Shape memory alloys constitutive relations – micromechanics, phenomenology, thermodynamics
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 152 (2010) no. 4, pp. 180-194 Cet article a éte moissonné depuis la source Math-Net.Ru

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A model of shape memory alloys nonlinear straining at thermoelastic phase and structural transitions is proposed. The formulated system of constitutive relations adequately describes such properties and unique phenomena of shape memory alloys as the change of elastic modules at the martensitic transitions, direct transformation strain accumulation, oriented transition, monotonic shape memory, martensitic unelasticity, superelasticity, latent heat release and absorption at the phase transitions, and the dissipative phenomena.
Keywords: shape memory alloy, nonlinear deformation, micromechanics, structural transitions, thermodynamics, latent heat, energy balance equation.
Mots-clés : constitutive relations, phase transitions
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A. A. Movchan; L. G. Silchenko; S. A. Kazarina; Thant Zin Aung. Shape memory alloys constitutive relations – micromechanics, phenomenology, thermodynamics. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 152 (2010) no. 4, pp. 180-194. http://geodesic.mathdoc.fr/item/UZKU_2010_152_4_a16/

[1] Likhachev V. A., Kuzmin S. L., Kamentseva Z. P., Effekt pamyati formy, Izd-vo LGU, L., 1987, 216 pp.

[2] Volkov A. E., Likhachev V. A., Razov A. I., “Mekhanika plastichnosti materialov s fazovymi prevrascheniyami”, Vestn. LGU, 1984, no. 4(19), 30–37

[3] Abdrakhmanov S. A., Deformatsii materialov s pamyatyu formy pri termosilovom vozdeistvii, ILIM, Bishkek, 1991, 117 pp.

[4] Liang C., Rogers C. A., “One dimensional thermomechanical constitutive relations for shape memory materials”, J. Intell. Mater. Syst. Struct., 1:2 (1990), 207–234 | DOI

[5] Tanaka K. A., “A phenomenological description on thermomechanical behavior of shape memory alloys”, J. Pressure Vessel Technol. Trans ASME, 112:2 (1990), 158–193 | DOI

[6] Movchan A. A., “Mikromekhanicheskii podkhod k opisaniyu protsessov deformirovaniya i nakopleniya povrezhdenii pri slozhnom napryazhennom sostoyanii”, IV Simpozium “Prochnost materialov i elementov konstruktsii pri slozhnom napryazhennom sostoyanii”, Kiev, 1992, 45–46

[7] Movchan A. A., “Mikromekhanicheskie opredelyayuschie uravneniya dlya splavov s pamyatyu formy”, Problemy mashinostroeniya i nadezhnosti mashin, 1994, no. 6, 47–53

[8] Movchan A. A., “Mikromekhanicheskii podkhod k opisaniyu deformatsii martensitnykh prevraschenii v splavakh s pamyatyu formy”, Izv. RAN. MTT, 1995, no. 1, 197–205 | MR

[9] Movchan A. A., “Vybor approksimatsii diagrammy perekhoda i modeli ischeznoveniya kristallov martensita dlya splavov s pamyatyu formy”, PMTF, 1995, no. 2, 173–181

[10] Boyd J. G., Lagoudas D. C., “A thermodynamic constitutive model for shape memory materials. Part 1. The monolithic shape memory alloy”, Int. J. Plast., 12:6 (1996), 805–842 | DOI | Zbl

[11] Leclercq S., Lexcellent C., “A general macroscopic description of the thermomechanical behavior of shape memory alloys”, J. Mech. Phys. Solids, 44:6 (1996), 953–980 | DOI

[12] Volkov A. E., Sakharov V. Yu., “Termomekhanicheskaya makromodel splavov s effektom pamyati formy”, Izv. RAN. Ser. fiz., 67:6 (2003), 845–851

[13] Auricchio F., Sacco E., “A temperature dependent beam for shape memory alloys: constitutive modeling, finite element implementationand numerical simulations”, Comput. Meth. Appl. Mech. Eng., 174 (1999), 171–190 | DOI | Zbl

[14] Movchan A. A., “Nekotorye proyavleniya sposobnosti k orientirovannomu prevrascheniyu dlya splavov s pamyatyu formy”, PMTF, 37:6 (1996), 181–189

[15] Movchan A. A., Shelymagin P. V., Kazarina S. A., “Opredelyayuschie uravneniya dlya dvukhetapnykh termouprugikh fazovykh prevraschenii”, PMTF, 42:5 (2001), 152–160

[16] Movchan A. A., “Analiticheskoe reshenie zadach o pryamom i obratnom prevraschenii dlya splavov s pamyatyu formy”, Izv. RAN. MTT, 1996, no. 4, 136–144 | MR

[17] Movchan A. A., “Uchet peremennosti uprugikh modulei i vliyaniya napryazhenii na fazovyi sostav v splavakh s pamyatyu formy”, Izv. RAN. MTT, 1998, no. 1, 79–90 | MR

[18] Movchan A. A., “Issledovanie effektov svyaznosti v zadachakh izgiba balok iz splava s pamyatyu formy”, PMTF, 3:1 (1998), 87–97

[19] Movchan A. A., “Kruchenie prizmaticheskikh sterzhnei iz splavov s pamyatyu formy”, Izv. RAN. MTT, 2000, no. 6, 143–154 | Zbl

[20] Movchan A. A., Silchenko L. G., “Ustoichivost sterzhnya, preterpevayuschego pryamoe i obratnoe martensitnye prevrascheniya pod deistviem szhimayuschikh napryazhenii”, PMTF, 44:3 (2003), 169–178 | Zbl

[21] Movchan A. A., Silchenko L. G., “Ustoichivost plastiny iz splava s pamyatyu formy pri pryamom termouprugom prevraschenii”, PMM, 68:1 (2004), 60–72 | MR | Zbl

[22] Movchan A. A., Silchenko L. G., “Analiz ustoichivosti pri pryamom termouprugom prevraschenii pod deistviem szhimayuschikh napryazhenii”, Izv. RAN. MTT, 2004, no. 2, 132–144

[23] Movchan A. A., Silchenko L. G., “Analiticheskoe reshenie svyaznoi zadachi ob ustoichivosti plastiny iz splava s pamyatyu formy pri obratnom martensitnom prevraschenii”, Izv. RAN. MTT, 2004, no. 5, 153–167

[24] Movchan A. A., Silchenko L. G., “Ustoichivost krugloi plastiny iz splava s pamyatyu formy pri pryamom martensitnom prevraschenii”, PMM, 70:5 (2006), 869–881 | MR

[25] Movchan A. A., Silchenko L. G., “Poterya ustoichivosti krugloi plastiny iz splava s pamyatyu formy, vyzvannaya obratnym termouprugim martensitnym prevrascheniem”, Izv. RAN. MTT, 2008, no. 1, 117–130

[26] Likhachev V. A., Malinin V. G., Strukturno-analiticheskaya teoriya prochnosti, Nauka, SPb., 1993, 471 pp.

[27] Movchan A. A., Nyunt So., “Termodinamicheskoe opisanie povedeniya splavov s pamyatyu formy s pomoschyu additivnogo potentsiala Gibbsa”, PMTF, 47:4 (2006), 98–103 | Zbl

[28] Klopotov A. A., Marchenko E. S., Matyunin A. N., Kozlov E. V., “Deformatsiya Beina pri termouprugikh martensitnykh prevrascheniyakh v intermetallidakh na osnove nikelida titana”, Izv. RAN. Ser. fiz., 72:8 (2008), 1098–1101

[29] Movchan A .A., Movchan I. A., “Model nelineinogo deformirovaniya splavov s pamyatyu formy v aktivnykh protsessakh pryamogo prevrascheniya i strukturnogo perekhoda”, Mekhanika kompozitsionnykh materialov i konstruktsii, 14:1 (2008), 75–87

[30] Movchan A. A., Mishustin I. V., “Analiz neadditivnykh dobavok k potentsialu Gibbsa splava s pamyatyu formy”, Izv. RAN. Ser. fiz., 70:9 (2006), 1388–1395 | MR

[31] Wu X. D., Sun G. J., Wu J. S., “The nonlinear relationship between transformation strain and applied stress for nitinol”, Mater. Lett., 57 (2003), 1334–1338 | DOI

[32] Petrovskii I. G., Lektsii po teorii obyknovennykh differentsialnykh uravnenii, Gostekhizdat, M.–L., 1952, 232 pp. | MR

[33] Belyaev S. P., Volkov A. E., Ermolaev V. A. i dr., Materialy s effektom pamyati formy, Sprav. izd., ed. V. A. Likhachev, Izd-vo NIIKh SPbGU, SPb., 1998, 374 pp.