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High-rate dislocation motion in stable nanocrystalline metals

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  • Intrinsic and Extrinsic Size Effects in Materials
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Abstract

Dislocation-mediated plasticity in stable nanocrystalline metals, where grain boundary motion is suppressed, is revisited in the context of dislocation elastodynamics. The effect of transient waves that emanate from the generation and motion of dislocations is quantified for an idealized Cu–10 at.% Ta system with grain sizes on the order of 50 nanometers. Simulations indicate that for this material, as dislocation velocities approach 0.6–0.8 times the shear wave speed, grains several grain diameters away from the initial glide event experience a large transient shear stress for a finite duration. These transient shear stresses increase with increasing glide velocity and can activate nucleation sites far from the original nucleation event. These considerations are used to explain recent experimental observations of a lack of increase in flow stress with increasing loading rate, as well as localization resistance, in this class of stable nanocrystalline metals.

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References

  1. E. Orowan: Problems of plastic gliding. Proc. Phys. Soc. 52, 8 (1940).

    Article  Google Scholar 

  2. H. Conrad: Grain size dependence of the plastic deformation kinetics in Cu. Mater. Sci. Eng., A 341, 216–228 (2003).

    Article  Google Scholar 

  3. Q. Wei, S. Cheng, K. Ramesh, and E. Ma: Effect of nanocrystalline and ultrafine grain sizes on the strain rate sensitivity and activation volume: Fcc versus bcc metals. Mater. Sci. Eng., A 381, 71–79 (2004).

    Article  CAS  Google Scholar 

  4. A. Argon and S. Yip: The strongest size. Philos. Mag. Lett. 86, 713–720 (2006).

    Article  CAS  Google Scholar 

  5. M. Dao, L. Lu, R. Asaro, J.T.M. De Hosson, and E. Ma: Toward a quantitative understanding of mechanical behavior of nanocrystalline metals. Acta Mater. 55, 4041–4065 (2007).

    Article  CAS  Google Scholar 

  6. Y. Wei, A. Bower, and H. Gao: Enhanced strain-rate sensitivity in fcc nanocrystals due to grain-boundary diffusion and sliding. Acta Mater. 56, 1741–1752 (2008).

    Article  CAS  Google Scholar 

  7. K. Zhang, J. Weertman, and J. Eastman: Rapid stress-driven grain coarsening in nanocrystalline Cu at ambient and cryogenic temperatures. Appl. Phys. Lett. 87, 061921 (2005).

    Article  CAS  Google Scholar 

  8. C. Koch, R. Scattergood, K. Darling, and J. Semones: Stabilization of nanocrystalline grain sizes by solute additions. J. Mater. Sci. 43, 7264–7272 (2008).

    Article  CAS  Google Scholar 

  9. K. Darling, A.J. Roberts, Y. Mishin, S.N. Mathaudhu, and L.J. Kecskes: Grain size stabilization of nanocrystalline copper at high temperatures by alloying with tantalum. J. Alloys Compd. 573, 142–150 (2013).

    Article  CAS  Google Scholar 

  10. K. Darling, E. Huskins, B. Schuster, Q. Wei, and L. Kecskes: Mechanical properties of a high strength Cu–Ta composite at elevated temperature. Mater. Sci. Eng., A 638, 322–328 (2015).

    Article  CAS  Google Scholar 

  11. T. Frolov, K. Darling, L. Kecskes, and Y. Mishin: Stabilization and strengthening of nanocrystalline copper by alloying with tantalum. Acta Mater. 60, 2158–2168 (2012).

    Article  CAS  Google Scholar 

  12. R. Koju, K. Darling, K. Solanki, and Y. Mishin: Atomistic modeling of capillary-driven grain boundary motion in Cu–Ta alloys. Acta Mater. 148, 311–319 (2018).

    Article  CAS  Google Scholar 

  13. K. Darling, M. Rajagopalan, M. Komarasamy, M. Bhatia, B. Hornbuckle, R. Mishra, and K. Solanki: Extreme creep resistance in a microstructurally stable nanocrystalline alloy. Nature 537, 378 (2016).

    Article  CAS  Google Scholar 

  14. G. Regazzoni, U. Kocks, and P. Follansbee: Dislocation kinetics at high strain rates. Acta Metall. 35, 2865–2875 (1987).

    Article  CAS  Google Scholar 

  15. S. Turnage, M. Rajagopalan, K. Darling, P. Garg, C. Kale, B. Bazehhour, I. Adlakha, B. Hornbuckle, C. Williams, P. Peralta, and K. Solanki: Anomalous mechanical behavior of nanocrystalline binary alloys under extreme conditions. Nat. Commun. 9, 2699 (2018).

    Article  CAS  Google Scholar 

  16. I. Lin, J. Hirth, and E. Hart: Plastic instability in uniaxial tension tests. Acta Metall. 29, 819–827 (1981).

    Article  CAS  Google Scholar 

  17. Q. Wei: Strain rate effects in the ultrafine grain and nanocrystalline regimes influence on some constitutive responses. J. Mater. Sci. 42, 1709–1727 (2007).

    Article  CAS  Google Scholar 

  18. K. Darling, M. Tschopp, R. Guduru, W. Yin, Q. Wei, and L. Kecskes: Microstructure and mechanical properties of bulk nanostructured Cu–Ta alloys consolidated by equal channel angular extrusion. Acta Mater. 76, 168–185 (2014).

    Article  CAS  Google Scholar 

  19. M. Bhatia, M. Rajagopalan, K. Darling, M. Tschopp, and K. Solanki: The role of Ta on twinnability in nanocrystalline Cu–Ta alloys. Mater. Res. Lett. 5, 48–54 (2017).

    Article  CAS  Google Scholar 

  20. R. Clifton: On the analysis of elastic/visco-plastic waves of finite uniaxial strain. In Shock Waves and the Mechanical Properties of Solids, J. Burke and V. Weiss, eds. (Syracuse University Press, Syracuse, New York, 1971); pp. 73–116.

    Google Scholar 

  21. U. Kocks, A. Argon, and M. Ashby: Thermodynamics and kinetics of slip. Prog. Mater. Sci. 19, 1–281 (1975).

    Article  Google Scholar 

  22. D. Kuhlmann-Wilsdorf: Theory of plastic deformation: Properties of low energy dislocation structures. Mater. Sci. Eng., A 113, 1–41 (1989).

    Article  Google Scholar 

  23. J. Taylor: Dislocation dynamics and dynamic yielding. J. Appl. Phys. 36, 3146–3150 (1965).

    Article  Google Scholar 

  24. W. Johnston and J. Gilman: Dislocation multiplication in lithium fluoride crystals. J. Appl. Phys. 31, 632–643 (1960).

    Article  CAS  Google Scholar 

  25. Y. Gupta, G. Duvall, and G. Fowles: Dislocation mechanisms for stress relaxation in shocked LiF. J. Appl. Phys. 46, 532–546 (1975).

    Article  CAS  Google Scholar 

  26. F. Roters, D. Raabe, and G. Gottstein: Work hardening in heterogeneous alloys—A microstructural approach based on three internal state variables. Acta Mater. 48, 4181–4189 (2000).

    Article  CAS  Google Scholar 

  27. W. Johnston and J. Gilman: Dislocation velocities, dislocation densities, and plastic flow in lithium fluoride crystals. J. Appl. Phys. 30, 129–144 (1959).

    Article  CAS  Google Scholar 

  28. V. Yamakov, D. Wolf, S. Phillpot, A. Mukherjee, and H. Gleiter: Dislocation processes in the deformation of nanocrystalline aluminium by molecular-dynamics simulation. Nat. Mater. 1, 45 (2002).

    Article  CAS  Google Scholar 

  29. O. Jones and J. Mote: Shock-induced dynamic yielding in copper single crystals. J. Appl. Phys. 40, 4920–4928 (1969).

    Article  CAS  Google Scholar 

  30. J. Johnson, O. Jones, and T. Michaels: Dislocation dynamics and single crystal constitutive relations: Shock-wave propagation and precursor decay. J. Appl. Phys. 41, 2330–2339 (1970).

    Article  CAS  Google Scholar 

  31. R. Austin and D. McDowell: A dislocation-based constitutive model for viscoplastic deformation of fcc metals at very high strain rates. Int. J. Plast. 27, 1–24 (2011).

    Article  CAS  Google Scholar 

  32. J. Lloyd, J. Clayton, R. Austin, and D. McDowell: Plane wave simulation of elastic-viscoplastic single crystals. J. Mech. Phys. Solids 69, 14–32 (2014).

    Article  CAS  Google Scholar 

  33. J. Lloyd, J. Clayton, R. Becker, and D. McDowell: Simulation of shock wave propagation in single crystal and polycrystalline aluminum. Int. J. Plast. 60, 118–144 (2014).

    Article  CAS  Google Scholar 

  34. R. Austin: Elastic precursor wave decay in shock-compressed aluminum over a wide range of temperature. J. Appl. Phys. 123, 035103 (2018).

    Article  CAS  Google Scholar 

  35. T. Zhu, J. Li, A. Samanta, A. Leach, and L. Gall: Temperature and strain-rate dependence of surface dislocation nucleation. Phys. Rev. Lett. 100, 025502 (2008).

    Article  CAS  Google Scholar 

  36. H. Van Swygenhoven, P. Derlet, and A. Froseth: Nucleation and propagation of dislocations in nanocrystalline fcc metals. Acta Mater. 54, 1975–1983 (2006).

    Article  CAS  Google Scholar 

  37. T. Zhu, J. Li, A. Samanta, H. Kim, and S. Suresh: Interfacial plasticity governs strain rate sensitivity and ductility in nanostructured metals. Proc. Natl. Acad. Sci. U. S. A. 104, 3031–3036 (2007).

    Article  CAS  Google Scholar 

  38. T. Zhu and J. Li: Ultra-strength materials. Prog. Mater. Sci. 55, 710–757 (2010).

    Article  Google Scholar 

  39. T. Lee, I. Robertson, and H. Birnbaum: Prediction of slip transfer mechanisms across grain boundaries. Scr. Metall. 23, 799–803 (1989).

    Article  CAS  Google Scholar 

  40. A. Hunter, B. Leu, and I. Beyerlein: A review of slip transfer: Applications of mesoscale techniques. J. Mater. Sci. 53, 5584–5603 (2018).

    Article  CAS  Google Scholar 

  41. J. Weertman: High velocity dislocations. In Response of Metals to High Velocity Deformation. Metallurgical Society Conferences, Vol. 9, P. Shewmon and V. Zackay, eds. (Interscience, New York, 1961); pp. 205–249.

    Google Scholar 

  42. R. Clifton and X. Markenscoff: Elastic precursor decay and radiation from nonuniformly moving dislocations. J. Mech. Phys. Solids 29, 227–251 (1981).

    Article  Google Scholar 

  43. B. Gurrutxaga-Lerma, D. Balint, D. Dini, and A. Sutton: The mechanisms governing the activation of dislocation sources in aluminum at different strain rates. J. Mech. Phys. Solids 84, 273–292 (2015).

    Article  CAS  Google Scholar 

  44. W. Greenman, T. Vreeland, Jr., and D. Wood: Dislocation mobility in copper. J. Appl. Phys. 38, 3595–3603 (1967).

    Article  CAS  Google Scholar 

  45. J. Chen, M. Tschopp, and A. Dongare: Shock wave propagation and spall failure of nanocrystalline Cu/Ta alloys: Effect of Ta in solid-solution. J. Appl. Phys. 122, 225901 (2017).

    Article  CAS  Google Scholar 

  46. S. Joshi and K. Ramesh: Stability map for nanocrystalline and amorphous materials. Phys. Rev. Lett. 101, 025501 (2008).

    Article  CAS  Google Scholar 

  47. Y. Guo, Y. Li, Z. Pan, F. Zhou, and Q. Wei: A numerical study of microstructure effect on adiabatic shear instability: Application to nanostructured/ultrafine grained materials. Mech. Mater. 42, 1020–1029 (2010).

    Article  Google Scholar 

  48. J. Eshelby: Uniformly moving dislocations. Proc. Phys. Soc. 62, 307 (1949).

    Article  Google Scholar 

  49. E. Van der Giessen and A. Needleman: Discrete dislocation plasticity: A simple planar model. Modell. Simul. Mater. Sci. Eng. 3, 689 (1995).

    Article  Google Scholar 

  50. B. Gurrutxaga-Lerma, D. Balint, D. Dini, D. Eakins, and A. Sutton: Dynamic discrete dislocation plasticity. In Advances in Applied Mechanics, S. Bordas, ed. Vol. 47 (Elsevier, London, U.K., 2014); ch. 2, pp. 93–224.

    Google Scholar 

  51. X. Markenscoff and R. Clifton: The nonuniformly moving edge dislocation. J. Mech. Phys. Solids 29, 253–262 (1981).

    Article  Google Scholar 

  52. B. Gurrutxaga-Lerma, D. Balint, D. Dini, D. Eakins, and A. Sutton: A dynamic discrete dislocation plasticity method for the simulation of plastic relaxation under shock loading. Proc. R. Soc. A 469, 20130141 (2013).

    Article  Google Scholar 

  53. K. Darling, C. Kale, S. Turnage, B. Hornbuckle, T. Luckenbaugh, S. Grendahl, and K. Solanki: Nanocrystalline material with anomalous modulus of resilience and springback effect. Scr. Mater. 141, 36–40 (2017).

    Article  CAS  Google Scholar 

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Acknowledgments

I wish to thank Drs. Kris Darling and Heather Murdoch for fruitful discussions concerning the behavior of nanocrystalline metals, and Dr. Beñat Gurrutxaga-Lerma for discussing elastodynamic dislocation solutions and their implementation.

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  1. Impact Physics Branch, US Army Research Laboratory, Aberdeen Proving Ground, Adelphi, Maryland, 21005-5066, USA

    Jeffrey T. Lloyd

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Correspondence to Jeffrey T. Lloyd.

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Lloyd, J.T. High-rate dislocation motion in stable nanocrystalline metals. Journal of Materials Research 34, 2252–2262 (2019). https://doi.org/10.1557/jmr.2019.59

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