Skip to main content

Interphase Inclusion and Crack in an Inhomogeneous Anisotropic Plane

  • Conference paper
  • First Online:
Proceedings of the Second International Conference on Theoretical, Applied and Experimental Mechanics (ICTAEM 2019)

Abstract

In the inhomogeneous anisotropic plane the problem about interaction between interphase crack and inclusion, which is in the conditions of full cohesion, was considered. Using the method of singular integral relations for interphase defects, the problem was reduced to the system of singular integral equations, and the method for its solution is proposed. As a result, the effect of the distance between defects, the loading applied to them and the properties of anisotropic materials on the features of the stress fields in the neighborhood of defects was investigated. In particular, the critical distance between the crack and the inclusion, according to which the mutual influence of the defects is significant, was established. It was also established under what loads it is advisable to remain within the singular statement of the problem without taking into account the contact zones of the crack edges.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Krivoi, A.F., Radiollo, M.V.: Specific features of the stress field near inclusions in a composite anisotropic plane. Izv. Akad. Nauk SSSR Mekh. Tverd. Tela. № 3, 84–92 (1984)

    Google Scholar 

  2. Krivoi, A.F., Radiollo, M.V.: Fundamental solution of a plane problem of elasticity theory for a composite anisotropic medium. J. Sov. Math. 60(2), 1365–1368 (1992). https://doi.org/10.1007/BF01679639

    Article  Google Scholar 

  3. Krivoi, A.F.: A fundamental solution for a four-component anisotropic plane. Vest. Odessk. Nats. Univ. Fiz. Mat. Nauki 8, 140–149 (2003)

    Google Scholar 

  4. Krivoy, O.F., Arkhipenko, K.M.: A crack extending onto conjunction line between two different anisotropic half-planes. Math. Methods Phys. Mech. Fields 48(3), 110–116 (2005)

    Google Scholar 

  5. Krivoi, A.F., Popov, G.Y.: Interface tunnel cracks in a composite anisotropic space. J. Appl. Math. Mech. 72(4), 689–700 (2008). https://doi.org/10.1016/j.jappmathmech.2008.08.001

    Article  MathSciNet  Google Scholar 

  6. Kryvyi, O.F.: Tunnel inclusions in a piecewise homogeneous anisotropic space. Math. Methods Phys. Mech. Fields 50(2), 55–65 (2007)

    Google Scholar 

  7. Krivoi, A.F., Popov, G.Y.: Features of the stress field near tunnel inclusions in an inhomogeneous anisotropic space. Appl. Mech. 44(6), 626–634 (2008). https://doi.org/10.1007/s10778-008-0084-4

    Article  MathSciNet  Google Scholar 

  8. Kryvyy, O.F.: Tunnel internal crack in a piecewise homogeneous anisotropic space. J. Math. Sci. 198(1), 62–74 (2014). https://doi.org/10.1007/s10958-014-1773-7

    Article  MathSciNet  Google Scholar 

  9. Kryvyi, O.F.: Mutual influence of an interface tunnel crack and an interface tunnel inclusion in a piecewise homogeneous anisotropic space. J. Math. Sci. 208(4), 409–416 (2015). https://doi.org/10.1007/s10958-015-2455-9

    Article  Google Scholar 

  10. Arkhypenko, K.M., Kryvyi, O.F.: Some boundary-value problems for anisotropic quarter plane. IOP Conf. Ser. J. Phys. Conf. Series 991, 1–7 (2018). https://doi.org/10.1088/1742-6596/991/1/012004

    Google Scholar 

  11. Popov, G.Y.: Concentration of elastic stresses near dies, cuts, thin inclusions and reinforcements. Science, Moscow (1982)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Oleksandr Kryvyi .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Arkhypenko, K., Kryvyi, O. (2019). Interphase Inclusion and Crack in an Inhomogeneous Anisotropic Plane. In: Gdoutos, E. (eds) Proceedings of the Second International Conference on Theoretical, Applied and Experimental Mechanics. ICTAEM 2019. Structural Integrity, vol 8. Springer, Cham. https://doi.org/10.1007/978-3-030-21894-2_38

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-21894-2_38

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-21893-5

  • Online ISBN: 978-3-030-21894-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics