Statistical Thermodynamics of Crystal Plasticity

  • J. S. LangerEmail author


This article is written in memory of Pierre Hohenberg with appreciation for his deep commitment to the basic principles of theoretical physics. I summarize recent developments in the theory of dislocation-enabled deformation of crystalline solids. This topic is especially appropriate for the Journal of Statistical Physics because materials scientists, for decades, have asserted that statistical thermodynamics is not applicable to dislocations. By use of simple, first-principles analyses and comparisons with experimental data, I argue that these people have been wrong, and that this field should now be revitalized because of its wide-ranging intellectual and technological importance.


Crystal-plasticity Dislocations Statistical thermodynamics 



JSL was supported in part by the U.S. Department of Energy, Office of Basic Energy Sciences, Materials Science and Engineering Division, DE-AC05-00OR-22725, through a subcontract from Oak Ridge National Laboratory.


  1. 1.
    Taylor, G.I.: The mechanism of plastic deformation in crystals, Part 1—Theoretical. Proc. R. Soc. A 145, 362 (1934)ADSCrossRefzbMATHGoogle Scholar
  2. 2.
    Cottrell, A.H.: Dislocations and Plastic Flow in Crystals. Oxford University Press, London (1953)zbMATHGoogle Scholar
  3. 3.
    Friedel, J.: Dislocations. Pergamon, Oxford (1967)zbMATHGoogle Scholar
  4. 4.
    Hirth, J., Lothe, J.: Theory of Dislocations. McGraw Hill, New York (1968)zbMATHGoogle Scholar
  5. 5.
    Cottrell, A.H.: In: Nabarro, F.R.N., Duesbery, M.S. (eds.) Dislocations in Solids. Elsevier, Amsterdam (2002)Google Scholar
  6. 6.
    Langer, J.S., Bouchbinder, E., Lookman, T.: Thermodynamic theory of dislocation-mediated plasticity. Acta Mater. 58, 3718 (2010)CrossRefGoogle Scholar
  7. 7.
    Kocks, U.F., Mecking, H.: Physics and phenomenology of strain hardening: the FCC case. Prog. Matls. Sci. 48, 171 (2003)CrossRefGoogle Scholar
  8. 8.
    Preston, D.L., Tonks, D.L., Wallace, D.C.: Model of plastic deformation for extreme loading conditions. J. Appl. Phys. 93, 211 (2003)ADSCrossRefGoogle Scholar
  9. 9.
    Gray III, G.T.: High-strain-rate deformation: mechanical behavior and deformation substructures induced. Annu. Rev. Mater. Res. 42, 285 (2012)ADSCrossRefGoogle Scholar
  10. 10.
    Armstrong, R.W.: 60 Years of Hall–Petch: past to present nano-scale connections. Mater. Trans. 55, 2–12 (2014). (Special issue on strength of fine grained materials, The Japan Institute of Metals and Materials 2013)CrossRefGoogle Scholar
  11. 11.
    Langer, J.S.: Thermodynamic analysis of the Livermore molecular-dynamics simulations of dislocation-mediated plasticity. Phys. Rev. E 98, 023006 (2018)ADSCrossRefGoogle Scholar
  12. 12.
    Fleck, N., Muller, G., Ashby, M., Hutchinson, J.: Strain gradient plasticity: theory and experiment. Acta Metall. Mater. 42, 475 (1994)CrossRefGoogle Scholar
  13. 13.
    Devincre, B., Hoc, T., Kubin, L.: Dislocation mean free paths and strain hardening of crystals. Science 320, 1745 (2008)ADSCrossRefGoogle Scholar
  14. 14.
    LeSar, R.: Simulations of dislocation structure and response. Annu. Rev. Condens. Matter Phys. 5, 375 (2014)ADSCrossRefGoogle Scholar
  15. 15.
    Zepeda-Ruiz, L.A., Stukowski, A., Oppelstrup, T., Bulatov, V.V.: Probing the limits of metal plasticity with molecular dynamics simulations. Nature 550, 492 (2017)ADSCrossRefGoogle Scholar
  16. 16.
    Langer, J.S.: Statistical thermodynamics of strain hardening in polycrystalline solids. Phys. Rev. E 92, 032125 (2015)ADSCrossRefGoogle Scholar
  17. 17.
    Langer, J.S.: Thermodynamic theory of dislocation-enabled plasticity. Phys. Rev. E 96, 053005 (2017)ADSCrossRefGoogle Scholar
  18. 18.
    Falk, M.L., Langer, J.S.: Deformation and failure of amorphous, solidlike materials. Annu. Rev. Condens. Matter Phys. 2, 353 (2011)ADSCrossRefGoogle Scholar
  19. 19.
    Langer, J.S.: Thermal effects in dislocation theory II. Shear banding. Phys. Rev. E 95, 013004 (2017)ADSCrossRefGoogle Scholar
  20. 20.
    Le, K.C., Tran, T.M., Langer, J.S.: Thermodynamic dislocation theory of high-temperature deformation in aluminum and steel. Phys. Rev. E 96, 013004 (2017)ADSCrossRefGoogle Scholar
  21. 21.
    Le, K.C., Tran, T.M., Langer, J.S.: Thermodynamic dislocation theory of adiabatic shear banding in steel. Scr. Mater. 149, 62 (2018)ADSCrossRefGoogle Scholar
  22. 22.
    Chen, S.R., Maudlin, P.J., Gray, G.T.: In: Seventh International Symposium on Plasticity and Its Current Applications, pp. 623–626, A.S. Khan, ed. Cancun, Neat Press (1999)Google Scholar
  23. 23.
    Meyers, M., Andrade, U., Chokshi, A.: The effect of grain size on the high-strain, high-strain-rate behavior of copper. Metall. Mater. Trans. A 26A, 2881 (1995)ADSCrossRefGoogle Scholar
  24. 24.
    Marchand, A., Duffy, J.: An experimental study of the formation process of adiabatic shear bands in a structural steel. J. Mech. Phys. Solids 36, 251 (1988)ADSCrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Department of PhysicsUniversity of CaliforniaSanta BarbaraUSA

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