Skip to main content
SpringerLink
Log in

Comparative Study of Two Multiscale Thermomechanical Models of Polycrystalline Shape Memory alloys: Application to a Representative volUme Element of Titanium–Niobium

  • ESOMAT 2018
  • Published:
Shape Memory and Superelasticity Aims and scope Submit manuscript

Abstract

This paper presents a comparative study between two micro–macro modeling approaches to simulate stress-induced martensitic transformation in shape memory alloys (SMA). One model is a crystal plasticity-based model and the other describes the evolution of the microstructure with a Boltzmann-type statistical approach. Both models consider a self-consistent scheme to perform the scale transition from the local thermomechanical behavior to the global one. The way the two modeling approaches describe the local behavior is analyzed. Similarities and differences are pointed out. Numerical simulations of the thermomechanical behavior of an isotropic titanium-niobium SMA are performed. These alloys have known a growing interest of scientific community given their high potential for application in the biomedical field. Stress–strain curves obtained from the two simulations are compared with experimental results. Evolutions of volume fractions of martensite variants predicted by the two approaches are compared for <100>, <110>, and <111> tensile directions. Due to the absence of comparative studies between multiscale models dedicated for SMA, this paper fills a gap in the state of the art in this field and provides a significant step toward the definition of an efficient numerical tool for the analysis of SMA behavior under multiaxial loadings.

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

Similar content being viewed by others

Notes

  1. The so-called R-phase of equi-atomic NiTi can be considered in this modeling in addition to martensite and austenite phases.

References

  1. Cisse C, Zaki W, Ben Zineb T (2016) A review of constitutive models and modeling techniques for shape memory alloys. Int J Plast 76:244–284

    Article  Google Scholar 

  2. Mohd Jani J, Leary M, Subic A, Gibson MA (2014) A review of shape memory alloy research, applications and opportunities. Mater Des 56:1078–1113

    Article  Google Scholar 

  3. Auricchio F, Bonetti E, Scalet G, Ubertini F (2014) Theoretical and numerical modeling of shape memory alloys accounting for multiple phase transformations and martensite reorientation. Int J Plast 59:30–54

    Article  Google Scholar 

  4. Chemisky Y, Duval A, Patoor E, Zineb TB (2011) Constitutive model for shape memory alloys including phase transformation, martensitic reorientation and twins accommodation. Mech Mater 43(7):361–376

    Article  Google Scholar 

  5. Lagoudas D, Hartl D, Chemisky Y, Machado L, Popov P (2012) Constitutive model for the numerical analysis of phase transformation in polycrystalline shape memory alloys. Int J Plast 32:155–183

    Article  Google Scholar 

  6. Chemisky Y, Meraghni F, Bourgeois N, Cornell S, Echchorfi R, Patoor E (2015) Analysis of the deformation paths and thermomechanical parameter identification of a shape memory alloy using digital image correlation over heterogeneous tests. Int J Mech Sci 96–97:13–24

    Article  Google Scholar 

  7. Mamivand M, Zaeem MA, ElKadiri H (2013) A review on phase field modeling of martensitic phase transformation. Comput Mater Sci 77:304–311

    Article  Google Scholar 

  8. Lagoudas DC, Entchev PB, Popov P, Patoor E, Brinson C, Xiujie G (2006) Shape memory alloys, Part II: modeling of polycrystals. Mech Mater 38:430–462

    Article  Google Scholar 

  9. Laheurte P, Prima F, Eberhardt A, Gloriant T, Wary M, Patoor E (2010) Mechanical properties of low modulus beta titanium alloys designed from the electronic approach. J Mech Behav Biomed Mater 3:65–573

    Article  Google Scholar 

  10. Miyazaki S, Kim HY, Hosoda H (2006) Development and characterization of Ni-free Ti-base shape memory and superelastic alloys. Mater Sci Eng, A 440:18–24

    Article  Google Scholar 

  11. Sittner P, Heller L, Pilch J, Sedlak P, Frost M, Chemisky Y, Duval A, Piotrowski B, Ben Zineb T, Patoor E, Auricchio F, Morganti S, Reali A, Rio G, Favier D, Liu Y, Gibeau E, Lexcellent C, Boubakar L, Hartl D, Oehler S, Lagoudas DC, Van Humbeeck J (2009) Roundrobin SMA modelling. In: Proceedings of ESOMAT 2009, published by EDP Sciences

  12. Fischlschweiger M, Oberaigner ER (2012) Kinetics and rates of martensitic phase transformation based on statistical physics. Comput Mater Sci 52(1):189–192

    Article  Google Scholar 

  13. Siredey N, Patoor E, Berveiller M, Eberhardt A (1999) Constitutive equations for polycrystalline thermoelastic shape memory alloys: part I. Intragranular interactions and behavior of the grain. Int J Solids Struct 36(28):4289–4315

    Article  Google Scholar 

  14. Maynadier A, Depriester D, Lavernhe-Taillard K, Hubert O (2011) Thermo-mechanical description of phase transformation in Ni-Ti shape memory alloy. Proc Eng 10:2208–2213

    Article  Google Scholar 

  15. McMahon RE, Ji M, Verkhoturov SV, Munoz-Pinto D, Karaman I, Rubitschek F, Maier HJ, Hahn MS (2012) A comparative study of the cytotoxicity and corrosion resistance of nickel-titanium and titanium-niobium shape memory alloys. Acta Biomater 8:2863–2870

    Article  Google Scholar 

  16. Elmay W, Prima F, Gloriant T, Zhong Y, Patoor E, Laheurte P (2013) Effects of thermomechanical process on the microstructure and mechanical properties of a fully martensitic titanium-based biomedical alloy. J Mech Behav Biomed Mater 18:47–56

    Article  Google Scholar 

  17. Hon Y-H, Wang J-Y, Pan Y-N (2003) Composition/phase structure and properties of titanium-niobium alloys. Mater Trans 44(11):2384–2390

    Article  Google Scholar 

  18. Piotrowski B, Ben Zineb T, Patoor E, Eberhardt A (2012) Modeling of niobium precipitates effect on the Ni47 Ti44 Nb9 shape memory alloy behavior. Int J Plast 36:130–147

    Article  Google Scholar 

  19. Fall MD, Hubert O, Mazaleyrat F, Lavernhe-Taillard K, Pasko A (2016) A multiscale modeling of magnetic shape memory alloys: application to Ni 2 MnGa single crystal. IEEE Trans Magn 52:4

    Article  Google Scholar 

  20. Kim HY, Ikehara Y, Kim JI, Hosoda H, Miyazaki S (2006) Martensitic transformation, shape memory effect and superelasticity of Ti-Nb binary alloys. Acta Mater 54:2419–2429

    Article  Google Scholar 

Download references

Acknowledgment

The authors gratefully acknowledge the financial support of the Conseil Régional du Grand Est, France.

Author information

Authors and Affiliations

  1. Georgia-Tech Lorraine (Georgia-Tech/CNRS UMI 2958), 57070, Metz, France

    M. D. Fall & E. Patoor

  2. LMT (ENS-Paris Saclay/CNRS, Université Paris-Saclay), 94235, Cachan Cedex, France

    O. Hubert & K. Lavernhe-Taillard

Authors
  1. M. D. Fall
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. Patoor
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. O. Hubert
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. K. Lavernhe-Taillard
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. D. Fall.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This article is an invited submission to Shape Memory and Superelasticity selected from presentations at the 11th European Symposium on Martensitic Transformations (ESOMAT2018) held August 27–31, 2018 in Metz France and has been expanded from the original presentation.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fall, M.D., Patoor, E., Hubert, O. et al. Comparative Study of Two Multiscale Thermomechanical Models of Polycrystalline Shape Memory alloys: Application to a Representative volUme Element of Titanium–Niobium. Shap. Mem. Superelasticity 5, 163–171 (2019). https://doi.org/10.1007/s40830-019-00216-7

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40830-019-00216-7

Keywords

Search

Navigation