Skip to main content
SpringerLink
Log in

An interface crack with contact zones in a piezoelectric/piezomagnetic bimaterial

  • Original
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

Abstract

An interface crack with a frictionless contact zone at the right crack tip between two semi-infinite piezoelectric/piezomagnetic spaces under the action of a remote mechanical loading, magnetic and electric fluxes as well as concentrated forces at the crack faces is considered. Assuming that all fields are independent on the coordinate x 2 co-directed with the crack front, the stresses, the electrical and the magnetic fluxes as well as the derivatives of the jumps of the displacements, the electrical and magnetic potentials are presented via a set of analytic functions in the (x 1, x 3)-plane with a cut along the crack region. Two cases of magneto-electric conditions at the crack faces are considered. The first case assumes that the crack is electrically and magnetically permeable, and in the second case the crack is assumed electrically permeable while the open part of the crack is magnetically impermeable. For both these cases due to the above-mentioned representation the combined Dirichlet–Riemann boundary value problems have been formulated and solved exactly. Stress, electric and magnetic induction intensity factors are found in a simple analytical form. Transcendental equations and a closed form analytical formula for the determination of the real contact zone length have been derived for both cases of magnetic conditions in the crack region. For a numerical illustration of the obtained results a bimaterial BaTiO3–CoFe2O4 with different volume fractions of BaTiO3 has been used, and the influence of the mechanical loading and the intensity of the magnetic flux upon the contact zone length and the associated intensity factors as well as the energy release rate has been shown.

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. Gao C.-F., Kessler H., Balke H.: Crack problems in magnetoelectroelastic solids. Part I: exact solution of a crack. Int. J. Eng. Sci. 41, 969–981 (2003)

    Article  MathSciNet  Google Scholar 

  2. Gao C.-F., Kessler H., Balke H.: Crack problems in magnetoelectroelastic solids. Part II: general solution of collinear cracks. Int. J. Eng. Sci. 41, 983–994 (2003)

    Article  MathSciNet  Google Scholar 

  3. Nirauala O.P., Wang B.L.: A magneto-electro-elastic material with a penny-shaped crack subjected to temperature loading. Acta Mech. 187, 151–168 (2006)

    Article  Google Scholar 

  4. Feng W.J., Su R.K.L., Pan E.: Fracture analysis of penny-shaped magnetically dialectric crack in a magnetoelectroelastic material. Int. J. Fract. 146, 125–138 (2007)

    Article  Google Scholar 

  5. Gao C.-F., Tong P., Zhang T.-Y.: Interfacial crack problem in magneto-electroelastic solids. Int. J. Eng. Sci. 41, 2105–2121 (2003)

    Article  Google Scholar 

  6. Li R., Kardomateas G.A.: The mixed mode I and II interface crack in piezoelectromagneto-elastic anisotropic bimaterials. Trans. ASME J. Appl. Mech. 74, 614–627 (2007)

    Google Scholar 

  7. Sih G.C., Song Z.F.: Magnetic and electric poling effects associated with crack growth in BaTiO 3–CoFe 2 O 4 composite. Theor. Appl. Fract. Mech. 39, 209–227 (2003)

    Article  Google Scholar 

  8. Song Z.F., Sih G.C.: Crack initiation behaviour in magnetoelectroelastic composite under in-plane deformation. Theor. Appl. Fract. Mech. 39, 189–207 (2003)

    Article  Google Scholar 

  9. Gao C.-F., Noda N.: Thermal-induced interfacial cracking of magnetoelectroelastic materials. Int. J. Eng. Sci. 42, 1347–1360 (2004)

    Article  Google Scholar 

  10. Gao C.-F., Tong P., Zhang T.-Y.: Fracture mechanics for a mode III crack in a magnetoelectroelastic solid. Int. J. Solids Struct. 41, 6613–6629 (2004)

    Article  MATH  Google Scholar 

  11. Li R., Kardomateas G.A.: The mode III interface crack in piezo-electro-magneto-elastic dissimilar bimaterials. Trans. ASME J. Appl. Mech. 73, 220–227 (2006)

    Article  MATH  Google Scholar 

  12. Williams M.L.: The stresses around a fault or cracks in dissimilar media. Bull. Seismological Soc. Am. 49, 199–204 (1959)

    Google Scholar 

  13. Rice J.R.: Elastic fracture mechanics concept for interfacial cracks. J. Appl. Mech. 55, 98–103 (1988)

    Article  Google Scholar 

  14. Comninou M.: The interface crack. J. Appl. Mech. 44, 631–636 (1977)

    MATH  Google Scholar 

  15. Atkinson C.: The interface crack with contact zone (an analytical treatment). Int. J. Fract. 18, 161–177 (1982)

    Google Scholar 

  16. Simonov I.V.: The interface crack in homogeneous field of stresses. Mech. Compos. Mater. 969–976 (1985)

  17. Dundurs J., Gautesen A.K.: An opportunistic analysis of the interface crack. Int. J. Fract. 36, 151–159 (1988)

    Article  Google Scholar 

  18. Qin Q.-H., Mai Y.-W.: A closed crack tip model for interface cracks in thermopiezoelectric materials. Int. J. Solids Struct. 36, 2463–2479 (1999)

    Article  MATH  Google Scholar 

  19. Herrmann K.P., Loboda V.V.: Fracture mechanical assessment of electrically permeable interface cracks in piezoelectric bimaterials by consideration of various contact zone models. Arch. Appl. Mech. 70, 127–143 (2000)

    Article  MATH  Google Scholar 

  20. Herrmann K.P., Loboda V.V., Govorukha V.B.: On contact zone models for an electrically impermeable interface crack in a piezoelectric bimaterial. Int. J. Fract. 111, 203–227 (2001)

    Article  Google Scholar 

  21. Hao T.H., Shen Z.Y.: A new electric boundary condition of electric fracture mechanics and its applications. Eng. Fract. Mech. 47, 793–802 (1994)

    Article  Google Scholar 

  22. Gruebner O., Kamlah M., Munz D.: Finite element analysis of cracks in piezoelectric materials taking into account the permittivity of the crack medium. Eng. Fract. Mech. 70, 1399–1413 (2003)

    Article  Google Scholar 

  23. Wang B.-L., Mai Y.-W.: Applicability of the crack faces electromagnetic boundary conditions for fracture of magnetoelectroelastic materials. Int. J. Solids Struct. 44, 387–398 (2007)

    Article  MATH  Google Scholar 

  24. Kharun I.V., Loboda V.V.: A set of interface cracks with contact zones in combined tension-shear field. Acta Mech. 166, 43–56 (2003)

    Article  MATH  Google Scholar 

  25. Herrmann K.P., Loboda V.V., Komarov A.V.: Contact zone assessment for a fast growing interface crack in an anisotropic bimaterial. Arch. Appl. Mech. 74, 118–129 (2004)

    MATH  Google Scholar 

  26. Winch R.: Electricity and Magnetism. Prentice-Hall, New Jersey (1963)

    Google Scholar 

  27. Muskhelishvili N.I.: Some Basic Problems of the Mathematical Theory of Elasticity. Noordhoff, Leyden (1975)

    MATH  Google Scholar 

  28. Eshelby J.D., Read W.T., Shockley W.: Anisotropic elasticity with application to dislocation theory. Acta Metall. 1, 251–259 (1953)

    Article  Google Scholar 

  29. Suo Z., Kuo C.M., Barnett D.M., Willis J.R.: Fracture mechanics for piezoelectric ceramics. J. Mech. Phys. Solids 40, 739–765 (1992)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, LTM, Paderborn University, Pohlweg 47-49, 33098, Paderborn, Germany

    K. P. Herrmann

  2. Department of Theoretical and Applied Mechanics, National University, Nauchni Str. 13, Dniepropetrovsk, 49050, Ukraine

    V. V. Loboda & T. V. Khodanen

Authors
  1. K. P. Herrmann
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. V. Loboda
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. T. V. Khodanen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. V. Loboda.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Herrmann, K.P., Loboda, V.V. & Khodanen, T.V. An interface crack with contact zones in a piezoelectric/piezomagnetic bimaterial. Arch Appl Mech 80, 651–670 (2010). https://doi.org/10.1007/s00419-009-0330-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-009-0330-1

Keywords

Search

Navigation