Skip to main content
SpringerLink
Log in

On phase transitions in a domain of material inhomogeneity. II. Interaction of a crack with an inclusion experiencing a phase transition

  • Published:
Mechanics of Solids Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

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].

    Google Scholar 

  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)].

    MathSciNet  Google Scholar 

  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.

    Google Scholar 

  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].

    Google Scholar 

  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)].

    MathSciNet  Google Scholar 

  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)].

    MathSciNet  Google Scholar 

  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)].

    MathSciNet  Google Scholar 

  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).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  11. A. B. Freidin, “On New Phase Inclusions in Elastic Solids,” ZAMM 87(2), 102–116 (2007).

    Article  MATH  MathSciNet  Google Scholar 

  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].

    Google Scholar 

  13. L. B. Kublanov and A. B. Freidin, “Solid Phase Seeds in a DeformableMaterial,” Prikl. Mat. Mekh. 52(3), 493–501 (1988) [J. Appl.Math. Mech. (Engl. Transl.) 52 (3), 382–389 (1988)].

    MathSciNet  Google Scholar 

  14. V. M. Pestrikov and E. M. Morozov, Fracture Mechanics of Solids (Professiya, St. Petersburg, 2002) [in Russian].

Download references

Author information

Authors and Affiliations

  1. Institute for Problems inMechanical Engineering, Russian Academy of Sciences, Boluri45929shoy pr-t 61, St. Petersburg, 199178, Russia

    E. N. Vilchevskaya, I. K. Korolev & A. B. Freidin

Authors
  1. E. N. Vilchevskaya
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. K. Korolev
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. B. Freidin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. N. Vilchevskaya.

Additional information

Original Russian Text © E.N. Vilchevskaya, I.K. Korolev, A.B. Freidin, 2011, published in Izvestiya Akademii Nauk. Mekhanika Tverdogo Tela, 2011, No. 5, pp. 32–42.

About this article

Cite this article

Vilchevskaya, E.N., Korolev, I.K. & Freidin, A.B. On phase transitions in a domain of material inhomogeneity. II. Interaction of a crack with an inclusion experiencing a phase transition. Mech. Solids 46, 683–691 (2011). https://doi.org/10.3103/S0025654411050049

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0025654411050049

Keywords

Search

Navigation