Metals and Materials International

, Volume 25, Issue 1, pp 159–167 | Cite as

Modeling the Anisotropic Flow Behavior of Precipitate-Hardened Al–Cu Alloys During Plane Strain Compression

  • Nozar AnjabinEmail author


In this study, the effects of plate-shaped precipitates on the mechanical properties and plastic anisotropy of Al–Cu alloys during plane strain loading were investigated. The modified aging kinetics model of Shercliff and Ashby was used to obtain the precipitate size and volume fraction after different schedules of aging treatment. An explicit term, named as weighting function was obtained based on the elastic inclusion model for the directional dependency of strengthening developed by non-shearable plate shape precipitates during plane strain compression. This orientation dependent term was used along with the precipitate features obtained from the kinetics model, and dislocation density varying during deformation, to calculate the slip system strength. Also, a Kocks–Mecking type dislocation evolution model of single phase materials was modified to assess the anisotropic influence of non-shearable precipitates on the flow behavior of age hardenable alloy. The proposed model is validated by comparing the modeling results for precipitates size, precipitates volume fraction and stress–strain curves under different aging conditions, with that of experiments. It is found that the presence of non-shearable precipitates can reduce crystallography anisotropy, in fact, the weak orientations are strengthened more by precipitates than hard orientations. The developed model can be applied to single crystals and also textured polycrystals.


Al–Cu alloys Aging kinetics Flow anisotropy Taylor–Bishop–Hill analysis 


  1. 1.
    W.F. Smith, Structure and Properties of Engineering Alloy (McGraw-Hill Publishing Company, New York City, 1981)Google Scholar
  2. 2.
    O.R. Myhr, Q. Grong, K.O. Pedersen, Metall. Mater. Trans. A 41, 2276 (2010)CrossRefGoogle Scholar
  3. 3.
    N. Anjabin, A. Karimi Taheri, H.S. Kim, Metall. Mater. Trans. A 44, 5853 (2013)CrossRefGoogle Scholar
  4. 4.
    G. Fribourg, Y. Brechet, A. Deschamps, A. Simar, Acta Mater. 59, 3621 (2011)CrossRefGoogle Scholar
  5. 5.
    A. Biswas, D.J. Siegel, C. Wolverton, D.N. Seidman, Acta Mater. 59, 6187 (2011)CrossRefGoogle Scholar
  6. 6.
    G.F. Vander Voort, Metallography and Microstructures, vol. 9 (ASM Handbook, Materials Park, 2004)CrossRefGoogle Scholar
  7. 7.
    J.F. Nie, B.C. Muddle, Acta Mater. 56, 3490 (2008)CrossRefGoogle Scholar
  8. 8.
    H. Liu, B. Bellon, J. Llorca, Acta Mater. 132, 611 (2017)CrossRefGoogle Scholar
  9. 9.
    F. Barlat, J. Liu, J.C. Brem, Model. Simul. Mater. Sci. Eng. 8, 435 (2008)CrossRefGoogle Scholar
  10. 10.
    C.S. Han, R.H. Wagoner, F. Barlat, Int. J. Plast. 20, 477 (2004)CrossRefGoogle Scholar
  11. 11.
    H. Sehitoglu, T. Foglesong, H.J. Maier, Metall. Mater. Trans. A 36, 1 (2005)CrossRefGoogle Scholar
  12. 12.
    F. Barlat, J. Liu, J.C. Brem, Model. Simul. Mater. Sci. Eng. 8, 435 (2000)CrossRefGoogle Scholar
  13. 13.
    W.F. Hosford, R.H. Zeisloft, Metall. Trans. A 3, 113 (1972)CrossRefGoogle Scholar
  14. 14.
    P. Bate, W.T. Roberts, D.V. Wilson, Acta Metall. 22, 1797 (1981)CrossRefGoogle Scholar
  15. 15.
    F. Roters, P. Eisenlohr, T.R. Bieler, D. Raabe, Crystal Plasticity Finite Element Methods in Materials Science and Engineering (Wiley-VCH, Hoboken, 2010)CrossRefGoogle Scholar
  16. 16.
    M.T. Lyttle, J.A. Wert, Metall. Mater. Trans. A 30, 1283 (1999)CrossRefGoogle Scholar
  17. 17.
    H. Hargarter, M.T. Lyttle, E.A. Starke, Mater. Sci. Eng., A 257, 87 (1998)CrossRefGoogle Scholar
  18. 18.
    S. Mishra, M. Yadava, K. Kulkarni, N.P. Gurao, Mater. Sci. Eng., A 699, 217 (2017)CrossRefGoogle Scholar
  19. 19.
    H.R. Shercliff, M.F. Ashby, Acta Metall. Mater. 38, 1789 (1990)CrossRefGoogle Scholar
  20. 20.
    S. Esmaeili, D.J. Lloyd, W.J. Poole, Acta Mater. 51, 2243 (2003)CrossRefGoogle Scholar
  21. 21.
    G. Liu, G.J. Zhang, X.D. Ding, J. Sun, K.H. Chen, Mater. Sci. Eng., A 344, 113 (2003)CrossRefGoogle Scholar
  22. 22.
    O.R. Myhr, Q. Grong, S.J. Andersen, Acta Mater. 49, 65 (2001)CrossRefGoogle Scholar
  23. 23.
    O.R. Myhr, Q. Grong, H.G. Fjaer, C.D. Marioara, Acta Mater. 52, 4997 (2004)CrossRefGoogle Scholar
  24. 24.
    L.M. Cheng, W.J. Poole, J.D. Embury, D.J. Lloyd, Metall. Mater. Trans. A 34, 2473 (2003)CrossRefGoogle Scholar
  25. 25.
    A. Simar, Y. Brechet, D.B. Meester, A. Denquin, T. Pardoen, Acta Mater. 55, 6133 (2007)CrossRefGoogle Scholar
  26. 26.
    N. Anjabin, A. Karimi Taheri, H.S. Kim, Comput. Mater. Sci. 83, 78 (2014)CrossRefGoogle Scholar
  27. 27.
    J.C. Teixeira, L. Bourgeois, C.W. Sinclair, C.R. Hutchinson, Acta Mater. 57, 6075 (2009)CrossRefGoogle Scholar
  28. 28.
    W.F. Hosford, Acta Metall. 14, 1085 (1966)CrossRefGoogle Scholar
  29. 29.
    N. Anjabin, A. Karimi Taheri, Mater. Sci. Tech. 29, 968 (2013)CrossRefGoogle Scholar
  30. 30.
    L.M. Brown, D.R. Clarke, Acta Metall. 23, 821 (1975)CrossRefGoogle Scholar
  31. 31.
    T. Mura, Micromechanics of Defects in Solids (Dordrecht Publishers, Dordrecht, 1987)CrossRefGoogle Scholar
  32. 32.
    Y. Estrin, J. Mater. Proc. Tech. 80, 33 (1998)CrossRefGoogle Scholar
  33. 33.
    S. Gouttebroze, A. Mo, Q. Grong, K.O. Pedersen, H.G. Fjaer, Metall. Mater. Trans. A 39, 522 (2008)CrossRefGoogle Scholar
  34. 34.
    H. Mecking, U.F. Kocks, Acta Metall. 29, 1865 (1981)CrossRefGoogle Scholar
  35. 35.
    W.H. Hosford, The Mechanics of Crystals and Textured Polycrystals (Oxford University Press, Oxford, 1994)Google Scholar

Copyright information

© The Korean Institute of Metals and Materials 2018

Authors and Affiliations

  1. 1.Department of Materials Science and Engineering, School of EngineeringShiraz UniversityShirazIran

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