Skip to main content

Advertisement

SpringerLink
Log in

Finite element simulation of phase field model for nanoscale martensitic transformation

  • Original Paper
  • Published:
Computational Mechanics Aims and scope Submit manuscript

Abstract

A finite element framework of a phase field model for nanoscale martensitic transformation is proposed on the basis of time-dependent Ginzburg–Landau kinetic equations. The bulk total free energy consists of the chemical driving energy, the interfacial energy, the elastic energy, the inertial energy (for a dynamic case), the energy due to applied field and the effects of surface energy which need to be considered at the nanoscale. Single-variant and multi-variant martensitic phase transformations in a nano-sized NiAl plate are considered. The numerical results show the effects of each energy item on the phase transformation and the self-accommodating twinned morphologies as the result of strain energy minimization.

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

References

  1. Chen L-Q, Wang Y (1996) The continuum field approach to modeling microstructural evolution. JOM 48:13–18

    Article  Google Scholar 

  2. Barrales-Mora LA, Mohles V, Konijnenberg PJ, Molodov DA (2007) A novel implementation for the simulation of 2-D grain growth with consideration to external energetic fields. Comput Mater Sci 39(1):160–165

    Article  Google Scholar 

  3. Boettinger WJ, Warren JA, Beckermann C, Karma A (2002) Phase-field simulation of solidification. Annu Rev Mater Res 32:163–194

    Article  Google Scholar 

  4. Wang YU, Jin YM, Cuitino AM, Khachaturyan AG (2001) Phase field microelasticity theory and modeling of multiple dislocation dynamics. Appl Phys Lett 78(16):2324–2326

    Article  Google Scholar 

  5. Patoor E, Lagoudas DC, Entchev PB, Brinson LC, Gao X (2006) Shape memory alloys, Part I: general properties and modeling of single crystals. Mech Mater 38:391–429

    Article  Google Scholar 

  6. Olson GB, Hartman H (1982) Martensite and life : displacive transformations as biological processes. J Phys Colloques 43(C4):855–865

    Google Scholar 

  7. Bhattacharya K (2003) Why it forms and how it gives rise to the shape-memory effect. Oxford University Press, New York

    Google Scholar 

  8. James RD, Hane KF (2000) Martensitic transformations and shape-memory materials. Acta Mater 48(1):197–222

    Article  Google Scholar 

  9. Artemev A, Jin Y, Khachaturyan AG (2001) Three-dimensional phase field model of proper martensitic transformation. Acta Mater 49(7):1165–1177

    Article  Google Scholar 

  10. Khachaturyan AG (1983) Theory of structural transformation in solids. Wiley, New York

    Google Scholar 

  11. Wang Y, Khachaturyan AG (1997) Three-dimensional field model and computer modeling of martensitic transformations. Acta Mater 45(2):759–773

    Article  Google Scholar 

  12. Chen L-Q (2002) Phase-field models for microstructure evolution. Annu Rev Mater Res 32(1):113–140

    Article  Google Scholar 

  13. Moelans N, Blanpain B, Wollants P (2008) An introduction to phase-field modeling of microstructure evolution. CALPHAD 32(2):268–294

    Article  Google Scholar 

  14. Lei CH, Li LJ, Shu YC, Li JY (2010) Austenite–martensite interface in shape memory alloys. Appl Phys Lett 96(14):141910

    Article  Google Scholar 

  15. Li LJ, Yang Y, Shu YC, Li JY (2010) Continuum theory and phase-field simulation of magnetoelectric effects in multiferroic bismuth ferrite. J Mech Phys Solids 58(10):1613–1627

    Article  MathSciNet  MATH  Google Scholar 

  16. Shu YC, Yen JH (2008) Multivariant model of martensitic microstructure in thin films. Acta Mater 56(15):3969–3981

    Article  MathSciNet  Google Scholar 

  17. Levitas VI, Preston DL (2002) Three-dimensional Landau theory for multivariant stress-induced martensitic phase transformations. I. Austenite to martensite. Phys Rev B 66(13):134206

    Article  Google Scholar 

  18. Levitas VI, Preston DL (2002) Three-dimensional Landau theory for multivariant stress-induced martensitic phase transformations. II. Multivariant phase transformations and stress space analysis. Phys Rev B 66(13):134207

    Article  Google Scholar 

  19. Chen LQ, Shen J (1998) Applications of semi-implicit Fourier-spectral method to phase field equations. Comput Phys Commun 108:147–158

    Article  MATH  Google Scholar 

  20. Yamanaka A, Takaki T, Tomita Y (2008) Elastoplastic phase-field simulation of self- and plastic accommodations in martensitic transformation. Mater Sci Eng A 491:378–384

    Article  Google Scholar 

  21. Mahapatra DR, Melnik RVN (2006) Finite element analysis of phase transformation dynamics in shape memory alloys with a consistent Landau–Ginzburg free energy model. Mech Adv Mater Struct 13(6):443–455

    Article  Google Scholar 

  22. Alexander VI, Joon-Yeoun C, Valery IL (2008) Finite element modeling of dynamics of martensitic phase transitions. Appl Phys Lett 93(4):043102

    Article  Google Scholar 

  23. Cho JY (2009) Finite element model of martensitic phase transformation. Ph.D. thesis, Texas Tech. University

  24. Cho JY, Idesman AV, Levitas VI, Park T (2012) Finite element simulations of dynamics of multivariant martensitic phase transitions based on Ginzburg–Landau theory. Int J Solids Struct 49(14):1973–1992

    Article  Google Scholar 

  25. She H, Liu Y, Wang B (2013) Phase field simulation of heterogeneous cubic to tetragonal martensite nucleation. Int J Solids Struct 50:1187–1191

    Article  Google Scholar 

  26. Finel A, Le Bouar Y, Gaubert A, Salman U (2010) Phase field methods: microstructures, mechanical properties and complexity. Comptes Rendus Physique 11:245–256

    Article  Google Scholar 

  27. She H, Wang B (2009) A geometrically nonlinear finite element model of nanomaterials with consideration of surface effects. Finite Elem Anal Des 45:463–467

    Article  MathSciNet  Google Scholar 

  28. Gao W, Yu S, Huang G (2006) Finite element characterization of the size-dependent mechanical behaviour in nanosystems. Nanotechnology 17(4):1118–1122

    Article  Google Scholar 

  29. Park HS, Klein PA, Wagner GJ (2006) A surface Cauchy–Born model for nanoscale materials. Int J Numer Methods Eng 68(10):1072–1095

    Article  MathSciNet  MATH  Google Scholar 

  30. Dingreville R, Qu J, Mohammed C (2005) Surface free energy and its effect on the elastic behavior of nano-sized particles, wires and films. J Mech Phys Solids 53(8):1827–1854

    Article  MathSciNet  MATH  Google Scholar 

  31. Miller RE, Shenoy VB (2000) Size-dependent elastic properties of nanosized structural elements. Nanotechnology 11(3):139–147

    Google Scholar 

  32. Shenoy VB (2005) Atomistic calculations of elastic properties of metallic fcc crystal surfaces. Phys Rev B 71(9):094104

    Google Scholar 

  33. Levitas VI, Levin VA, Zingerman KM, Freiman EI (2009) Displacive phase transitions at large strains: phase-field theory and simulations. Phys Rev Lett 103(2):025702

    Article  Google Scholar 

  34. Levitas VI, Lee D-W, Preston DL (2010) Interface propagation and microstructure evolution in phase field models of stress-induced martensitic phase transformations. Int J Plast 26(3):395–422

    Article  MATH  Google Scholar 

  35. Bando Y (1964) Characteristics of phase transformation in metallic fine particles (martensitic transformation of FeNi alloys and ordering of CuAu and Cu3Au alloys). T Jpn I Met 5:135–141

    Google Scholar 

Download references

Acknowledgments

This project is grateful for support from the National Natural Science Foundation of China (Nos. 10902128, 10732100, 50802026, 10972239, 11072271), the Fundamental Research Funds for the Central Universities. Hui She wishes to thank Dr. Wang Gang for instructions and help on COMSOL.

Author information

Authors and Affiliations

  1. School of Engineering, Sun Yat-Sen University, 135 Xingang West Road, Guangzhou, 510275, China

    Hui She & Yulan Liu

  2. School of Physics and Engineering, Sun Yat-Sen University, 135 Xingang West Road, Guangzhou, 510275, China

    Biao Wang & Decai Ma

Authors
  1. Hui She
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yulan Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Biao Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Decai Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hui She.

Rights and permissions

Reprints and permissions

About this article

Cite this article

She, H., Liu, Y., Wang, B. et al. Finite element simulation of phase field model for nanoscale martensitic transformation. Comput Mech 52, 949–958 (2013). https://doi.org/10.1007/s00466-013-0856-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00466-013-0856-5

Keywords

Search

Navigation