Skip to main content
SpringerLink
Log in

A Cyclic Constitutive Model Based on Crystal Plasticity for Body-Centered Cubic Cyclic Softening Metals

  • Published:
Acta Mechanica Solida Sinica Aims and scope Submit manuscript

Abstract

Under the framework of the small deformation crystal plasticity theory, a crystal plastic cyclic constitutive model for body-centered cubic (BCC) cyclic softening polycrystalline metals is established. The constitutive model introduces the isotropic softening rule that includes two different mechanisms: namely softening under monotonic deformation and softening under cyclic deformation on each slip system. Meanwhile, a modified Armstrong-Frederick nonlinear kinematic hardening rule is adopted. The appropriate explicit scale transition rule is selected to extend the single crystal constitutive model to the polycrystalline constitutive model. Then the model is used to predict the uniaxial and multiaxial ratcheting deformation of BCC axle steel EA4T to verify the rationality of the proposed model. The simulation results indicate that the newly established crystal plasticity model can not only describe the cyclic softening characteristics of BCC axle steel EA4T well, but also reasonably describe the evolution laws of uniaxial ratcheting and nonproportional multiaxial ratcheting deformation. Moreover, the established crystal plastic cyclic constitutive model can reasonably predict the ratcheting behavior of BCC single crystal as well.

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

Similar content being viewed by others

Availability of data and material

Data will be made available upon request.

References

  1. Chaboche JL. A review of some plasticity and viscoplasticity constitutive theories. Int J Plast. 2008;24(10):1642–93.

    Article  CAS  Google Scholar 

  2. Kang GZ. Ratchetting: Recent progresses in phenomenon observation, constitutive modeling and application. Int J Fatigue. 2008;30(8):1448–72.

    Article  CAS  Google Scholar 

  3. Chaboche JL, Kanoute P, Azzouz F. Cyclic inelastic constitutive equations and their impact on the fatigue life predictions. Int J Plast. 2012;35:44–66.

    Article  CAS  Google Scholar 

  4. Ohno N. Material models of cyclic plasticity with extended isotropic hardening: a review. Mech Eng Rev. 2015;2(1):14–00425.

    Article  MathSciNet  Google Scholar 

  5. Xu B, Jiang Y. A cyclic plasticity model for single crystals. Int J Plast. 2004;20(12):2161–78.

    Article  CAS  Google Scholar 

  6. Cailletaud G, Sai K. A polycrystalline model for the description of ratchetting: effect of intergranular and intragranular hardening. Mater Sci Eng A. 2008;480(1–2):24–39.

    Article  Google Scholar 

  7. Abdeljaoued D, Naceur I, Sai K, Cailletaud G. A new polycrystalline plasticity model to improve ratchetting strain prediction. Mech Res Commun. 2009;36(3):309–15.

    Article  Google Scholar 

  8. Kang G, Bruhns OT. A new cyclic crystal visco-plasticity model based on combined nonlinear kinematic hardening rule for single crystals. Mater Res Innov. 2011;15(S1):S11–4.

    Article  ADS  Google Scholar 

  9. Kang G, Bruhns OT, Sai K. Cyclic polycrystalline visco-plastic model for ratchetting of 316L stainless steel. Comput Mater Sci. 2011;50(4):1399–405.

    Article  CAS  Google Scholar 

  10. Luo J, Kang GZ, Bruhns OT, et al. Cyclic polycrystalline viscoplastic model for ratchetting of a body centered cubic metal. Key Eng Mater. 2013;535–536:173–6.

    Article  Google Scholar 

  11. 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.

    Article  CAS  Google Scholar 

  12. Dong Y, Xie D, Zhang Y, et al. On the study of cyclic crystal plasticity ratchetting constitutive model for polycrystalline pure copper. Int J Appl Mech. 2019;11(4):1950041.

    Article  Google Scholar 

  13. Yu C, Kang G, Kan Q, et al. A cyclic crystal viscoplastic model considering both dislocation slip and twinning. In: Advanced materials modelling for structures. Berlin: Springer; 2013.

  14. Ren XH, Yang SP, Wen GL, Zhao WJ. A crystal-plasticity cyclic constitutive model for the ratchetting of polycrystalline material considering dislocation substructures. Acta Mech Solida Sin. 2020;33(2):268–80.

    Article  Google Scholar 

  15. Zhao WJ. Cyclic constitutive model of high-speed railway train axle steel EA4T and finite element implementation. Hunan University; 2021. p.14–26.

  16. 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.

    Article  Google Scholar 

  17. Cruzado A, Llorca J, Segurado J. Modeling cyclic deformation of inconel 718 superalloy by means of crystal plasticity and computational homogenization. Int J Solids Struct. 2017;122:148–61.

    Article  Google Scholar 

  18. Cruzado A, Lucarini S, LLorca J, et al. Crystal plasticity simulation of the effect of grain size on the fatigue behavior of polycrystalline Inconel 718. Int J Fatigue. 2018;113:236–45.

    Article  CAS  Google Scholar 

  19. Asaro RJ, Needleman A. Overview no. 42 Texture development and strain hardening in rate dependent polycrystals. Acta Metall. 1985;33(6):923–53.

    Article  CAS  Google Scholar 

  20. Tome C, Canova GR, Kocks UF, et al. The relation between macroscopic and microscopic strain hardening in FCC polycrystals. Acta Metall. 1984;32(10):1637–53.

    Article  CAS  Google Scholar 

  21. Armstrong PJ, Frederick CO. A mathematical representation of the multiaxial Bauschinger effect. Central Electricity Generating Board [and] Berkeley Nuclear Laboratories. Research & Development Department; 1966.

  22. 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.

    Article  Google Scholar 

  23. Hill R. Continuum micro-mechanics of elastoplastic polycrystals. J Mech Phys Solids. 1965;13(2):89–101.

    Article  ADS  MathSciNet  CAS  Google Scholar 

  24. Yu C, Kang GZ, Sun Q, et al. Modeling the martensite reorientation and resulting zero/negative thermal expansion of shape memory alloys. J Mech Phys Solids. 2019;127:295–331.

    Article  ADS  MathSciNet  CAS  Google Scholar 

  25. Yu C, Chen T, Yin H, et al. Modeling the anisotropic elastocaloric effect of textured NiMnGa ferromagnetic shape memory alloys. Int J Solids Struct. 2020;191–192:509–28.

    Article  Google Scholar 

  26. Dong Y, Zhu Y, Wu F, et al. A dual-scale elasto-viscoplastic constitutive model of metallic materials to describe thermo-mechanically coupled monotonic and cyclic deformations. Int J Mech Sci. 2022;224: 107332.

    Article  Google Scholar 

  27. Cailletaud G, Pilvin P. Utilisation de modèlespolycristallins pour le calcul par élémentsfinis. Revue européenne des élémentsfinis. 1994;3(4):515–41.

    Article  Google Scholar 

  28. Paquin A, Berbenni S, Favier V, et al. Micromechanical modeling of the elastic visco-plastic behaviour of polycrystalline steels. Int J Plast. 2001;17(9):1267–302.

    Article  CAS  Google Scholar 

  29. Chaboche JL. Constitutive equations for cyclic plasticity and cyclic viscoplasticity. Int J Plast. 1989;5(3):247–302.

    Article  Google Scholar 

  30. Ohno N, Wang JD. Kinematic hardening rules with critical state of dynamic recovery, part I: Formulation basic features for ratcheting behaviour behaviour. Int J Plast. 1993;9(3):370–90.

    Google Scholar 

  31. Ohno N, Wang JD. Kinematic hardening rules with critical state of dynamic recovery, part II: application to experiments of ratchetting behavior. Int J Plast. 1993;9(3):391–403.

    Article  CAS  Google Scholar 

  32. Abdel-Karim M, Ohno N. Kinematic hardening model suitable for ratchetting with steady-state. Int J Plast. 2000;16(3):225–40.

    Article  CAS  Google Scholar 

  33. Zhao WJ, Yang SY, Wen GL, et al. Fractional-order visco-plastic constitutive model for uniaxial ratcheting behaviors. Appl Math Mech. 2019;40(1):49–62.

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The present work is supported by the National Natural Science Foundation of China (Nos.12032017, 11790282).

Funding

National Natural Science Foundation of China, 12032017, Shaopu Yang.

Author information

Authors and Affiliations

  1. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, 410082, China

    Xuehong Ren & Guilin Wen

  2. School of Mechanical Engineering, Tianjin Sino-German University of Applied Sciences, Tianjin, 300350, China

    Wenjie Zhao

  3. State Key Laboratory of Mechanical Behavior in Traffic Engineering Structure and System Safety, Shijiazhuang Tiedao University, Shijiazhuang, 050043, China

    Shaopu Yang

Authors
  1. Xuehong Ren
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wenjie Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shaopu Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Guilin Wen
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

XR provided all the data for this paper and was a major contributor to its writing. SY conceived the main idea of this paper and also put forward valuable suggestions for its revision. WZ and GW made great contributions to the revision of this paper. All authors have read and approved the final manuscript.

Corresponding author

Correspondence to Wenjie Zhao.

Ethics declarations

Competing interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Consent for publication

All authors have approved the final manuscript and its submission to the journal.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ren, X., Zhao, W., Yang, S. et al. A Cyclic Constitutive Model Based on Crystal Plasticity for Body-Centered Cubic Cyclic Softening Metals. Acta Mech. Solida Sin. 37, 33–42 (2024). https://doi.org/10.1007/s10338-023-00430-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10338-023-00430-y

Keywords

Search

Navigation