A Crystal-Plasticity Cyclic Constitutive Model for the Ratchetting of Polycrystalline Material Considering Dislocation Substructures

  • Xuehong Ren
  • Shaopu YangEmail author
  • Guilin Wen
  • Wenjie Zhao


A crystal-plasticity cyclic constitutive model of polycrystalline material considering intra-granular heterogeneous dislocation substructures, in terms of three dislocation categories: mobile dislocations, immobile dislocations in the cell interiors and in the cell walls, is proposed based on the existing microscopic and macroscopic experimental results. The multiplication, annihilation, rearrangement and immobilization of dislocations on each slip system are taken as the basic evolutionary mechanism of the three dislocation categories, and the cross-slip of screw dislocations is viewed as the dynamic recovery mechanism at room temperature. The slip resistance associated with the isotropic hardening rule results from the interactions of dislocations on the slip systems. Meanwhile, a modified nonlinear kinematic hardening rule and a rate-dependent flow rule at the slip system level are employed to improve the predictive capability of the model for ratchetting deformation. The predictive ability of the developed model to uniaxial and multiaxial ratchetting in macroscopic scale is verified by comparing with the experimental results of polycrystalline 316L stainless steel. The ratchetting in intra-granular scale which is obviously dependent on the crystallographic orientation and stress levels can be reasonably predicted by the proposed model.


Ratchetting Dislocation substructures Crystal plasticity Polycrystalline materials Constitutive model 



This research is supported by the National Natural Science Foundation of China (11790282, U1534204, 11472179) and the Natural Science Foundation of Hebei Province (A2016210099).


  1. 1.
    Ohno N. Recent topics in constitutive modeling of cyclic plasticity and viscoplasticity. Appl Mech Rev. 1990;43(11):283–95.Google Scholar
  2. 2.
    Chaboche JL. A review of some plasticity and viscoplasticity constitutive theories. Int J Plast. 2008;24(10):1642–93.zbMATHGoogle Scholar
  3. 3.
    Bari S, Hassan T. An advancement in cyclic plasticity modeling for multiaxial ratchetting simulation. Int J Plast. 2002;18(7):873–94.zbMATHGoogle Scholar
  4. 4.
    Kang G. Ratchetting: recent progresses in phenomenon observation, constitutive modeling and application. Int J Fatigue. 2008;30(8):1448–72.Google Scholar
  5. 5.
    Buque C, Bretschneider J, Schwab A, et al. Dislocation structures in cyclically deformed nickel polycrystals. Mater Sci Eng A. 2001;300(1):254–62.Google Scholar
  6. 6.
    El-Madhoun Y, Mohamed A, Bassim MN. Cyclic stress-strain response and dislocation structures in polycrystalline aluminum. Mater Sci Eng A. 2003;359(1):220–7.Google Scholar
  7. 7.
    Zhang J, Jiang Y. An experimental investigation on cyclic plastic deformation and substructures of polycrystalline copper. Int J Plast. 2005;21(11):2191–211.Google Scholar
  8. 8.
    Cho S, Bettati R. On the evolution of cyclic deformation microstructure during relaxation test in austenitic stainless steel at 823K. Mater Sci Eng A. 2008;483(1):422–5.Google Scholar
  9. 9.
    Lakhdar T, Annie H. Multiscale experimental investigations about the cyclic behavior of the 304L SS. Int J Plast. 2009;25(7):1359–85.zbMATHGoogle Scholar
  10. 10.
    Dong Y, Kang G, Liu Y, et al. Dislocation evolution in 316 L stainless steel during multiaxial ratchetting deformation. Mater Charact. 2012;65:62–72.Google Scholar
  11. 11.
    Dong Y, Kang G, Liu Y, et al. Multiaxial ratchetting of 20 carbon steel: macroscopic experiments and microscopic observations. Mater Charact. 2013;83(3):1–12.Google Scholar
  12. 12.
    Kang G, Dong Y, Wang H, et al. Dislocation evolution in 316L stainless steel subjected to uniaxial ratchetting deformation. Mater Sci Eng A Struct Mater Prop Microstruct Process. 2010;527(21–22):5952–61.Google Scholar
  13. 13.
    Bocher L, Delobelle P, Robinet P, et al. Mechanical and microstructural investigations of an austenitic stainless steel under non-proportional loadings in tension-torsion-internal and external pressure. Int J Plast. 2001;17(11):1491–530.zbMATHGoogle Scholar
  14. 14.
    Gaudin C, Feaugas X. Cyclic creep process in AISI 316L stainless steel in terms of dislocation patterns and internal stresses. Acta Mater. 2004;52(10):3097–110.zbMATHGoogle Scholar
  15. 15.
    Cailletaud G, Sai K. A polycrystalline model for the description of ratchetting: Effect of intergranular and intragranular hardening. Mater Sci Eng A. 2008;480(1):24–39.Google Scholar
  16. 16.
    Kang G, Bruhns OT, Sai K. Cyclic polycrystalline visco-plastic model for ratchetting of 316L stainless steel. Comput Mat Sci. 2011;50(4):1399–405.Google Scholar
  17. 17.
    Sai K, Cailletaud G, Forest S. Micro-mechanical modeling of the inelastic behavior of directionally solidified materials. Mech Mater. 2006;38(3):203–17.Google Scholar
  18. 18.
    Dong Y, Kang G, Yu C. A dislocation-based cyclic polycrystalline visco-plastic constitutive model for ratchetting of metals with face-centered cubic crystal structure. Comput Mater Sci. 2014;91(2):75–82.Google Scholar
  19. 19.
    Nix WD, Gibeling JC, Hughes DA. Time-dependent deformation of metals. Metall Trans A Phys Metall Mater Sci. 1985;16(12):2215–26.Google Scholar
  20. 20.
    Nes E. Modelling of work hardening and stress saturation in FCC metals. Prog Mater Sci. 1997;41(3):129–93.Google Scholar
  21. 21.
    Roters F, Raabe D, Gottstein G. Work hardening in heterogeneous alloys–a microstructural approach based on three internal state variables. Acta Mater. 2000;48(17):4181–9.Google Scholar
  22. 22.
    Ma A, Roters F. A constitutive model for fcc single crystals based on dislocation densities and its application to uniaxial compression of aluminium single crystals. Acta Mater. 2004;52(12):3603–12.Google Scholar
  23. 23.
    Harder J. A crystallographic model for the study of local deformation processes in polycrystals. Int J Plast. 1999;15(6):605–24.zbMATHGoogle Scholar
  24. 24.
    Berbenni S, Favier V, Lemoine X, et al. Micromechanical modeling of the elastic-viscoplastic behavior of polycrystalline steels having different microstructures. Mater Sci Eng A. 2004;372(1):128–36.zbMATHGoogle Scholar
  25. 25.
    Zhang H, Dong X, Du D, et al. A unified physically based crystal plasticity model for FCC metals over a wide range of temperatures and strain rates. Mater Sci Eng A. 2013;564(3):431–41.Google Scholar
  26. 26.
    Armstrong P, Frederick C. A Mathematical Representation of Multiaxial Bauschinger Effect, CEGB Report rd/b/n731. Berkeley, UK: Berkeley Nuclear Laboratories; 1966.Google Scholar
  27. 27.
    Zhang KS, Ju JW, Li Z, et al. Micromechanics based fatigue life prediction of a polycrystalline metal applying crystal plasticity. Mech Mater. 2015;85:16–37.Google Scholar
  28. 28.
    Hill R. Continuum micro-mechanics of elastoplastic polycrystals. J Mech Phys Solids. 1965;13(2):89–101.zbMATHGoogle Scholar
  29. 29.
    Cailletaud G, Pilvin P. Utilisation de modèles polycristallins pour le calcul par éléments finis. Revue européenne des éléments finis. 1994;3(4):515–41.zbMATHGoogle Scholar
  30. 30.
    Berveiller M, Zaoui A. An extension of the self-consistent scheme to plastically-flowing polycrystals. J Mech Phys Solids. 1978;26(5):325–44.zbMATHGoogle Scholar
  31. 31.
    Harder J. Simulation lokaler Fliefivorgänge in Polykristallen. Oberbayern: Mechanik-Zentrum; 1997.Google Scholar
  32. 32.
    Berbenni S, Favier V, Lemoine X, et al. Micromechanical modeling of the elastic-viscoplastic behavior of polycrystalline steels having different microstructures. Mater Sci Eng A (Struct Mater Prop Microstruct Process). 2004;372(1–2):128–36.zbMATHGoogle Scholar
  33. 33.
    Mareau C, Favier Véronique, B Weber, et al. Micromechanical modeling of the interactions between the microstructure and the dissipative deformation mechanisms in steels under cyclic loading. Int J Plast. 2012;32–33:106–20.Google Scholar
  34. 34.
    Paquin A, Berbenni S, Favier V, et al. Micromechanical modeling of the elastic-viscoplastic behavior of polycrystalline steels. Int J Plast. 2001;17(9):1267–302.zbMATHGoogle Scholar
  35. 35.
    Argon AS, Haasen P. A new mechanism of work hardening in the late stages of large strain plastic flow in F.C.C. and diamond cubic crystals. Acta Metall Mater. 1993;41(11):3289–306.Google Scholar
  36. 36.
    Müller M, Zehetbauer M, Borbély A, et al. Stage IV work hardening in cell forming materials, part I: features of the dislocation structure determined by X-ray line broadening. Scr Mater. 2015;35(12):1461–6.Google Scholar
  37. 37.
    Tabourot L, Fivel M, Rauch E. Generalised constitutive laws for f.c.c. single crystals. Mater Sci Eng A. 1997;234(97):639–42.Google Scholar
  38. 38.
    Alcala J, Casals O, Ocenasek J. Micromechanics of pyramidal indentation in fcc metals: Single crystal plasticity finite element analysis. J Mech Phys Solids. 2008;56(11):3277–303.zbMATHGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics 2019

Authors and Affiliations

  1. 1.State Key Laboratory of Advanced Design and Manufacturing for Vehicle BodyHunan UniversityChangshaChina
  2. 2.State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering StructuresShijiazhuang Tiedao UniversityShijiazhuangChina

Personalised recommendations