Letter

Probing the limits of metal plasticity with molecular dynamics simulations

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Published online:

Abstract

Ordinarily, the strength and plasticity properties of a metal are defined by dislocations—line defects in the crystal lattice whose motion results in material slippage along lattice planes1. Dislocation dynamics models are usually used as mesoscale proxies for true atomistic dynamics, which are computationally expensive to perform routinely2. However, atomistic simulations accurately capture every possible mechanism of material response, resolving every “jiggle and wiggle”3 of atomic motion, whereas dislocation dynamics models do not. Here we present fully dynamic atomistic simulations of bulk single-crystal plasticity in the body-centred-cubic metal tantalum. Our goal is to quantify the conditions under which the limits of dislocation-mediated plasticity are reached and to understand what happens to the metal beyond any such limit. In our simulations, the metal is compressed at ultrahigh strain rates along its [001] crystal axis under conditions of constant pressure, temperature and strain rate. To address the complexity of crystal plasticity processes on the length scales (85–340 nm) and timescales (1 ns–1μs) that we examine, we use recently developed methods of in situ computational microscopy4,5 to recast the enormous amount of transient trajectory data generated in our simulations into a form that can be analysed by a human. Our simulations predict that, on reaching certain limiting conditions of strain, dislocations alone can no longer relieve mechanical loads; instead, another mechanism, known as deformation twinning (the sudden re-orientation of the crystal lattice6), takes over as the dominant mode of dynamic response. Below this limit, the metal assumes a strain-path-independent steady state of plastic flow in which the flow stress and the dislocation density remain constant as long as the conditions of straining thereafter remain unchanged. In this distinct state, tantalum flows like a viscous fluid while retaining its crystal lattice and remaining a strong and stiff metal.

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References

  1. 1.

    & Computer Simulations of Dislocations 196–240 (Oxford Univ. Press, 2006)

  2. 2.

    et al. Parametric dislocation dynamics: a thermodynamics-based approach to investigations of mesoscopic plastic deformation. Phys. Rev. B. 61, 913–927 (2000)

  3. 3.

    Lectures on Physics Vol. 1, 3–6 (1963)

  4. 4.

    Visualization and analysis of atomistic simulation data with OVITO — the Open Visualization Tool. Model. Simul. Mater. Sci. Eng. 18, 015012 (2010)

  5. 5.

    & Extracting dislocations and non-dislocation crystal defects from atomistic simulation data. Model. Simul. Mater. Sci. Eng. 18, 085001 (2010)

  6. 6.

    & Deformation twinning. Prog. Mater. Sci. 39, 1–157 (1995)

  7. 7.

    & The temperature and strain rate dependence of the flow stress of tantalum. J. Mater. Sci. 12, 1666–1672 (1977)

  8. 8.

    et al. Molecular dynamics simulations of shock-induced plasticity in tantalum. High Energy Density Phys. 10, 9–15 (2014)

  9. 9.

    & Three-stage hardening in tantalum single crystals. Acta Metall. 13, 1169–1179 (1965)

  10. 10.

    & Multiplication processes for slow moving dislocations. Phys. Rev. 79, 722–723 (1950)

  11. 11.

    et al. The onset of twinning in metals: a constitutive description. Acta Mater. 49, 4025–4039 (2001)

  12. 12.

    et al. Deformation of high purity tantalum single crystals at 4.2 K. Mater. Sci. Eng. 20, 71–81 (1975)

  13. 13.

    Does dislocation density have a natural limit? Phys. Lett. A 60, 61–62 (1977)

  14. 14.

    et al. Effect of strain rate and dislocation density on the twinning behavior in tantalum. AIP Adv. 6, 045120 (2016)

  15. 15.

    1/2〈111〉 screw dislocations and nucleation of {112}〈111〉 twins in the b.c.c. lattice. Phil. Mag. 8, 1467–1486 (1963)

  16. 16.

    , & Dynamic transitions from smooth to rough to twinning in dislocation motion. Nat. Mater. 3, 158–163 (2004)

  17. 17.

    & Maximum entropy production principle in physics, chemistry and biology. Phys. Rep. 426, 1–45 (2006)

  18. 18.

    Shock-induced phase transformation in tantalum. J. Phys. Condens. Matter 22, 385702 (2010)

  19. 19.

    et al. Microstructure of high-strain, high-strain-rate deformed tantalum. Acta Mater. 46, 1307–1325 (1998)

  20. 20.

    et al. Phase transformation in tantalum under extreme laser deformation. Sci. Rep. 5, 15064 (2015)

  21. 21.

    et al. A unified approach for extracting strength information from non-simple compression waves. Part II. Experiment and comparison with simulation. J. Appl. Phys. 110, 113506 (2011)

  22. 22.

    & Dislocation velocities, dislocation densities and plastic flow in lithium fluoride crystals. J. Appl. Phys. 30, 129–144 (1959)

  23. 23.

    & Kinetics of flow and strain hardening. Acta Metall. 29, 1865–1875 (1981)

  24. 24.

    Evidence of enhanced self-organization in the work-hardening stage V of fcc metals. Philos. Mag. Lett. 81, 129–136 (2001)

  25. 25.

    Barreling of solid cylinders under axial compression. J. Eng. Mater. Technol. 107, 138–144 (1985)

  26. 26.

    Stress–Strain Curves (MIT OpenCourseWare, 2001)

  27. 27.

    & Continuum Theory of Plasticity 37–40 (Wiley-Interscience, 1995)

  28. 28.

    et al. Constrained deformation of molybdenum single crystals. Acta Metall. 23, 1473–1478 (1975)

  29. 29.

    On hardening due to the recombination of dislocations. Acta Metall. 8, 841–847 (1960)

  30. 30.

    et al. Dislocation multi-junctions and strain hardening. Nature 440, 1174–1178 (2006)

  31. 31.

    & Ordinary dislocations in γ-TiAl: cusp unzipping, jog dragging and stress anomaly. Philos. Mag. A 80, 765–779 (2000)

  32. 32.

    & Low-temperature deformation of body-centered cubic metals. Proc. R. Soc. Lond. A 281, 223–239 (1964)

  33. 33.

    Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117, 1–19 (1995)

  34. 34.

    et al. Embedded-atom-method tantalum potential developed by force-matching method. Phys. Rev. B 67, 125101 (2003)

  35. 35.

    IBM’s Sequoia tops the world’s fastest supercomputer list. Digital Trends (2012)

  36. 36.

    & Improbability of void growth in aluminum via dislocation nucleation under typical laboratory conditions. Phys. Rev. Lett. 108, 035501 (2012)

  37. 37.

    & Unified physics of stretched exponential relaxation and Weibull fracture statistics. Physica A 391, 6121–6127 (2012)

  38. 38.

    et al. Fractal dislocation patterning during plastic deformation. Phys. Rev. Lett. 81, 2470–2473 (1998)

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Acknowledgements

This work was performed under the auspices of the US Department of Energy by Lawrence Livermore National Laboratory under contract W-7405-Eng-48. This work was supported by the NNSA ASC programme. Computing support for this work came from the Lawrence Livermore National Laboratory (LLNL) Institutional Computing Grand Challenge programme and Jülich Supercomputing Centre at Forschungszentrum Jülich, Germany.

Author information

Affiliations

  1. Lawrence Livermore National Laboratory, Livermore, California, USA

    • Luis A. Zepeda-Ruiz
    • , Tomas Oppelstrup
    •  & Vasily V. Bulatov
  2. Technische Universität Darmstadt, Darmstadt, Germany

    • Alexander Stukowski

Authors

  1. Search for Luis A. Zepeda-Ruiz in:

  2. Search for Alexander Stukowski in:

  3. Search for Tomas Oppelstrup in:

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Contributions

L.A.Z.-R. ran most of the molecular dynamics simulations and analysed the results, A.S. ran molecular dynamics simulations and developed methods for computational microscopy and visualization, T.O. optimized run-time efficiency and data management of molecular dynamics simulations, and V.V.B. developed the concept, planned the research, generated starting configurations for molecular dynamics simulations, analysed the results and wrote the paper.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Vasily V. Bulatov.

Reviewer Information Nature thanks M. Zaiser and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Supplementary information

Videos

  1. 1.

    Dislocation multiplication from the initial sources results in the development of a dense dislocation network.

    Crystal containing dislocations sources (loops) is subjected to uniaxial compression along the [001] axis at a constant true straining rate of 2.78.108 1/s (x25). The simulation volume contains about 268 million atoms of tantalum. The video sequence progresses through extension of the initial hexagon-shaped loops, to dislocation collisions resulting in the formation of dislocation junctions, to an increasingly dense dislocation network. Dislocation positions, shapes and Burgers vectors were extracted using the DXA algorithm5. All atoms and defects other than dislocations, such as vacancies, interstitials and clusters, are removed for clarity. The green lines represent ½<111> dislocations and the pink lines depict <100> junction dislocations.

  2. 2.

    Crystal microstructure evolution under straining at rate x50.

    In this MD simulation a crystal containing dislocations sources (loops) was subjected to uniaxial compression along the [001] axis at a constant true straining rate of 5.56.108 1/s (x50). The simulation volume contains about 33 million atoms of tantalum. This video sequence progresses through extension of the initial loops, to nucleation of embryonic twins on screw dislocations, to rapid propagation and growth of twinning particles. The meaning of colours is as defined in the caption to Fig. 1: the outer surfaces bounding the twins are coloured light grey whereas the insides of twin particles are coloured red, yellow, magenta or cyan depending to each twin's rotational variant.

  3. 3.

    “Metal kneading” at rate x25.

    This MD simulation was performed on a brick-shaped tantalum crystal with the ratio of initial box dimensions 1:2:4. After full compression along Z axis to ¼ of its initial dimension the brick’s shape becomes 2:4:1 (due to Poisson’s expansion in two lateral dimensions, the brick’s volume remains very nearly constant under compression) another MD simulation starts in which the brick is compressed along its now longest Y-axis. After the second compression cycle is completed, the brick is compressed along its now longest X-axis. After three compression cycles the brick recovers its initial shape 1:2:4 and one more Z-axis compression cycle is performed (see related stress-strain plots in Extended Data Figure 5).

  4. 4.

    Dislocation motion in more detail

    This simulation was performed at rate 1.11.107 1/s (x1) from a configuration attained past yield under pre-straining at rate 5.55.107 1/s (x5). Reduction in dislocation density can be observed over the first few frames immediately following the sudden drop in the straining rate from x5 to x1 at time t=0. Subsequently the network attains a dynamic steady state in which dislocation multiplication is balanced by dislocation annihilation. Taken at more frequent time intervals, this sequence reveals various events in the life of dislocations in greater detail than in the other videos. One can observe that dislocation motion is not steady but proceeds in a stop-and-go manner which is also revealed in Extended Data Fig. 9a.