 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| A. A. Vakulenko, "On micro and macro kinetics of martensitic transformations," Mech. Solids. 36 (5), 31-46 (2001) |
| Year |
2001 |
Volume |
36 |
Number |
5 |
Pages |
31-46 |
| Title |
On micro and macro kinetics of martensitic transformations |
| Author(s) |
A. A. Vakulenko (St. Petersburg) |
| Abstract |
In some publications of the last two decades, martensitic transformations
in metals and alloys have been approached by the methods of continuum
mechanics. A notable place among these works belongs to the publications
by M. A. Grinfeld, who has used the classical variational
principles of thermodynamics, formulated by J. Gibbs [1], for the
investigation of solid state phase transformations [2]. In these
investigations by M. A. Grinfeld, summarized in his monograph [2], the
conditions of equilibrium of phases are constructed in a mathematically
rigorous way, without any restrictions on the form of the stress state of
the phases and the magnitude of their strain (in the classical work by
J. Gibbs [1], the famous "phase rule" is obtained under the assumption
that the stresses and the strains of all phases are in a "spherical"
state). However, the studies described in [2] do not go beyond the
conditions of phase equilibrium: the kinetics of martensitic
transformations is left untouched. Moreover, for some reason, martensitic
transformations are defined in [2] merely as transformations with a
coherent interface between the phases, with no additional conditions,
although the coherence is neither the only nor the most important
feature of martensitic transformations. The basic feature of martensitic
transformations is the absence of diffusion, as noticed by
G. V. Kurdyumov [3]. All other characteristics of typical martensitic
transformations ultimately follow from their being diffusion-free [4]. As
shown below, this can be more or less fully taken into account in the
framework of continuum mechanics (and thermodynamics). And this provides
the possibility for a rigorous derivation of relations that describe the
development of martensitic transformations on the macro and the micro
levels, in particular, transformations related to the effects of "shape
memory" of metallic bodies. To demonstrate this possibility and the
ways of its realization is the aim of the present paper. |
| References |
| 1. | J. W. Gibbs, "On the equilibrium of heterogeneous substances,"
Trans. Connect. Acad., Vol. 3, pp. 108-203, 1876; Vol. 3,, pp. 345-524,
1878. |
| 2. | M. A. Grinfeld, Methods of Continuum Mechanics
in the Theory of Phase Transformations [in Russian], Nauka, Moscow, 1990. |
| 3. | G. V. Kurdyumov and L. G. Khandros,
"On thermoelastic equilibrium in martensitic transformations,"
Doklady AN SSSR, Vol. 66, No. 2, pp. 211-214, 1949. |
| 4. | G. Christian, Theory of Transformations in Metals and Alloys.
Part 1. Thermodynamics and the General Kinetic Theory [Russian translation], Mir, Moscow,
1978. |
| 5. | K. M. Weiman, "Martensitic transformations. Investigations
by electron microscope and diffraction methods," in Diffraction and
microscoping methods in materials science [Russian translation], pp. 128-181, Mir,
Moscow, 1984. |
| 6. | Shape Memory Effects in Alloys [in Russian], Metallurgia, Moscow, 1979. |
| 7. | A. I. Lur'e, Nonlinear Theory of Elasticity [in Russian], Nauka, Moscow, 1980. |
| 8. | A. I. Lur'e, Theory of Elasticity, Nauka, Moscow, 1970. |
| 9. | A. Goland, "Modern studies on point defects in metals," in
Point Defects in Solids [Russian translation], Mir, Moscow, 1979. |
| 10. | P. Honeycomb, Plastic Deformation of Metals [Russian translation],
Mir, Moscow, 1972. |
| 11. | J. P. Hirth and J. Lothe, Theory of Dislocations [Russian translation],
Atomizdat, Moscow, 1972. |
| 12. | L. A. Girifalco, Statistical Physics of Materials [Russian translation], Mir,
Moscow, 1975. |
| 13. | L. M. Zubov and A. N. Rudev,
"A canonical representation for the deviator of a symmetric tensor,"
Doklady AN, Vol. 358, No. 1, pp. 44-47, 1998. |
| 14. | I. R. Prigogine, "Étude thermodynamique des processes
irreversible", Dunod, Paris, 1947. |
| 15. | A. A. Vakulenko, "On the theory of irreversible processes",
Vestnik LGU, Vol. 7, No. 2, pp. 84-91, 1969. |
| 16. | A. A. Vakulenko, "Superposition in the rheology of
continuous media," Izv. AN SSSR. MTT [Mechanics of Solids],
No. 1, pp. 69-76, 1970. |
| 17. | A. A. Vakulenko, "Relations between micro and macro
properties of elastic-plastic media," in
Advances in Science and Technology. Ser. Mechanics of
Solids. Volume 22 [in Russian], pp. 3-54, VINITI, Moscow, 1991. |
|
| Received |
01 February 2000 |
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