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Shape Memory and Superelasticity

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01-09-2015

Modelling Shape-Memory Effects in Ferromagnetic Alloys

Authors: Jonathan F. Gebbia, Pol Lloveras, Teresa Castán, Avadh Saxena, Antoni Planes

Published in: Shape Memory and Superelasticity | Issue 3/2015

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Abstract

We develop a combined Ginzburg–Landau/micromagnetic model dealing with conventional and magnetic shape-memory properties in ferromagnetic shape-memory materials. The free energy of the system is written as the sum of structural, magnetic and magnetostructural contributions. We first analyse a mean field linearized version of the model that does not take into account long-range terms arising from elastic compatibility and demagnetization effects. This model can be solved analytically and in spite of its simplicity allows us to understand the role of the magnetostructural term in driving magnetic shape-memory effects. Numerical simulations of the full model have also been performed. They show that the model is able to reproduce magnetostructural microstructures reported in magnetic shape-memory materials such as Ni₂MnGa as well as conventional and magnetic shape-memory behaviour.

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While not thermodynamically reversible, the transition is crystallographically reversible and occurs with weak (or relatively weak) hysteresis.

Some authors use the term magnetic superelasticity to describe the stress-induced reorientation of martensitic variants under an applied magnetic field. See for instance [11].

Even if the model is 2-d, assuming that magnetization is a 3-component vector with two components in-plane is important since it allows to consider a more realistic magnetization dynamics that takes into account precession of the magnetic vector around the applied magnetic field

Acet M, Mañosa L, Planes A (2011) Magnetic-field-induced effects in martensitic Heusler-based magnetic shape memory alloys. In: Buschow KHJ (ed) Handbook of magnetic materials, vol 19. Elsevier, Amsterdam, pp 231–289 references therein

Ullakko K, Huang JK, Kantner C, O’Handley RC, Kokorin VV (1996) Large magneticfieldinduced strains in Ni\(_2\)MnGa single crystals. Appl Phys Lett 69:1966–1968CrossRef

Libermann HH, Graham CD (1976) Plastic and magnetoplastic deformation of Dy single crystals. Acta Metall 25:715–720CrossRef

Ziebeck KA, Newmann KU (2001) Landolt-Bornstein III, Supl. vol. 19, vol 32., Springer, Berlin

Graf T, Felser C, Parkin SS (2011) Simple rules for understanding Heusler alloys. Prog Solid Stat Chem 39:1–50CrossRef

Entel P, Buchelnikov VD, Khovailo VV, Zayak AT, Adeagbo WA, Gruner ME, Herper HC, Wassermann EF (2006) Modelling the phase diagram of magnetic shape memory Heusler alloys. J Phys D 39:865–889CrossRef

Albertini F, Paretti L, Paoluzi A, Morellon L, Algarabel PA, Ibarra MR, Righi L (2002) Composition and temperature dependence of the magnetocrystalline anisotropy in Ni\(_{2+x}\) Mn\(_{1+y}\) Ga\(_{1+z}\) (x + y + z = 1) Heusler alloys. Appl Phys Lett 81:4032–4034CrossRef

Otsuka K, Wayman CM (eds) (1998) Shape memory materials. Cambridge University Press, Cambridge

Kohl M, Gueltig M, Pinneker V, Yin R, Wendler F, Krevet B (2014) Magnetic shape memory microactuators. Micromachines 5:1135–1160CrossRef

10.

Söderberg O, Sozinov A, Ge Y, Hannula S-P, Lindroos VK (2006) Giant magnetostrictive materials. In: Buschow KHJ (ed) Handbook of magnetic materials, vol 16. Elsevier, Amsterdam, pp 1–37

11.

Chernenko VA, Lvov VA, Müllner P, Kostorz G, Takagi T (2004) Magnetic-field-induced superelasticity of ferromagnetic thermoelastic martensites: experiment and modeling. Phys. Rev. B 69:134410CrossRef

12.

Planes A, Mañosa L, Acet M (2009) Magnetocaloric effect and its relation to shape-memory properties in ferromagnetic Heusler alloys. J Phys Condens Matter 21:233201CrossRef

13.

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

14.

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 87:4712–4717CrossRef

15.

Kainuma R, Imano Y, Ito W, Sutou Y, Oikawa K, Fujita A, Kanomata T, Ishida K (2006) Magnetic-field-induced shape recovery by reverse phase transition. Nature 439:957–960CrossRef

16.

Krenke T, Duman E, Acet M, Wassermann EF, Moya X, Mañosa L, Planes A, Suard E, Ouladdiaf B (2007) Magnetic superelasticity and inverse magnetocaloric effect in Ni–Mn–In. Phys Rev B 75:104414CrossRef

17.

Karaca HE, Karaman I, Basaran B, Ren Y, Chumlyakov YI, Maier HJ (2009) Magnetic field-induced phase transformation in NiMnCoIn magnetic shape-memory alloys a new actuation mechanism with large work output. Adv Func Mater 19:983–998CrossRef

18.

Landis CM (2008) A continuum thermodynamics formulation for micro-magnetomechanics with applications to ferromagnetic shape memory alloys. J Mech Phys Solids 56:3059–3076CrossRef

19.

Ball JM, James RD (1987) Fine phase mixtures as minimizers of energy. Arch Ration Mech Anal 100:13–52 This approach has been developed in detail. In: K. Bhattacharya, Theory of martensitic microstructure: Why it forms and how it gives rise to the shape-memory effect, Oxford Series on Materials Modelling, Oxford University Press, Oxford, 2004CrossRef

20.

James RD, Wuttig M (1998) Magnetostriction of martensite. Philos Mag A 77:1273CrossRef

21.

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

22.

Ma YF, Lia JY (2007) Magnetization rotation and rearrangement of martensite variants in ferromagnetic shape memory alloys. Appl Phys Lett 90:172504CrossRef

23.

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

24.

Khachaturyan AG (2008) Theory of structural transformation in solids. Dover, New York

25.

Zhang J, Chen LQ (2005) Phase-field microelasticity theory and micromagnetic simulations of domain structures in giant magnetostrictive materials. Acta Mater 53:2845–2855CrossRef

26.

Chen LQ (2002) Phase-field models for microstructure evolution. Annu Rev Mater Res 32:113–140CrossRef

27.

Jin YM (2009) Domain microstructure evolution in magnetic shape memory alloys: phase-field model and simulation. Acta Mater 57:2488–2495CrossRef

28.

Peng Q, Hea YJ, Moumni Z (2015) A phase-field model on the hysteretic magneto-mechanical behaviors of ferromagnetic shape memory alloy. Acta Mater 88:13–24CrossRef

29.

Mennerich C, Wendler F, Jainta M, Nestler B (2013) Rearrangement of martensitic variants in Ni\(_2\) MnGa studied with the phase-field method. Eur Phys J 86:171CrossRef

30.

Soutlas-Little RW (1999) Elasticity. Dover, New York

31.

Lookman T, Shenoy SR, Rasmussen KO, Saxena A, Bishop AR (2003) Ferroelastic dynamics and strain compatibility. Phys Rev B 67:024114CrossRef

32.

Kittel C (1949) Physical theory of ferromagnetic domains. Rev Mod Phys 21:541–583CrossRef

33.

Aharoni A (1996) Introduction to the theory of ferromagnetism. Oxford University Press, New York

34.

Shenoy SR, Lookman T, Saxena A, Bishop AR (1999) Martensitic textures: multiscale consequences of elastic compatibility. Phys Rev B 60:R12537CrossRef

35.

Lloveras P (2010) Ph.D. Thesis, Universitat de Barcelona

36.

Porta M, Castán T, Lloveras P, Lookman T, Saxena A, Shenoy SR (2009) Interfaces in ferroelastics: fringing fields, microstructure, and size and shape effects. Phys Rev B 79:214117CrossRef

37.

Arlt J, Hennings D, de With G (1985) Dielectric-properties of fine-grained barium-titanate ceramics. J Appl Phys 58:1619–1625CrossRef

38.

Wang J, Steinmann P (2012) A variational approach towards the modeling of magnetic field-induced strains in magnetic shape memory alloys. J Mech Phys Sol 60:1179–1200CrossRef

39.

Kiefer B, Lagoudas DC (2009) Modeling the coupled strain and magnetization response of magnetic shape memory alloys under magnetomechanical loading. J Intell Mater Sys Struc 20:143–170CrossRef

40.

Auricchio F, Bessoud A-L, Reali A, Stefanelli U (2015) A phenomenological model for the magneto-mechanical response of single-crystal magnetic shape memory alloys. Eur J Mech A Sol 52:1–11CrossRef

41.

Chen X, Moumni Z, He Y, Zhang W (2014) A three-dimensional model of magneto-mechanical behaviors of martensite reorientation in ferromagnetic shape memory alloys. J Mech Phys Sol 64:249–286CrossRef

42.

LaMaster DH, Feigenbaum HP, Nelson ID, Ciocanel C (2014) A full two-dimensional thermodynamic-based model for magnetic shape memory alloys. J Appl Mech 81:061003CrossRef

43.

Shankaraiah N, Murthy KPN, Lookman T, Shenoy SR (2011) Monte Carlo simulations of strain pseudospins: athermal martensites, incubation times, and entropy barriers. Phys Rev B 84:064119CrossRef

44.

Heczko O, Sozinov A, Ullakko K (2000) Giant field-induced reversible strain in magnetic shape memory NiMnGa alloy. IEEE Trans Magn 36:3266–3268CrossRef

45.

Likhachev AA, Ullakko K (2000) Magnetic-field-controlled twin boundaries motion and giant magneto-mechanical effects in Ni–Mn–Ga shape memoy alloy. Phys Lett A 275:142–151CrossRef

46.

Straka L, Heczko O (2005) Reversible 6% strain of Ni–Mn–Ga martensite using opposing external stress in static and variable magnetic fields. J Magn Magn Mater 290–291:829–831CrossRef

47.

Heczko O (2005) Magnetic shape memory effect and magnetization reversal. J Magn Magn Mater 290–291:787–794CrossRef

48.

Karaca HE, Karaman I, Basaran B, Chumlyakov YI, Maier HJ (2006) Magnetic field and stress induced martensite reorientation in NiMnGa ferromagnetic shape memory alloy single crystals. Acta Mater 54:233–245CrossRef

49.

Lloveras P, Touchagues G, Castán T, Lookman T, Porta M, Saxena A, Planes A (2014) Modelling magnetostructural textures in magnetic shape-memory alloys: strain and magnetic glass behaviour. Phys Stat Sol B 251:2080–2087CrossRef

50.

Lloveras P, Castán T, Porta M, Planes A, Saxena A (2008) Influence of elastic anisotropy on structural nanoscale textures. Phys Rev Lett 100:165707CrossRef

51.

Armstrong JN, Sullivan MR, Romancer ML, Chernenko VA, Chopra HD (2008) Role of magnetostatic interactions in micromagnetic structure of multiferroics. J Appl Phys 103:023905CrossRef

Title: Modelling Shape-Memory Effects in Ferromagnetic Alloys
Authors: Jonathan F. Gebbia
Pol Lloveras
Teresa Castán
Avadh Saxena
Antoni Planes
Publication date: 01-09-2015
Publisher: Springer International Publishing
Published in: Shape Memory and Superelasticity / Issue 3/2015
Print ISSN: 2199-384X
Electronic ISSN: 2199-3858
DOI: https://doi.org/10.1007/s40830-015-0025-0

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