Skip to main content
SpringerLink
Log in

Improved dislocation density-based models for describing hot deformation behaviors of a Ni-based superalloy

  • Articles
  • Published:
Journal of Materials Research Aims and scope Submit manuscript

Abstract

Generally, the obvious work hardening, dynamic recrystallization (DRX), and dynamic recovery behaviors can be found during hot deformation of Ni-based superalloys. In the present study, the classical dislocation density theory is improved by introducing a new dislocation annihilation item to represent the influences of DRX on dislocation density evolution for a Ni-based superalloy. Based on the improved dislocation density theory, the peak strain corresponding to peak stress and the critical strain for initiating DRX can be determined, and the improved DRX kinetics equations and grain size evolution models are developed. The physical framework and algorithmic idea of the improved dislocation density theory are clarified. Moreover, the deformed microstructures are characterized and quantitatively correlated to validate the improved dislocation density theory. It is found that the improved dislocation density-based models can precisely characterize hot deformation and DRX behaviors for the studied superalloy under the tested conditions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

FIG. 1
FIG. 2
FIG. 3
FIG. 4
FIG. 5
FIG. 6
FIG. 7
FIG. 8
FIG. 9
FIG. 10

Similar content being viewed by others

References

  1. Y.C. Lin and X.M. Chen: A critical review of experimental results and constitutive descriptions for metals and alloys in hot working. Mater. Des. 32, 1733 (2011).

    CAS  Google Scholar 

  2. Y.C. Lin, D.X. Wen, Y.C. Huang, X.M. Chen, and X.W. Chen: A unified physically based constitutive model for describing strain hardening effect and dynamic recovery behavior of a Ni-based superalloy. J. Mater. Res. 30, 3784 (2015).

    CAS  Google Scholar 

  3. H.Q. Liang, H.Z. Guo, Y.Q. Ning, X.N. Peng, C. Qin, Z.F. Shi, and Y. Nan: Dynamic recrystallization behavior of Ti–5Al–5Mo–5V–1Cr–1Fe alloy. Mater. Des. 63, 798 (2015).

    Google Scholar 

  4. G.Z. Quan, W.Q. Lv, Y.P. Mao, Y.W. Zhang, and J. Zhou: Prediction of flow stress in a wide temperature range involving phase transformation for as-cast Ti–6Al–2Zr–1Mo–1V alloy by artificial neural network. Mater. Des. 50, 51 (2013).

    CAS  Google Scholar 

  5. M.H. Maghsoudi, A. Zarei-Hanzaki, P. Changizian, and A. Marandi: Metadynamic recrystallization behavior of AZ61 magnesium alloy. Mater. Des. 57, 487 (2014).

    CAS  Google Scholar 

  6. Y.H. Liu, Y.Q. Ning, Z.K. Yao, and M.W. Fu: Hot deformation behavior of the 1.15C–4.00Cr–3.00V–6.00W–5.00Mo powder metallurgy high speed steel. Mater. Des. 54, 854 (2014).

    CAS  Google Scholar 

  7. A. Momeni, G.R. Ebrahimi, and H.R. Faridi: Effect of chemical composition and processing variables on the hot flow behavior of leaded brass alloys. Mater. Sci. Eng., A 626, 1 (2015).

    CAS  Google Scholar 

  8. G.Z. Quan, Y.P. Mao, G.S. Li, W.Q. Lv, Y. Wang, and J. Zhou: A characterization for the dynamic recrystallization kinetics of as-extruded 7075 aluminum alloy based on true stress–strain curves. Comput. Mater. Sci. 55, 65 (2012).

    CAS  Google Scholar 

  9. S. Serajzadeh, S. Ranjbar Motlagh, S.M.H. Mirbagheri, and J.M. Akhgar: Deformation behavior of AA2017-SiCp in warm and hot deformation regions. Mater. Des. 67, 318 (2015).

    CAS  Google Scholar 

  10. T. Sakai, A. Belyakov, R. Kaibyshev, H. Miura, and J.J. Jonas: Dynamic and post-dynamic recrystallization under hot cold and severe plastic deformation conditions. Prog. Mater. Sci. 60, 130 (2014).

    CAS  Google Scholar 

  11. L. Gambirasio and E. Rizzi: An enhanced Johnson–Cook strength model for splitting strain rate and temperature effects on lower yield stress and plastic flow. Comput. Mater. Sci. 113, 231 (2016).

    Google Scholar 

  12. A.R. Abbasi-Bani, A. Zarei-Hanzaki, M.H. Pishbin, and N. Haghdadi: A comparative study on the capability of Johnson–Cook and Arrhenius-type constitutive equations to describe the flow behavior of Mg–6Al–1Zn alloy. Mech. Mater. 71, 52 (2014).

    Google Scholar 

  13. Y.C. Lin, M.S. Chen, and J. Zhong: Constitutive modeling for elevated temperature flow behavior of 42CrMo steel. Comput. Mater. Sci. 42, 470 (2008).

    CAS  Google Scholar 

  14. Y.C. Lin, D.X. Wen, J. Deng, G. Liu, and J. Chen: Constitutive models for high-temperature flow behaviors of a Ni-based superalloy. Mater. Des. 59, 115 (2014).

    CAS  Google Scholar 

  15. R. Bobbili, A. Paman, and V. Madhu: High strain rate tensile behavior of Al–4.8Cu–1.2Mg alloy. Mater. Sci. Eng., A 651, 753 (2016).

    CAS  Google Scholar 

  16. L. Chen, G.Q. Zhao, and J.Q. Yu: Hot deformation behavior and constitutive modeling of homogenized 6026 aluminum alloy. Mater. Des. 75, 57 (2015).

    Google Scholar 

  17. D. Trimble and G.E. O’Donnell: Constitutive modelling for elevated temperature flow behaviour of AA7075. Mater. Des. 76, 150 (2015).

    CAS  Google Scholar 

  18. D.M. Collins and H.J. Stone: A modelling approach to yield strength optimisation in a nickel–base superalloy. Int. J. Plast. 54, 96 (2014).

    CAS  Google Scholar 

  19. L.T. Li, Y.C. Lin, L. Li, L.M. Shen, and D.X. Wen: Three-dimensional crystal plasticity finite element simulation of hot compressive deformation behaviors of 7075 Al alloy. J. Mater. Eng. Perform. 24, 1294 (2015).

    CAS  Google Scholar 

  20. A. He, G.L. Xie, X.Y. Yang, X.T. Wang, and H.L. Zhang: A physically-based constitutive model for a nitrogen alloyed ultralow carbon stainless steel. Comput. Mater. Sci. 98, 64 (2015).

    CAS  Google Scholar 

  21. Y.H. Liu, Y.Q. Ning, Y. Nan, H.Q. Liang, Y. Li, and Z.L. Zhao: Characterization of hot deformation behavior and processing map of FGH4096–GH4133B dual alloys. J. Alloys Compd. 633, 505 (2015).

    CAS  Google Scholar 

  22. C. Zhang, L.W. Zhang, M.F. Li, W.F. Shen, and S.D. Gu: Effects of microstructure and γ′ distribution on the hot deformation behavior for a powder metallurgy superalloy FGH96. J. Mater. Res. 29, 2799 (2014).

    CAS  Google Scholar 

  23. Y.C. Lin, X.Y. Wu, X.M. Chen, J. Chen, D.X. Wen, J.L. Zhang, and L.T. Li: EBSD study of a hot deformed nickel-based superalloy. J. Alloys Compd. 640, 101 (2015).

    CAS  Google Scholar 

  24. D.X. Wen, Y.C. Lin, J. Chen, X.M. Chen, J.L. Zhang, Y.J. Liang, and L.T. Li: Work-hardening behaviors of typical solution–treated and aged Ni-based superalloys during hot deformation. J. Alloys Compd. 618, 372 (2015).

    CAS  Google Scholar 

  25. J.B. Le Graverend, J. Cormier, F. Gallerneau, P. Villechaise, S. Kruch, and J. Mendez: A microstructure-sensitive constitutive modeling of the inelastic behavior of single crystal nickel-based superalloys at very high temperature. Int. J. Plast. 59, 55 (2014).

    Google Scholar 

  26. F.M. Shore, M. Morakabati, S.M. Abbasi, A. Momeni, and R. Mahdavi: Hot ductility of Incoloy 901 produced by vacuum arc remelting. ISIJ Int. 54, 1353 (2014).

    Google Scholar 

  27. H.B. Zhang, K.F. Zhang, S.S. Jiang, and Z. Lu: The dynamic recrystallization evolution and kinetics of Ni–18.3Cr–6.4Co–5.9W–4Mo–2.19Al–1.16Ti superalloy during hot deformation. J. Mater. Res. 30, 1029 (2015).

    CAS  Google Scholar 

  28. S.S. Satheesh Kumar, T. Raghu, P.P. Bhattacharjee, G. Appa Rao, and U. Borah: Constitutive modeling for predicting peak stress characteristics during hot deformation of hot isostatically processed nickel-base superalloy. J. Mater. Sci. 50, 6444 (2015).

    CAS  Google Scholar 

  29. M. Fisk, J.C. Ion, and L.E. Lindgren: Flow stress model for IN718 accounting for evolution of strengthening precipitates during thermal treatment. Comput. Mater. Sci. 82, 531 (2014).

    CAS  Google Scholar 

  30. Y. Bergström: A dislocation model for the stress-strain behaviour of polycrystalline α-Fe with special emphasis on the variation of the densities of mobile and immobile dislocations. Mater. Sci. Eng. 5, 193 (1970).

    Google Scholar 

  31. Y. Bergström: The plastic deformation of metals—A dislocation model and its applicability. Rev. Powder Metall. Phys. Ceram. 2, 79 (1983).

    Google Scholar 

  32. U.F. Kocks and H. Mecking: Physics and phenomenology of strain hardening: The FCC case. Prog. Mater. Sci. 48, 171 (2003).

    CAS  Google Scholar 

  33. H. Mecking and U.F. Kocks: Kinetics of flow and strain-hardening. Acta Metall. 29, 1865 (1981).

    CAS  Google Scholar 

  34. M. Bambach, S. Heppner, D. Steinmetz, and F. Roters: Assessing and ensuring parameter identifiability for a physically-based strain hardening model for twinning-induced plasticity. Mech. Mater. 84, 127 (2015).

    Google Scholar 

  35. Y. Estrin, L.S. Tóth, A. Molinari, and Y. Bréchet: A dislocation-based model for all hardening stages in large strain deformation. Acta Mater. 46, 5509 (1998).

    CAS  Google Scholar 

  36. E.I. Galindo-Nava and P.E.J. Rivera-Díaz-del-Castillo: Thermostatistical modelling of hot deformation in FCC metals. Int. J. Plast. 47, 202 (2013).

    CAS  Google Scholar 

  37. Y. Estrin, A. Molotnikov, C. Davies, and R. Lapovok: Strain gradient plasticity modelling of high-pressure torsion. J. Mech. Phys. Solids 56, 1186 (2008).

    CAS  Google Scholar 

  38. E. Hug, P.A. Dubos, C. Keller, L. Duchêne, and A.M. Habraken: Size effects and temperature dependence on strain-hardening mechanisms in some face centered cubic materials. Mech. Mater. 91, 136 (2015).

    Google Scholar 

  39. Y.Q. Ning, X. Luo, H.Q. Liang, H.Z. Guo, J.L. Zhang, and K. Tan: Competition between dynamic recovery and recrystallization during hot deformation for TC18 titanium alloy. Mater. Sci. Eng., A 635, 77 (2015).

    CAS  Google Scholar 

  40. D. Wedberg and L.E. Lindgren: Modelling flow stress of AISI 316L at high strain rates. Mech. Mater. 91, 194 (2015).

    Google Scholar 

  41. T. Csanádi, N.Q. Chinh, J. Gubicza, G. Vörös, and T.G. Langdon: Characterization of stress-strain relationships in Al over a wide range of testing temperatures. Int. J. Plast. 54, 178 (2014).

    Google Scholar 

  42. P. Shanthraj and M.A. Zikry: Dislocation density evolution and interactions in crystalline materials. Acta Mater. 59, 7695 (2011).

    CAS  Google Scholar 

  43. H.S. Leung, P.S.S. Leung, B. Cheng, and A.H.W. Ngan: A new dislocation-density-function dynamics scheme for computational crystal plasticity by explicit consideration of dislocation elastic interactions. Int. J. Plast. 67, 1 (2015).

    CAS  Google Scholar 

  44. B. Babu and L.E. Lindgren: Dislocation density based model for plastic deformation and globularization of Ti–6Al–4V. Int. J. Plast. 50, 94 (2013).

    CAS  Google Scholar 

  45. E.D. Cyr, M. Mohammadi, R.K. Mishra, and K. Inal: A three dimensional (3D) thermos-elasto-viscoplastic constitutive model for fcc polycrystals. Int. J. Plast. 70, 166 (2015).

    CAS  Google Scholar 

  46. M. Borodachenkova, F. Barlat, W. Wen, A. Bastos, and J.J. Grácio: A microstructure-based model for describing the material properties of Al–Zn alloys during high pressure torsion. Int. J. Plast. 68, 150 (2015).

    CAS  Google Scholar 

  47. A. Marandi, R. Zarei-Hanzaki, A. Zarei-Hanzaki, and H.R. Abedi: Dynamic recrystallization behavior of new transformation–twinning induced plasticity steel. Mater. Sci. Eng., A 607, 397 (2014).

    CAS  Google Scholar 

  48. H.Q. Liang and H.Z. Guo: The integrated influence on hot deformation of dual-phase titanium alloys incorporating dynamic recrystallization evolution and α/β phase transformation. Mater. Lett. 151, 57 (2015).

    CAS  Google Scholar 

  49. H.B. Zhang, K.F. Zhang, H.P. Zhou, Z. Lu, C.H. Zhao, and X.L. Yang: Effect of strain rate on microstructure evolution of a nickel-based superalloy during hot deformation. Mater. Des. 80, 51 (2015).

    CAS  Google Scholar 

  50. Y. Estrin and H. Mecking: A unified phenomenological description of work hardening and creep based on one-parameter models. Acta Metall. 32, 57 (1984).

    Google Scholar 

  51. G. Engberg and L. Lissel: A physically based microstructure model for predicting the microstructural evolution of a C–Mn steel during and after hot deformation. Steel Res. Int. 79, 47 (2008).

    CAS  Google Scholar 

  52. H.W. Li, C. Wu, and H. Yang: Crystal plasticity modeling of the dynamic recrystallization of two-phase titanium alloys during isothermal processing. Int. J. Plast. 51, 271 (2013).

    CAS  Google Scholar 

  53. R. Ding and Z.X. Guo: Coupled quantitative simulation of microstructural evolution and plastic flow during dynamic recrystallization. Acta Mater. 49, 3163 (2001).

    CAS  Google Scholar 

  54. E. Popova, Y. Staraselski, A. Brahme, R.K. Mishra, and K. Inal: Coupled crystal plasticity-probabilistic cellular automata approach to model dynamic recrystallization in magnesium alloys. Int. J. Plast. 66, 85 (2015).

    CAS  Google Scholar 

  55. T. Takaki, C. Yoshimoto, A. Yamanaka, and Y. Tomita: Multiscale modeling of hot-working with dynamic recrystallization by coupling microstructure evolution and macroscopic mechanical behavior. Int. J. Plast. 52, 105 (2014).

    Google Scholar 

  56. Y.C. Lin, Y.X. Liu, M.S. Chen, M.H. Huang, X. Ma, and Z.L. Long: Study of static recrystallization behavior in hot deformed Ni-based superalloy using cellular automaton model. Mater. Des. 99, 107 (2016).

    CAS  Google Scholar 

  57. Y. Estrin: Dislocation-density-related constitutive modeling. In Unified Constitutive Laws of Plastic Deformation, A.S. Krausz and K. Krausz, eds. (San Diego: Academic Press, 1996); p. 69.

    Google Scholar 

  58. L.E. Lindgren, K. Domkin, and S. Hansson: Dislocations, vacancies and solute diffusion in physical based plasticity model for AISI 316L. Mech. Mater. 40, 907 (2008).

    Google Scholar 

  59. H. Mecking, U.F. Kocks, and C. Hartig: Taylor factors in materials with many deformation modes. Scr. Mater. 35, 465 (1996).

    CAS  Google Scholar 

  60. Y.X. Liu, Y.C. Lin, H.B. Li, D.X. Wen, X.M. Chen, and M.S. Chen: Study of dynamic recrystallization in a Ni-based superalloy by experiments and cellular automaton model. Mater. Sci. Eng., A 626, 432 (2015).

    CAS  Google Scholar 

  61. D.X. Wen, Y.C. Lin, J. Chen, J. Deng, X.M. Chen, J.L. Zhang, and M. He: Effects of initial aging time on processing map and microstructures of a nickel-based superalloy. Mater. Sci. Eng., A 620, 319 (2015).

    Google Scholar 

  62. Y.C. Lin, X.M. Chen, D.X. Wen, and M.S. Chen: A physically-based constitutive model for a typical nickel-based superalloy. Comput. Mater. Sci. 83, 282 (2014).

    CAS  Google Scholar 

  63. E.I. Galindo-Nava and P.E.J. Rivera-Díaz-del-Castillo: A thermostatistical theory of low and high temperature deformation in metals. Mater. Sci. Eng., A 543, 110 (2012).

    CAS  Google Scholar 

  64. D.X. Wen, Y.C. Lin, H.B. Li, X.M. Chen, J. Deng, and L.T. Li: Hot deformation behavior and processing map of a typical Ni-based superalloy. Mater. Sci. Eng., A 591, 183 (2014).

    CAS  Google Scholar 

  65. A. Laasraoui and J.J. Jonas: Prediction of steel flow stresses at high temperatures and strain rates. Metall. Trans. A 22, 1545 (1991).

    Google Scholar 

  66. E.I. Galindo-Nava and P.E.J. Rivera-Díaz-del-Castillo: A thermodynamic theory for dislocation cell formation and misorientation in metals. Acta Mater. 60, 4370 (2012).

    CAS  Google Scholar 

  67. E.O. Hall: The deformation and ageing of mild steel: III discussion of results. Proc. Phys. Soc. B 64, 747 (1951).

    Google Scholar 

  68. F. Chen, Z.S. Cui, J. Liu, W. Chen, and S.J. Chen: Mesoscale simulation of the high–temperature austenitizing and dynamic recrystallization by coupling a cellular automaton with a topology deformation technique. Mater. Sci. Eng., A 527, 5539 (2010).

    Google Scholar 

  69. B. Derby: The dependence of grain size on stress during dynamic recrystallization. Acta Metall. Mater. 39, 955 (1991).

    CAS  Google Scholar 

  70. G.A. Henshall, M.E. Kassner, and H.J. McQueen: Dynamic restoration mechanisms in Al-5.8 At. Pct Mg deformed to large strains in the solute drag regime. Metall. Trans. A 23, 881 (1992).

    Google Scholar 

  71. M. Fukuhara and A. Sanpei: Elastic moduli and internal frictions of Inconel 718 and Ti–6Al–4V as a function of temperature. J. Mater. Sci. Lett. 12, 1122 (1993).

    CAS  Google Scholar 

  72. H.J. Frost and M.F. Ashby: Deformation Mechanism Maps: The Plasticity and Creep of Metals and Ceramics, 1st ed. (Pergamon Press, Oxford, 1982); p. 20.

    Google Scholar 

Download references

ACKNOWLEDGMENTS

This work was supported by the National Natural Science Foundation Council of China (Grant Nos. 51375502, 51305466), the National Key Basic Research Program (Grant No. 2013CB035801), the Project of Innovation-driven Plan in Central South University (Grant No. 2016CX008), and the Natural Science Foundation for Distinguished Young Scholars of Hunan Province (Grant No. 2016JJ1017).

Author information

Authors and Affiliations

  1. School of Mechanical and Electrical Engineering, Central South University, Changsha, Hunan Province, 410083, China

    Y. C. Lin, Dong-Xu Wen, Ming-Song Chen, Yan-Xing Liu & Xiao-Min Chen

  2. Light Alloy Research Institute of Central South University, Changsha, Hunan Province, 410083, China

    Y. C. Lin, Dong-Xu Wen, Ming-Song Chen, Yan-Xing Liu & Xiao-Min Chen

  3. State Key Laboratory of High Performance Complex Manufacturing, Changsha, Hunan Province, 410083, China

    Y. C. Lin

  4. SINTEF Materials and Chemistry, Blindern, 0314, Oslo, Norway

    Xiang Ma

Authors
  1. Y. C. Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dong-Xu Wen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ming-Song Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yan-Xing Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Xiao-Min Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Xiang Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Y. C. Lin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lin, Y.C., Wen, DX., Chen, MS. et al. Improved dislocation density-based models for describing hot deformation behaviors of a Ni-based superalloy. Journal of Materials Research 31, 2415–2429 (2016). https://doi.org/10.1557/jmr.2016.220

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1557/jmr.2016.220

Search

Navigation