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Magneto-thermo-mechanical modeling of a Magnetic Shape Memory Alloy Ni-Mn-Ga single crystal

  • Original Article
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Annals of Solid and Structural Mechanics

Abstract

In the frame of Thermodynamics of irreversible process, a model describing the thermomagneto-mechanical behavior of a single crystal of Ni-Mn-Ga is built. The choice of internal variables is linked to the physics of the problem (fraction of martensite variants, fraction of Weiss domains, magnetization angle). The simulations permit to describe the paths in the space (stress, temperature, magnetic field) in agreement with experimental tests. A special attention will be devoted to the control laws required to use these functional materials as sensors or actuators.

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References

  1. Adly A, Davino D, Visone C (2006) Simulation of field effects on the mechanical hysteresis of terfenol rods and magnetic shape memory materials using vector preisach-type models. Phys B 372:207–210

    Article  Google Scholar 

  2. Ahluwalia R, Lookman T, Saxena A (2006) Dynamic strain loading of cubic to tetragonal martensites. Acta Mater 54:2109–2120

    Article  Google Scholar 

  3. Ball J, James R (1987) Fine phase mixtures as minimizers of energy. Arch Rational Mech Anal 100:13–52

    Article  MathSciNet  MATH  Google Scholar 

  4. Ball J, James R (1992) Proposed experimental tests of the theory of fine microstructure and the two well problem. Phil Trans Royal Soc London A 338:389–450

    Article  MATH  Google Scholar 

  5. Bhattacharya K (2003) Microstructure of martensite : why it forms and how it gives rise to the shape-memory effect. Oxford series on materials modelling

  6. Brinson L (1993) One-dimensional constitutive behavior of shape memory alloys: Thermomechanical derivation with non-constant material functions and redefined martensite internal variable. J Intell Mater Syst Struct 4:229–242

    Article  Google Scholar 

  7. Buchelnikov V, Bosko S (2003) The kinetics of phase transformations in ferromagnetic shape memory alloys ni-mn-ga. J Magn Magn Mater 258(259):497–499

    Article  Google Scholar 

  8. Callaway JD, Hamilton RF, Sehitoglu H, Miller N, Maier HJ, Chumlyakov Y (2007) Shape memory and martensite deformation response of ni2mnga. Smart Mater Struct 16:108–114

    Article  Google Scholar 

  9. Chernenko V, L’vov V, Pons J, Cesari E (2003) Superelasticity in high-temperature ni-mn-ga alloys. J Appl Phys 93(5):2394–2399

    Article  Google Scholar 

  10. Chernenko V, L’vov V, Cesari E, Pons J, Rudenko A, Date H, Matsumoto M, Kanomatad T (2004) Stress-strain behaviour of ni-mn-ga alloys: experiment and modelling. Mater Sci Eng A 378:349–352

    Article  Google Scholar 

  11. Couch RN, Chopra I (2007) A quasi-static model for nimnga magnetic shape memory alloy. Smart Mater Struct 16:S11–S21

    Article  Google Scholar 

  12. Creton N (2004) Etude du comportement magnéto-mécanique des alliages à mémoire de forme de type heusler ni-mn-ga. PhD thesis, Université de Franche-Comté (France), Besançon

  13. Creton N, Hirsinger L (2005) Rearrangement surfaces under magnetic field and/or stress in ni-mn-ga. J Magn Magn Mater 290(291):832–835

    Article  Google Scholar 

  14. DeSimone A, James RD (2002) A constrained theory of magnetoelasticity. J Mech Phys Solids 50(2):283–320

    Article  MathSciNet  MATH  Google Scholar 

  15. Gans E, Henry C, Carman GP (2004) Reduction in required magnetic field to induce twin-boundary motion in ferromagnetic shape memory alloys. J Appl Phys 95(11):6965–6967

    Article  Google Scholar 

  16. Gauthier JY, Hubert A, Abadie J, Lexcellent C, Chaillet N (2006) Multistable actuator based on magnetic shape memory alloy. In: ACTUATOR 2006, 10th international conference on new actuators, Bremen, Germany, pp 787–790

  17. Gauthier JY, Hubert A, Abadie J, Lexcellent C, Chaillet N (2007a) Original hybrid control for robotic structures using magnetic shape memory alloys actuators. In: IEEE/RSJ international conference on intelligent robots and systems, pp 787–790

  18. Gauthier JY, Lexcellent C, Hubert A, Abadie J, Chaillet N (2007) Modeling rearrangement process of martensite platelets in a magnetic shape memory alloy Ni2MnGa single crystal under magnetic field and (or) stress action. J Intell Mater Syst Struct 18(3):289–299

    Article  Google Scholar 

  19. Gauthier JY, Hubert A, Abadie J, Chaillet N, Lexcellent C (2008) Nonlinear hamiltonian modelling of magnetic shape memory alloy based actuators. Sens Actuators A: Phys 141(2):536–547

    Article  Google Scholar 

  20. Gauthier JY, Lexcellent C, Hubert A, Abadie J, Chaillet N (2010) Ni-Mn-Ga single crystal shape memory alloy magneto-thermomechanical modeling. In: Proceedings of the 14th international conference on experimental mechanics, EDP Sciences, vol 6, 29003

  21. Glavatska N, Rudenko A, Glavatskiy I, L’vov V (2003) Statistical model of magnetostrain effect in martensite. J Magn Magn Mater 265:142–151

    Article  Google Scholar 

  22. Halphen B, Nguyen Q (1974) Plastic and visco-plastic materials with generalized potential. Mech Res Commun 1:43–47

    Article  MATH  Google Scholar 

  23. Hane KF (1999) Bulk and thin film microstructures in untwinned martensites. J Mech Phys Solids 47(9):1917–1939

    Article  MathSciNet  MATH  Google Scholar 

  24. Heczko O (2005) Determination of ordinary magnetostriction in ni-mn-ga magnetic shape memory alloy. J Magn Magn Mater 290–291:846–849

    Article  Google Scholar 

  25. Heczko O, Straka L (2003) Temperature dependence and temperature limits of magnetic shape memory effect. J Appl Phys 94:7139–7143

    Article  Google Scholar 

  26. Heczko O, Ullakko K (2001) Effect of temperature on magnetic properties of ni-mn-ga magnetic shape memory (msm) alloys. IEEE Trans Magn 37(4):2672–2674

    Article  Google Scholar 

  27. Hirsinger L (2004) Ni-mn-ga shape memory alloys: modelling of magneto-mechanical behaviour. Int J Appl Electromagn Mech/IOS Press 19(1–4):473–477

    Google Scholar 

  28. Hirsinger L, Lexcellent C (2002) Modelling detwinning of martensite platelets under magnetic and (or) stress actions in ni-mn-ga alloys. J Magn Magn Mater 254–255:275–277

    Google Scholar 

  29. Hirsinger L, Creton N, Lexcellent C (2004) From crystallographic properties to macroscopic detwinning strain and magnetisation of ni-mn-ga magnetic shape memory alloys. J Phys IV 115:111–120

    Google Scholar 

  30. Hirsinger L, Creton N, Lexcellent C (2004) Stress-induced phase transformations in ni-mn-ga alloys: experiments and modelling. Mater Sci Eng A 378(1–2):365–369

    Google Scholar 

  31. Karaca H, Karaman I, Basaran B, Chumlyakov Y, Maier H (2006) Magnetic field and stress induced martensite reorientation in nimnga ferromagnetic shape memory alloy single crystals. Acta Mater 54:233–245

    Article  Google Scholar 

  32. Kiang J, Tong L (2005) Modelling of magneto-mechanical behaviour of ni-mn-ga single crytals. J Magn Magn Mater 292:394–412

    Article  Google Scholar 

  33. Kiefer B, Lagoudas DC (2005) Magnetic field-induced martensitic variant reorientation in magnetic shape memory alloys. Philosophical Magazine Special Issue: Recent Advances in Theoretical Mechanics, in Honor of SES 2003 AC Eringen Medalist GA Maugin 85(33–35):4289–4329

  34. Kiefer B, Karaca H, Lagoudas D, Karaman I (2007) Characterization and modeling of the magnetic field-induced strain and work output in ni2mnga magnetic shape memory alloys. J Magn Magn Mater 312:164–175

    Article  Google Scholar 

  35. Koistinen D, Marburger R (1959) A general equation prescribing the extent of the austenite-martensite transformation in pure iron-carbon alloys and plain carbon steels. Acta Metall 7(1):59–60

    Article  Google Scholar 

  36. Lexcellent C, Blanc P (2004) Phase transformation yield surface determination for some shape memory alloys. Acta Mater 52(8):2317–2324

    Article  Google Scholar 

  37. Likhachev A, Ullakko K (2000) Magnetic-field-controlled twin boundaries motion and giant magneto-mechanical effects in ni-mn-ga shape memory alloy. Phys Lett A 275:142–151

    Article  Google Scholar 

  38. Müllner P, Chernenko VA, Wollgarten M, Kostorz G (2002) Large cyclic deformation of a ni-mn-ga shape memory alloy induced by magnetic fields. J Appl Phys 92(11):6708–6713

    Article  Google Scholar 

  39. Müllner P, Chernenko V, Kostorz G (2003) A microscopic approach to the magnetic-field-induced deformation of martensite (magnetoplasticity). J Magn Magn Mater 267:325–334

    Article  Google Scholar 

  40. Murray S, Marioni M, Tello P, Allen S, O‘Handley R (2001) Giant magnetic-field-induced strain in ni-mn-ga crystals: experimental results and modeling. J Magn Magn Mater 226–230:945–947

    Article  Google Scholar 

  41. Murray SJ, Allen SM, O’Handley RC, Lograsso TA (2000) Magnetomechanical performance and mechanical properties of ni-mn-ga ferromagnetic shape memory alloys. In: SPIE Proceedings, 3992, 387

  42. Murray SJ, O’Handley RC, Allen SM (2001) Model for discontinuous actuation of ferromagnetic shape memory alloy under stress. J Appl Phys 89(2):1295–1301

    Article  Google Scholar 

  43. O’Handley RC (1998) Model for strain and magnetization in magnetic shape-memory alloys. J Appl Phys 83(6):3263–3270

    Article  Google Scholar 

  44. O’Handley RC, Murray SJ, Marioni M, Nembach H, Allen SM (2000) Phenomenology of giant magnetic-field-induced strain in ferromagnetic shape-memory materials. J Appl Phys 87(9):4712–4717

    Article  Google Scholar 

  45. Patoor E, Lagoudas D, Entchev P, Brinson L, Gao X (2006) Shape memory alloys, part i: general properties and modeling of single crystals. Mech Mater 38(5–6):391–429

    Article  Google Scholar 

  46. Straka L, Heczko O (2006) Magnetization changes in ni-mn-ga magnetic shape memory single crystal during compressive stress reorientation. Scripta Mater 54:1549–1552

    Article  Google Scholar 

  47. Straka L, Heczko O, Hannula SP (2006) Temperature dependence of reversible field-induced strain in ni-mn-ga single crystal. Scripta Mater 54:1497–1500

    Article  Google Scholar 

  48. Suorsa I, Tellinen J, Aaltio I, Pagounis E, Ullakko K (2004) Design of active element for msm-actuator. In: ACTUATOR 2004 / 9th International Conference on New Actuators, Bremen (Germany)

  49. Tickle R (2000) Ferromagnetic shape memory materials. PhD thesis, Faculty of the graduate school of the university of Minnesota, Minneapolis (USA)

  50. Tickle R, James RD, Wuttig M, Kokorin VV (1999) Ferromagnetic shape memory in the NiMnGa system. IEEE Trans Magn 35(5):4301–4310

    Article  Google Scholar 

  51. Vivet A, Lexcellent C (1998) Micromechanical modelling for tension-compression pseudoelastic behavior of AuCd single crystals. EPJ Appl Phys 4(2):125–132

    Article  Google Scholar 

  52. Zhu Y, Dui G (2007) Micromechanical modeling of the stress-induced superelastic strain in magnetic shape memory alloy. Mech Mater 39:1025–1034

    Article  Google Scholar 

  53. Zhu Y, Dui G (2008) Model for field-induced reorientation strain in magnetic shape memory alloy with tensile and compressive loads. J Alloys Compd 459:55–60

    Article  Google Scholar 

  54. Zuo F, Su X, Wu K (1998) Magnetic properties of the premartensitic transition in ni2mnga alloys. Phys Rev B 58(17):11,127–11,130

    Article  Google Scholar 

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Authors and Affiliations

  1. LGEF, Université de Lyon, INSA-Lyon, 8 rue de la physique, 69621, Villeurbanne, France

    Jean-Yves Gauthier

  2. Applied Mechanics Department, FEMTO-ST Institute, CNRS/UFC/ENSMM/UTBM, 24 rue de l’Épitaphe, 25000, Besançon, France

    Christian Lexcellent

  3. Automatic Control and Micro-Mechatronic Systems Department, FEMTO-ST Institute, CNRS/UFC/ENSMM/UTBM, 24 rue Alain Savary, 25000, Besançon, France

    Arnaud Hubert, Joël Abadie & Nicolas Chaillet

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  1. Jean-Yves Gauthier
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  2. Christian Lexcellent
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  4. Joël Abadie
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Correspondence to Christian Lexcellent.

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Gauthier, JY., Lexcellent, C., Hubert, A. et al. Magneto-thermo-mechanical modeling of a Magnetic Shape Memory Alloy Ni-Mn-Ga single crystal. Ann. Solid Struct. Mech. 2, 19–31 (2011). https://doi.org/10.1007/s12356-011-0014-8

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  • DOI: https://doi.org/10.1007/s12356-011-0014-8

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