 | | 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: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| E.N. Vilchevskaya, I.K. Korolev, and A.B. Freidin, "On Phase Transitions in a Domain of Material Inhomogeneity. II. Interaction of a Crack with an Inclusion Experiencing a Phase Transition," Mech. Solids. 46 (5), 683-691 (2011) |
| Year |
2011 |
Volume |
46 |
Number |
5 |
Pages |
683-691 |
| DOI |
10.3103/S0025654411050049 |
| Title |
On Phase Transitions in a Domain of Material Inhomogeneity. II. Interaction of a Crack with an Inclusion Experiencing a Phase Transition |
| Author(s) |
E.N. Vilchevskaya (Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, Bol'shoy pr-t 61, St. Petersburg, 199178 Russia, vilchevska@gmail.com)
I.K. Korolev (Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, Bol'shoy pr-t 61, St. Petersburg, 199178 Russia, i.korolev82@gmail.com)
A.B. Freidin (Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, Bol'shoy pr-t 61, St. Petersburg, 199178 Russia, freidin@mechanics.ipme.ru) |
| Abstract |
We pose and study the problem on the interaction between a crack and an inclusion experiencing a phase transition of martensite type. We develop an algorithm for determining the inclusion phase state, which is numerically implemented with the finite element method. This procedure is used to study the inclusion phase transitions in the crack-induced field including the effects of the interaction between the crack and the inclusion. The detailed strain fields are calculated depending on the relative position of the crack and the inclusion, the external field, and the material parameters. It is shown that, for sufficient residual strains arising in the inclusion because of the crack, the inclusion material experiences a phase transition, which, in turn, can change the character of the subsequent crack propagation. We demonstrate that a stress-independent intrinsic phase transition, which can be caused, for example, by a change in the temperature, can also affect the crack propagation path. We also show that the influence of the phase transition induced field on the crack propagation path can be suppressed by the external field. |
| Keywords |
phase transitions, crack propagation, material inhomogeneity, finite element method |
| References |
| 1. | V. N. Antsiferov, F. F. Bezdudnyi, L. N. Belyanchikov, et al.,
New Materials,
Ed. by Yu. S. Karabasov
(MISIS, Moscow, 2002)
[in Russian]. |
| 2. | V. A. Eremeev and E. S. Nikitin,
"Phase Transitions in Elastic Bodies Containing Dislocations and Disclinations,"
Dokl. Ross. Akad. Nauk
345 (2), 188-192 (1995)
[Dokl. Phys. (Engl. Transl.)
40 (11), 595-599 (1995)]. |
| 3. | E. N. Vilchevskaya and A. B. Freidin,
"On Phase Transitions in a Domain of Material Inhomogeneity. I.
Phase Transitions of an Inclusions in a Homogeneous External Field,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 5, 188-208 (2007)
[Mech. Solids (Engl. Transl.)
42 (5), 823-840 (2007)]. |
| 4. | A. B. Freidin and E. N. Vilchevskaya,
"On the Phase Transformations of an Inclusion
in an External Strain Field,"
in Proc. XXXII Summer School APM-2004, St. Petersburg
(IPME RAS, St. Petersburg, 2004),
pp. 447-454. |
| 5. | A. B. Freidin,
"Small-Strain Approximation in the Theory of Phase Transitions
of Elastic Bodies under Deformation,"
in Strength and Fracture of Materials and Structures.
Intervuz. Collection of Papers, Vol. 18,
Studies in Elasticity and Plasticity, Ed. by N. F. Morozov
(Izd-vo St. Petersburg Univ., St. Petersburg, 1999),
pp. 266-290
[in Russian]. |
| 6. | N. F. Morozov and A. B. Freidin,
"Zones of Phase Transitions and Phase Transformations in
Elastic Bodies under Various Stress States,"
Trudy Mat. Inst. Steklov
223, 220-232 (1998)
[Proc. Steklov Inst. Math. (Engl. Transl.)
223, 219-232 (1998)]. |
| 7. | V. A. Eremeyev, A. B. Freidin, and L. L. Sharipova,
"The Stability of the Equilibrium of Two-Phase Elastic Solids,"
Prikl. Mat. Mekh.
71 (1), 66-92 (2007)
[J. Appl. Math. Mech. (Engl. Transl.)
71 (1), 61-84 (2007)]. |
| 8. | N. F. Morozov, I. R. Nazyrov, and A. B. Freidin,
"One-Dimensional Problem of the Phase Transformation of an Elastic Sphere,"
Dokl. Ross. Akad. Nauk
346 (2), 188-191 (1996)
[Russian Acad. Sci. Dokl. Math. (Engl. Transl.)
41 (1), 40-43 (1996)]. |
| 9. | I. R. Nazyrov and A. B. Freidin,
"Phase Transformations in Deformation of Solids
in a Model Problem of an Elastic Ball,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 5, 52-71 (1998)
[Mech. Solids (Engl. Transl.)
33 (5), 39-56 (1998)]. |
| 10. | J. D. Eshelby,
"The Determination of the Elastic Field on an Ellipsoidal Inclusion
and Related Problems,"
Proc. Roy. Soc. London. Ser. A
241, 376-396 (1957). |
| 11. | A. B. Freidin,
"On New Phase Inclusions in Elastic Solids,"
ZAMM
87 (2), 102-116 (2007). |
| 12. | A. B. Movchan and S. A. Nazarov,
"Trajectory Bending Caused by Quasistatic Crack Growth
in a Plane with Small Defects,"
in Strength and Fracture of Materials and Structures.
Intervuz. Collection of Papers, Vol. 18,
Studies in Elasticity and Plasticity,
Ed. by N. F. Morozov
(Izd-vo St. Petersburg Univ., St. Petersburg, 1999),
pp. 142-161
[in Russian]. |
| 13. | L. B. Kublanov and A. B. Freidin,
"Solid Phase Seeds in a Deformable Material,"
Prikl. Mat. Mekh.
52 (3), 493-501 (1988)
[J. Appl. Math. Mech. (Engl. Transl.)
52 (3), 382-389 (1988)]. |
| 14. | V. M. Pestrikov and E. M. Morozov,
Fracture Mechanics of Solids
(Professiya, St. Petersburg, 2002)
[in Russian]. |
|
| Received |
29 January 2009 |
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