Обзор математических моделей для описания фазовых превращений в сталях

1. Grinfeld M.A. Metody mekhaniki sploshnykh sred v teorii fa-

zovykh prevrashcheniy [Methods of continuum mechanics in the theory of 

phase transitions]. Moscow: Nauka, 1990. 312 p.  

2. Kashchenko  М.P., Chashchina V.G. Dinamicheskaya teoriya 

γ–α 

kriticheskogo razmera zerna [Dynamic theory of 

γ–α martensite phase 

transformation in Fe-based alloys and problem of grain critical size]. 

Мoscow, Izhevsk: NITS Regularnaya i khaoticheskaya dinamica, Izhevskiy 

institute kompyuternykh issledovaniy, 2010, 132 p. 

3. Kashchenko  М.P., Chashchina V.G. Formirovanie martensitnykh 

kristallov v predelnom sluchae sverkhzvukovoy skorosti rosta [Formation of 

martensitic crystals in the limiting case of supersonic growth speed]. 

Pisma 

o materialakh, 2011, vol. 1, pp. 7-14. 

4. Lebedev V.G., Danilov D.А., Galenko P.K. Ob uravneniyakh mod-

eli fazovogo polya dlya neizotermicheskoy kinetiki prevrashcheniya v 

mnogokomponentnykh i mnogofaznykh sistemakh [Phase-field model equa-

tions for non isothermal kinetics of transitions in a multi-component and 

multi-phase system]. 

5. Movchan  А.А., Movchan I.А. Odnomernaya mikromekhani-

cheskaya model nelineynogo deformirovaniya splavov s pamyatyu formy 

pri pryamom i obratnom termouprigikh prevrashcheniyakh [One-dimen-

sional micromechanical model of the nonlinear deformation of shape mem-

ory alloys for forward and reverse thermoelastic transformations]. 

pp. 297-322. 

6. Movchan  А.А., Movchan I.А., Silchenko L.G. Mikromekhani-

cheskaya model nelineynogo deformirovaniya splavov s pamyatyu formy 

pri fazovykh i strukturnykh prevrashcheniyakh [Micromechanical model of 

the nonlinear deformation of shape memory alloys during phase and struc-

tural transformations]. 

Izvestiya Rossiyskoy akademii nauk. Mekhanika tver-

dogo tela, 2010, no. 3, pp. 118-130. 

И.Л. Исупова, П.В. Трусов 

 

 

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7. Trusov P.V., Shveykin A.I. Mnogourovnevye fizicheskiy modeli 

mono- i polikristallov. Statisticheskie modeli [Multilevel physical models of 

single- and polycrystals. Statistical models]. 

Fizicheskaya mezomekhanika, 

2011, no. 4, pp. 17-28. 

8. Trusov P.V., Shveykin A.I. Mnogourovnevye fizicheskiy modeli 

mono- i polikristallov. Pryamye modeli [Multilevel physical models of sin-

gle- and polycrystals. Direct models]. 

Fizicheskaya mezomekhanika, 2011, 

vol. 14, no. 4, pp. 5-30. 

9. Freidin А.B., Sharipova L.L. Ravnovesnye dvukhfaznye deformat-

sii i zony fazovykh perekhodov v priblizhenii malykh deformatsiy [Equilib-

rium two-phase deformations and phase transitions zones in the small 

strain]. 

Izvestiya vuzov Severo-Kavkazskogo regiona. Nelineynye problemy 

mekhaniki sploshnykh sred. Special Issue, 2003, pp. 291-298. 

10. Avrami, M. Kinetics of phase change. II: transformation-time rela-

tions for random distribution of nuclei. 

Journal of Chemical Physics, 1940, 

vol. 8, pp. 212. 

11. Barbe F., Quey R., Taleb L. Numerical modelling of the plasticity 

induced during diffusive transformation. Case of a cubic array of nuclei. 

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