livermore National Laboratory LLNL-PRES-531393 7
11. Results: velocity of twinning edge dislocations in Ta 4.5 longitudinal waves 4.0 3.5 3.0 Velocity (km/s) 2.5 shear waves 2.0 1.5 1.0 50 K 150 K 0.5 300 K 500 K 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Stress (GPa) Velocity of twinning edge dislocations in Ta under a hydrostatic pressure of ∼ 0 GPa.Lawrence Livermore National Laboratory LLNL-PRES-531393 8
12. Results: velocity of twinning edge dislocations in Ta 4.5 longitudinal waves 4.0 • No static friction. 3.5 • Regime 1: dominant phonon 3.0 drag contribution. Velocity (km/s) 2.5 shear waves • Regime 2: dominant radiative 2.0 dissipation. 1.5 1.0 50 K • Regime 3: Singular behavior 150 K 0.5 300 K (function of temperature). 500 K 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 • Subsonic and transonic Stress (GPa) singularities. Velocity of twinning edge dislocations in Ta under a hydrostatic pressure of ∼ 0 GPa.Lawrence Livermore National Laboratory LLNL-PRES-531393 8
13. Results: velocity of twinning screw dislocations in Ta 4.5 longitudinal waves 50 K 4.0 150 K 300 K 3.5 500 K 3.0 Velocity (km/s) 2.5 shear waves 2.0 1.5 1.0 0.5 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Stress (GPa) Velocity of twinning screw dislocations in Ta under a hydrostatic pressure of ∼ 0 GPa.Lawrence Livermore National Laboratory LLNL-PRES-531393 9
14. Results: velocity of twinning screw dislocations in Ta 4.5 longitudinal waves 50 K 4.0 150 K 300 K 3.5 500 K • Static friction (function of 3.0 temperature). Velocity (km/s) 2.5 shear waves • Dominant radiative 2.0 dissipation on phonon drag. 1.5 1.0 • Subsonic singular behavior. 0.5 • No transonic transition 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 observed. Stress (GPa) Velocity of twinning screw dislocations in Ta under a hydrostatic pressure of ∼ 0 GPa.Lawrence Livermore National Laboratory LLNL-PRES-531393 9
15. Functional form2 (based on Eshelby’s expression3 ) longitudinal waves shear waves Shear stress v0 v* v1 Velocity  α σ0 (T ) + B(T )v + D0 v v0 −1 Θ(v − v0 ) if v < v ∗ σ(T , v ) = β (2) σ1 (T ) + D1 v v1 −1 Θ(v − v1 ) if v ≥ v ∗ 2 J. Marian and A. Caro, Phys. Rev. B 74, 024113 (2006). 3 J. D. Eshelby, Proc. Phys. Soc. London, Sect. B 69, 1013 (1956).Lawrence Livermore National Laboratory LLNL-PRES-531393 10
16. Twinning dislocation island • The diﬀerence between edge and screw velocities originates elliptic twinning dislocation loops. • Considering a mean front velocity of 2.8 km/s, and typical nucleation values from our MD simulations, we get a growth rate of ∼ 2.5 m/s. • Under similar conditions the pole mechanism gives a value of ∼ 40 m/s. Twinning dislocation island on the coherent twin boundary.Lawrence Livermore National Laboratory LLNL-PRES-531393 11
17. 3d ellipsoidal twin inclusion • 518 ×106 atoms at 50 K for a shear stress of 2.5 GPa. • Partial loops also form on ﬁnite-size 3-D ellipsoidal twin inclusions. • Only top surface is shown. • Supersonic motion occurs at higher shear stresses > 2 GPa.Lawrence Livermore National Laboratory LLNL-PRES-531393 12
18. Twinning edge dislocation in Ta Shear invariant of the local stress tensor.Lawrence Livermore National Laboratory LLNL-PRES-531393 13
19. Conclusions • Twinning edge and screw dislocations in Ta show quite diﬀerent behavior: • Static friction. • Phonon drag regime. • Radiative dissipation regime. • Singularities. • Transition to transonic regime. • This distinctive behavior has important consequences on the growth process of twin nucleus (shape, anisotropic growth velocity, etc.). • Phenomenological expression for mobility of twinning dislocations. • Additional techniques to study nucleation in extended time scales are required to get a complete picture.Lawrence Livermore National Laboratory LLNL-PRES-531393 14
20. Thanks!Lawrence Livermore National Laboratory LLNL-PRES-531393 15
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