Metallurgical and Materials Transactions A

, Volume 44, Issue 6, pp 2625–2644 | Cite as

An Atomistic-Based Hierarchical Multiscale Examination of Age Hardening in an Al-Cu Alloy


A large class of modern structural alloys derives its strength from precipitation hardening. Precipitates obstruct the motion of dislocations and thereby increase alloy strength. This paper examines the process using an atomistic-based hierarchical multiscale modeling framework. Atomistic modeling is employed to (1) compute solute-dislocation interaction energies for input into a semi-analytic solute hardening model and (2) evaluate precipitate strengths for use in dislocation line tension simulations. The precipitate microstructure in the dislocation line tension simulations is obtained from simple analytic precipitation kinetics relations. Fitting only the rate constants in the precipitation kinetics model, the macroscopic strength predictions of the hierarchical multiscale model are found to correspond reasonably well with experiments. By analyzing the potential sources of discrepancy between the model’s macroscopic predictions and experiments, this work illuminates the importance of specific atomic-scale processes and highlights important challenges that remain before truly predictive mechanism-based plasticity modeling can be realized.

Supplementary material

Movie 1 (corresponding to Fig. 2a): 60 deg interaction between edge dislocation and GP zone involving leading partial cutting and trailing partial looping. MPG (656 KB)

11661_2013_1614_MOESM2_ESM.mpg (343 kb)
Movie 2 (corresponding to Fig. 2b): 0 deg interaction between edge dislocation and GP zone involving full dislocation looping. MPG (342 KB)


  1. 1.
    Wilm A. (1911) Metallurgie 8:225–27Google Scholar
  2. 2.
    Gayle F.W., Goodway M. (1994) Science 266:1015–17CrossRefGoogle Scholar
  3. 3.
    Orowan E.Z. (1934) Phys. 89:634CrossRefGoogle Scholar
  4. 4.
    Polanyi M.Z. (1934) Phys. 89:660CrossRefGoogle Scholar
  5. 5.
    Taylor G.I. (1934) Proc. R. Soc. Lond. A, 145:362–87CrossRefGoogle Scholar
  6. 6.
    Guinier A. (1939) Ann. Phys. 12:161Google Scholar
  7. 7.
    Preston G.D. (1938) Phil. Mag. 26:855Google Scholar
  8. 8.
    I. J. Polmear and H. K. Hardy: J. Inst. Met., 1952–1953, vol. 81, pp. 427–32Google Scholar
  9. 9.
    Hornbogen E. (2001) JJ. Light Met. 1:127–32CrossRefGoogle Scholar
  10. 10.
    I. Polmear: Light Alloys: From Traditional Alloys to Nanocrystals, Butterworth-Heinemann, London, 2006Google Scholar
  11. 11.
    Liddicoat P.V., Liao X.-Z., Zhao Y., Zhu Y., Murashkin M.Y., Lavernia E.J., Valiev R.Z., Ringer S.P. (2010) Nat. Commun. 1:1–7CrossRefGoogle Scholar
  12. 12.
    R.Z. Valiev, N.A. Enikeev, Murashkin, V.U. Kazykhanov, and X. Sauvage: Scripta Materialia, 2010, vol. 63, pp. 949–52Google Scholar
  13. 13.
    A. Guinier: Heterogeneities in Solid Solutions, Vol. 9 of Solid State Physics, Elsevier, Amsterdam, 1959, pp. 293–398.Google Scholar
  14. 14.
    Hono K., Satoh T., Hirano K.-I. (1986) Philos. Mag. A 53:495–504CrossRefGoogle Scholar
  15. 15.
    Ringer S.P., Hono K. (2000) Mater. Charact. 44:101–31CrossRefGoogle Scholar
  16. 16.
    Karlik M., Bigot A., Jouffrey B., Auger P., Belliot S. (2004) Ultramicroscopy 98:219–30CrossRefGoogle Scholar
  17. 17.
    J.M. Silcock, T.J. Heal, and H.K. Hardy: J. Inst. Met., 1953–1954, vol. 82, pp. 239–48Google Scholar
  18. 18.
    N.F. Mott and F.R.N. Nabarro: Report on the Strength of Solids , The Physical Society, London, 1948, p. 1.Google Scholar
  19. 19.
    V. Gerold and H. Haberkorn: Phys. Stat. Solidi, 1996, vol. 16, p. 675.Google Scholar
  20. 20.
    G. Knowles and P.M. Kelly: BSC/ISI Conference, Scarborough, The Iron and Steel Institute, London, 1971, p. 9Google Scholar
  21. 21.
    Nembach E. (1983) Phys. Stat. Solidi (a) 78:571–81CrossRefGoogle Scholar
  22. 22.
    Hirsch P. B., Kelly A. (1965) Phil. Mag. 12:881CrossRefGoogle Scholar
  23. 23.
    Kelly A., Nicholson R.B. (1963) Progr. Mater. Sci. 10:151–91CrossRefGoogle Scholar
  24. 24.
    Kelly A., Fine M.E. (1957) Acta Metallurgica 5:365–67CrossRefGoogle Scholar
  25. 25.
    Harkness S.D., Hren J.J. (1970) Metall. Trans. Am. Clin. Climatol. Assoc. 1:43–49Google Scholar
  26. 26.
    L.M. Brown and R.K. Ham: Strengthening Methods in Crystals, Applied Science Publishers, London, 1971, p. 9Google Scholar
  27. 27.
    Eto T. (1980) Scripta Metallurgica 14:133CrossRefGoogle Scholar
  28. 28.
    Muraishi S., Niwa N., Maekawa A., Kumai S., Sato A. (2002) Philos. Mag. A 82:2755–71CrossRefGoogle Scholar
  29. 29.
    Van Swygenhoven H., Derlet P.M. (2001) Phys. Revi. B 64:224105–9CrossRefGoogle Scholar
  30. 30.
    Rao S.I., Parthasarathy T.A., Dimiduk D.M., Hazzledine P.M. (2004) Phil. Mag. 84:3195–15CrossRefGoogle Scholar
  31. 31.
    Dewald M.P., Curtin W.A. (2007) Modell. Simul. Mater. Sci. Eng. 15:193–95CrossRefGoogle Scholar
  32. 32.
    Zhu T., Li J., Samanta A., Kim H.G., Suresh S. (2007) PNAS 104:3031–36CrossRefGoogle Scholar
  33. 33.
    Osetsky Y.N., Bacon D.J. (2003) J. Nucl. Mater. 323:268–80CrossRefGoogle Scholar
  34. 34.
    Kohler C., Kizler P., Schmauder S. (2005) Model. Simul. Mater. Sci. Eng. 13:35–45CrossRefGoogle Scholar
  35. 35.
    Shim J.-H., Cho Y.W., Kwon S.C., Kim W.W., Wirth B.D. (2007) Appl. Phys. Lett. 90:021906CrossRefGoogle Scholar
  36. 36.
    Terentyev D., Bonny G., Malerba L. (2008) Acta Materialia 56:3229–35Google Scholar
  37. 37.
    Takahashi A., Ghoniem N.M. (2008) J. Mech. Phys. Solids 56:1534–53CrossRefGoogle Scholar
  38. 38.
    Singh C.V., Warner D.H. (2010) Acta Materialia 58:5797–5805Google Scholar
  39. 39.
    Singh C.V., Mateos A., Warner D.H. (2011) Scripta Materialia 64:398–401CrossRefGoogle Scholar
  40. 40.
    D.J. Bacon, Y.N. Osetsky, and D. Rodney: Dislocation-Obstacle Interactions at the Atomic Level, vol. 15, chap. 88, pp. 1–90, 2009Google Scholar
  41. 41.
    Shercliff H., Ashby M. (1990) Acta Metallurgica et Materialia 38:1789–1802CrossRefGoogle Scholar
  42. 42.
    Schmauder S., Binkele P. (2002) Comput. Mater. Sci. 24:42–53CrossRefGoogle Scholar
  43. 43.
    Starink M.J., Gao N., Davin L., Yan J., Cerezo A. (2005) Phil. Mag. 85:1395–17CrossRefGoogle Scholar
  44. 44.
    G.E. Dieter: Mechanical Metallurgy, Materials Science and Engineering, 3rd ed., McGraw-Hill, New York, 1986Google Scholar
  45. 45.
    D. Hull and D. Bacon: Introduction to Dislocations, 4th edn., Butterworth-Heinemann, London, 2001Google Scholar
  46. 46.
    Kelchner C., Plimpton S., Hamilton J. (1998) Phys. Rev. B 58:11085–88CrossRefGoogle Scholar
  47. 47.
    Li J. (2003) Modell. Simul. Mater. Sci. Eng. 11:173–77CrossRefGoogle Scholar
  48. 48.
    Friedel J. (1956) Les Dislocations. Gauthier-Villars, Paris, FranceGoogle Scholar
  49. 49.
    Orowan E. (1984) Symposium on Internal Stresses in Metals and Alloys. Institute of Metals, LondonGoogle Scholar
  50. 50.
    Bacon D.J., Kocks U.F., Scattergood R.O. (1973) Phil. Mag. 28:1241–63CrossRefGoogle Scholar
  51. 51.
    Hirsch P.B. (1957) J. Inst. Met. 86:13–14Google Scholar
  52. 52.
    T. Hatano: Phys. Rev. B, 2006, vol. 74, pp. 020102+Google Scholar
  53. 53.
    Humphreys F.J., Hirsch P.B. (1970) Proc. R. Soc. Lond. A 318:73–92CrossRefGoogle Scholar
  54. 54.
    Leyson G.P., Curtin W.A., Hector L.G., Woodward C.F. (2010) Nat. Mater. 9:750–55CrossRefGoogle Scholar
  55. 55.
    Labusch R. (1970) Phys. Stat. Solidi (b) 41:659–69CrossRefGoogle Scholar
  56. 56.
    Labusch R. (1972) Acta Metallurgica 20:917–27CrossRefGoogle Scholar
  57. 57.
    Apostol F., Mishin Y. (2011) Phys. Rev. B 83:054116CrossRefGoogle Scholar
  58. 58.
    Olmsted D., Hectorjr L., Curtin W. (2006) J. Mech. Phys. Solids 4:1763–88CrossRefGoogle Scholar
  59. 59.
    olverton C., Ozolins V. (2006) Phys. Revi. B 73:144104CrossRefGoogle Scholar
  60. 60.
    Diak B., Saimoto S. (1997) Mater. Sci. Eng. A 234-236:1019–22Google Scholar
  61. 61.
    Mousa S.A., Bozarth J., Youssef A., Levine B., Diak B.J., Upadhyaya K.R., Saimoto S. (1998) Prog. Mater Sci. 43:223–63CrossRefGoogle Scholar
  62. 62.
    Foreman A.J.E., Makin M.J. (1967) Canad. J. Phys. 45:511–17CrossRefGoogle Scholar
  63. 63.
    T. Nogaret and D. Rodney: Phys. Rev. B, 2006, vol. 74, pp. 134110+.Google Scholar
  64. 64.
    Z. Xu and R.C. Picu: Phys. Rev. B, 2007, vol. 76, pp. 094112+.Google Scholar
  65. 65.
    Dong Y., Nogaret T., Curtin W.A. (2010) Metall. Mater. Trans. A 41:1954–60CrossRefGoogle Scholar
  66. 66.
    Binkele P., Schmauder S. (2003) Z. Metallkd 94:858–63Google Scholar
  67. 67.
    Taylor G.I. (1938) J. Inst. Met. 62:307–24Google Scholar
  68. 68.
    G.I. Taylor: Proceedings of the Colloquium on Deformation and Flow of Solids (Madrid, 1955), Springer, Berlin, 1956, pp. 3–12Google Scholar
  69. 69.
    Stoller R.E., Zinkle S.J. (2000) J. Nucl. Mater. 283-287:349–52CrossRefGoogle Scholar
  70. 70.
    Wang J., Wolverton C., Muller S., Liu Z., Chen L. (2005) Acta Materialia 53:2759–64CrossRefGoogle Scholar
  71. 71.
    Avrami M. (1939) J. Chem. Phys. 7:1103–12CrossRefGoogle Scholar
  72. 72.
    J. Christian: The Theory of Phase Transformations in Metals and Alloys, Pergamon Press, Oxford, 3rd edn., 2002Google Scholar
  73. 73.
    Hornbogen E. (1967) Aluminum 43:115–21Google Scholar
  74. 74.
    Massalski T. (1980) J. Phase Equilib. 1:27–33Google Scholar
  75. 75.
    Wagner C. (1961) Z. Elektrochem. 65:581–91Google Scholar
  76. 76.
    Nie J.F., Muddle B.C., Polmear I.J. (1996) Mater. Sci. Forum 217-222:1257–62CrossRefGoogle Scholar
  77. 77.
    J. Yan: Ph.D. Thesis, School of Engineering Sciences, University of Southampton, 2006Google Scholar
  78. 78.
    Starink M. (2004) Int. Mater. Rev. 49:191–26CrossRefGoogle Scholar
  79. 79.
    J. W. Martin: Precipitation Hardening, Butterworth-Heinemann, London, 2nd edn., 1998Google Scholar
  80. 80.
    Badini C., Marino F., Verne E. (1995) Mater. Sci. Eng. A 191:185–91CrossRefGoogle Scholar
  81. 81.
    Smith G. (1998) Thermochim. Acta 317:7–23CrossRefGoogle Scholar
  82. 82.
    Bassani P., Gariboldi E., Vimercati G. (2007) J. Therm. Anal. Calorim. 87:247–53CrossRefGoogle Scholar
  83. 83.
    Ardell A. (1985) Metall. Trans. A 16A:2131–65Google Scholar
  84. 84.
    Argon A. (2007) Strengthening Mechanisms in Crystal Plasticity (Oxford Series on Materials Modelling). Oxford University Press, OxfordCrossRefGoogle Scholar
  85. 85.
    T. Hatano and H. Matsui: Phys. Rev. B, 2005, vol. 72, pp. 094105+Google Scholar
  86. 86.
    Ney H., Labusch R., Haasen P. (1977) Acta Metallurgica 25:1257–69CrossRefGoogle Scholar
  87. 87.
    Olmsted D.L., Hector Jr. L.G., Curtin W., Clifton R. (2005) Modell. Simul. Mater. Sci. Eng. 13:371–88CrossRefGoogle Scholar
  88. 88.
    Hirth J., Lothe J. (1968) Theory of Dislocations. McGraw-Hill, New YorkGoogle Scholar
  89. 89.
    Nguyen L., Baker K., Warner D. (2011) Phys. Rev. B, 2011 84:024118CrossRefGoogle Scholar
  90. 90.
    Warner D.H., Curtin W.A., Qu S. (2007) Nat. Mat. 6:876–81CrossRefGoogle Scholar
  91. 91.
    Warner D., Curtin W. (2009) Acta Materialia 57:4267–77CrossRefGoogle Scholar
  92. 92.
    Trinkle D.R., Woodward C. (2005) Science 310:1665–67CrossRefGoogle Scholar
  93. 93.
    Plimpton S.J. (1995) J. Comp. Phys. 117:1–19CrossRefGoogle Scholar
  94. 94.
    M. S. Daw and M. I. Baskes: Phys. Rev. B, 1984, vol. 29, pp. 6443–53Google Scholar
  95. 95.
    Mishin Y., Mehl M., Papaconstantopoulos D. (2005) Acta Materialia 53:4029–41CrossRefGoogle Scholar
  96. 96.
    E. Nembach and G. Neite: Prog. Mat. Sci., 1985, vol. 29, pp. 177–319CrossRefGoogle Scholar

Copyright information

© The Minerals, Metals & Materials Society and ASM International 2013

Authors and Affiliations

  1. 1.Department of Materials Science and EngineeringUniversity of TorontoTorontoCanada
  2. 2.School of Civil and Environmental EngineeringCornell UniversityIthacaUSA

Personalised recommendations