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Acta Mechanica Sinica

, Volume 22, Issue 3, pp 233–242 | Cite as

Discussion on electromagnetic crack face boundary conditions for the fracture mechanics of magneto-electro-elastic materials

  • Baolin Wang
  • Jiecai Han
Article

Abstract

This paper discusses electromagnetic boundary conditions on crack faces in magneto- electroelastic materials, where piezoelectric, piezomagnetic and magnetoelectric effects are coupled. A notch of finite thickness in these materials is also addressed. Four idealized electromagnetic boundary conditions assumed for the crack-faces are separately investigated, i.e. (a) electrically and magnetically impermeable (crack-face), (b) electrically impermeable and magnetically permeable, (c) electrically permeable and magnetically impermeable, and (d) electrically and magnetically permeable. The influence of the notch thickness on important parameters, such as the field intensity factors, the energy release rate at the notch tips and the electromagnetic fields inside the notch, are studied and the results are obtained in closed-form. Results under different idealized electromagnetic boundary conditions on the crack-face are compared, and the applicability of these idealized assumptions is discussed.

Keywords

Fracture mechanics Magnetoelectroelastic materials Boundary conditions Notch Crack 

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References

  1. 1.
    Alshits, I., Darinskii, A.N., Lothe, J.: On the existence of surface waves in half-anisotropic elastic media with piezoelectric and piezomagnetic properties. Wave Motion, 16, 265–283 (1992)Google Scholar
  2. 2.
    Avellaneda, M., Harshe, G.: Magnetoelectric effect in piezoelectric/magnetostrictive multilayer composites. J. Intell. Mater. Syst. Struct., 5, 501–513 (1994)Google Scholar
  3. 3.
    Barnet, D.M., Lothe, J.: Dislocations and line charges in anisotropic piezoelectric insulators. Phys. Stat. Sol. B-Basic Research, 67, 105–111 (1975)Google Scholar
  4. 4.
    Benveniste, Y.: Magnetoelectric effect in fibrous composites with piezoelectric and piezomagnetic phases. Phys. Rev. B, 51(9), 424–427(1995)Google Scholar
  5. 5.
    Harshe, G., Dougherty, J.P., Newnham, R.E.: Theoretical modelling of multilayer magnetoelectric composites. Int. J. Appl. Electromagn. Mater., 4, 145–159 (1993)Google Scholar
  6. 6.
    Huang, J.H., Kuo, W.S.: The analysis of piezoelectric/piezoelectric composite materials containing an ellipsoidal inclusion. J. Appl. Phys., 81(3), 1378–1386 (1997)Google Scholar
  7. 7.
    Kirchner, H.O.K., Alshits, V.I.: Elastic anisotropic angularly inhomogeneous media. II. The Green's function for piezoelectric, piezomagneitc and magnetoelectric media. Philos. Mag. A, 74, 861–885 (1996)Google Scholar
  8. 8.
    Li, J.Y., Dunn, M.L.: Micromechanics of magnetoelectroelastic composite materials: average fields and effective behavior. J. Intell. Mater. Syst. Struct., 7, 404–416 (1998)Google Scholar
  9. 9.
    Nan, C.W.: Magnetoelectric effect in composites of piezoelectric and piezomagnetic phases. Phys. Rev. B, 50(9), 6082–6088 (1994)Google Scholar
  10. 10.
    Liu, J.X., Liu, X., Zhao, Y.: Green's functions for anisotropic magnetoelectroelastic solids with an elliptical cavity or a crack. International Journal of Engineering Science, 39(12), 1405–1418 (2001)Google Scholar
  11. 11.
    Hu, K.Q., Li, G.Q.: Constant moving crack in a magnetoelectroelastic material under anti-plane shear loading. Int. J. Solids Struct., 42, 2823–2835 (2005)Google Scholar
  12. 12.
    Li, X.F.: Dynamic analysis of a cracked magnetoelectroelastic medium under antiplane mechanical and inplane electric and magnetic impacts. International Journal of Solids and Structures, 42, 3185–3205 (2005)Google Scholar
  13. 13.
    Liu, J.X., Liu, X., Zhao, Y.: Green's functions for anisotropic magnetoelectroelastic solids with an elliptical cavity or a crack. International Journal of Engineering Science, 39(12), 1405–1418(2001)Google Scholar
  14. 14.
    Gao, C.F., Tong, P., Zhang, T.Y.: Fracture mechanics for a mode III crack in a magnetoelectroelastic solid. International Journal of Solids and Structures, 41, 6613–6629 (2004)Google Scholar
  15. 15.
    Tian, W.Y., Gabbert, U.: Multiple crack interaction problem in magnetoelectroelastic solids. European Journal of Mechanics A-Solids, 23 (4), 599–614 (2004)Google Scholar
  16. 16.
    Tian, W.Y., Gabbert, U.: Macrocrack-microcrack interaction problem in magnetoelectroelastic solids. Mechanics of Materials, 37(5), 565–592 (2005)Google Scholar
  17. 17.
    Tian, W.Y., Gabbert, U.: Parallel crack near the interface of magnetoelectroelastic bimaterials. Computational Materials Science, 32(3–4), 562–567 (2005)Google Scholar
  18. 18.
    Li, X.F., Lee, K.Y.: Effects of electric field on crack growth for a penny-shaped dielectric crack in a piezoelectric layer. Journal of the Mechanics and Physics of Solids, 52(9), 2079–2100 (2004)Google Scholar
  19. 19.
    Li, X.F., Lee, K.Y.: Crack growth in a piezoelectric material with a Griffith crack perpendicular to the poling axis. Philosophical Magazine, 84(18), 1789–1820 (2004)Google Scholar
  20. 20.
    Zhang, T.Y., Zhao, M.H., Tong, P.: Fracture of piezoelectric ceramics. Advances in Applied Mechanics, 38, 147–289 (2002)Google Scholar
  21. 21.
    Qin, Q.H.: Fracture Mechanics of Piezoelectric Materials. WIT Press, Southampton, Boston, 2001Google Scholar
  22. 22.
    McMeeking, R.M.: Crack tip energy release rate for a piezoelectric compact tension specimen. Engng. Fract. Mech., 64, 217–244(1999)Google Scholar
  23. 23.
    Huang, J.H.: Magneto-electro-elastic Eshelby tensors for a piezoelectric-piezomagnetic composite reinforced by elliptical inclusions. J. Appl. Phys., 83, 5364–5370 (1998)Google Scholar
  24. 24.
    Aboudi, J.: Micromechanical analysis of fully coupled electro-magneto-thermo-elastic multiphase composites. Smart Mater. Struct., 10, 867–877 (2001)Google Scholar
  25. 25.
    Lage, R.G., Mota Soares, C.M., Mota Soares, C.A., Reddy, J.N.: Layerwise partial mixed finite element analysis of magneto-electro-elastic plates. Computers and Structures, 82, 1293–1301 (2004)Google Scholar
  26. 26.
    Chen, Z.R., Yu, S.W., Lu, M., Ye, L.: Effective properties of layered magneto-electro-elastic composites. Composite Structures, 57, 177–182(2002)Google Scholar
  27. 27.
    Sih, G.C., Song, Z.F.: Magnetic and electric poling effects associated with crack growth in BaTiO3-CoFe2O4 composite. Theor. Appl. Fract. Mech., 39, 209–277(2003)Google Scholar
  28. 28.
    Spyropoulos, C.P., Sih, G.C., Song, Z.F.: Magnetoelectroelastic composite with poling parallel to plane of line crack under out-of-plane deformation. Theoretical and Applied Fracture Mechanics, 39, 281–289 (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.Center for Composite MaterialsHarbin Institute of TechnologyHarbinChina

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