Skip to main content
SpringerLink
Log in

A new extended pre-fracture zone model for a limited permeable crack in an interlayer between magnetoelectroelastic materials

  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

This paper considers the plane problem for two identical semi-infinite magnetoelectroelastic (MEE) materials, which are adhered together by a thin interlayer. A limited permeable crack is assumed to form in the interlayer parallel to its faces, and the interlayer is softer than the adherent MEE materials. To avoid singularities in the vicinity of a crack, which do not exist in reality, the extended pre-fracture zones including three distinct zones, i.e., the mechanical yield zone, the electrical saturation zone and the magnetic saturation zone, of finite lengths are introduced as crack continuations. The problem is formulated mathematically as a system of three linear equations, which can be solved exactly. The unknown lengths of the extended pre-fracture zones are determined by requiring that the stress, the electrical displacement and the magnetic induction are all finite at the ends of these zones. The fracture parameters, such as the crack opening displacement, and the jumps in the electrical and/or magnetic potentials through the crack region as well as the energy release rate are obtained. All these parameters are presented in a simple explicit form which can be determined efficiently without complicated computation that makes the present results rather convenient for any theoretical analysis and engineering applications. Additionally, numerical results are presented to study the influence of various factors on fracture parameters.

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. Parton, V.Z., Kudryavtsev, B.A.: Electromagnetoelasticity. Gordon and Breach Science Publishers, New York (1988)

    Google Scholar 

  2. Zhou, Z.G., Wang, B., Sun, Y.G.: Two collinear interface cracks in magneto-electro-elastic composites. Int. J. Eng. Sci. 42, 1155–1167 (2004)

    Article  MATH  Google Scholar 

  3. 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 

  4. 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)

    Article  MATH  Google Scholar 

  5. Feng, W.J., Su, R.K.L.: Dynamic internal crack problem of a functionally graded magneto-electro-elastic strip. Int. J. Solids Struct. 43, 5196–5216 (2006)

    Article  MATH  Google Scholar 

  6. Feng, W.J., Pan, E., Wang, X.: Dynamic fracture analysis of a penny-shaped crack in a magnetoelectroelastic layer. Int. J. Solids Struct. 44, 7955–7974 (2007)

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  8. Wang, B.L., Han, J.C., Mai, Y.W.: Mode III fracture of a magnetoelectroelastic layer: exact solution and discussion of the crack face electromagnetic boundary conditions. Int. J. Fract. 139, 27–38 (2006)

    Article  MATH  Google Scholar 

  9. Yong, H.D., Zhou, Y.H.: Transient response of a cracked magnetoelectroelastic strip under anti-plane impact. Int. J. Solids Struct. 44, 705–717 (2007)

    Article  MATH  Google Scholar 

  10. Wang, B.L., Sun, Y.G., Zhang, H.Y.: Analysis of a penny-shaped crack in magnetoelectroelastic materials. J. Appl. Phys. 103, 083530 (2008)

    Article  Google Scholar 

  11. Li, X.F.: Dynamic analysis of a cracked magnetoelectroelastic medium under antiplane mechanical and inplane electric magnetic impacts. Int. J. Solids Struct. 42, 3185–3205 (2001)

    Article  Google Scholar 

  12. Singh, B.M., Rokne, J., Dhaliwal, R.S.: Closed-form solutions for two anti-plane collinear cracks in a magnetoelectroelastic layer. Eur. J. Mech. A Solid. 28, 599–609 (2009)

    Article  MATH  Google Scholar 

  13. 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  MATH  MathSciNet  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  15. Sih, G.C., Jones, R., Song, Z.F.: Piezomagnetic and piezoelectric poling effects on mode I and II crack initiation behavior of magnetoelectroelastic materials. Theor. Appl. Fract. Mech. 40, 161–186 (2003)

    Article  Google Scholar 

  16. Tian, W.Y., Gabbert, U.: Macrocrack–microcrack interaction problem in magnetoelectroelastic solids. Mech. Mater. 37, 565–592 (2005)

    Article  Google Scholar 

  17. Zhou, Z.G., Zhang, P.W., Wu, L.Z.: The closed form solution of a mode-I crack in the piezoelectric/piezomagnetic materials. Int. J. Solids Struct. 44, 419–435 (2007)

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  19. Chen, X.H.: Energy release rate and path-independent integral in dynamic fracture of magneto-electro-thermo-elastic solids. Int. J. Solids Struct. 46, 2706–2711 (2009)

    Article  MATH  Google Scholar 

  20. Zhong, X.C., Liu, F., Li, X.F.: Transient response of a magnetoelectroelastic solid with two collinear dielectric cracks under impacts. Int. J. Solids Struct. 46, 2950–2958 (2009)

    Article  MATH  Google Scholar 

  21. Zhong, X.C., Zhang, K.S.: Dynamic analysis of a penny-shaped dielectric crack in a magnetoelectroelastic solid under impacts. Eur. J. Mech. A Solids 29, 242–252 (2010)

    Article  MathSciNet  Google Scholar 

  22. Wünsche, M., Sáez, A., García-Sánchez, F., Zhang, Ch.: Transient dynamic crack analysis in linear magnetoelectroelastic solids by a hypersingular time-domain BEM. Eur. J. Mech. A Solids 32, 118–130 (2012)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  25. 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)

    Article  MATH  Google Scholar 

  26. Feng, W.J., Ma, P., Pan, E., Liu, J.X.: A magnetically impermeable and electrically permeable interface crack with a contact zone in a magnetoelectroelastic bimaterial under concentrated magnetoelectromechanical loads on the crack faces. Sci. China Phys. Mech. Astron. 54, 1666–1679 (2011)

    Article  Google Scholar 

  27. Ma, P., Feng, W.J., Su, R.K.L.: An electrically impermeable and magnetically permeable interface crack with a contact zone in a magnetoelectroelastic bimaterial under uniform magnetoelectromechanical loads. Eur. J. Mech. A Solids 32, 41–51 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  28. Zhao, M.H., Li, N., Fan, C.Y., Xu, G.T.: Analysis method of planar interface cracks of arbitrary shape in three-dimensional transversely isotropic magnetoelectroelastic bimaterials. Int. J. Solids Struct. 45, 1804–1824 (2008)

    Article  MATH  Google Scholar 

  29. Zhu, B.J., Shi, Y.L., Qin, T.Y., Sukop, M., Yu, S.H., Li, Y.B.: Mixed-mode stress intensity factors of 3D interface crack in fully coupled electromagnetothermoelastic multiphase composites. Int. J. Solids Struct. 46, 2669–2679 (2010)

    Article  Google Scholar 

  30. Ma, P., Feng, W.J., Su, R.K.L.: Pre-fracture zone model on electrically impermeable and magnetically permeable interface crack between two dissimilar magnetoelectroelastic materials. Eng. Fract. Mech. 102, 310–323 (2013)

    Article  Google Scholar 

  31. Zhao, M.H., Fan, C.Y.: Strip electric–magnetic breakdown model in magnetoelectroelastic medium. J. Mech. Phys. Solids. 56, 3441–3458 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  32. Fan, C.Y., Zhao, M.H.: Nonlinear fracture of 2D magnetoelectroelastic media: analytical and numerical solutions. Int. J. Solids Struct. 48, 2383–2392 (2011)

    Article  Google Scholar 

  33. Bhargava, R.R., Gupta, S.: Mathematical model for crack arrest of a transversely cracked piezoelectromagnetic strip-Part I. Appl. Math. Model. 36, 3502–3512 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  34. Loboda, V., Lapusta, Y., Sheveleva, A.: Limited permeable crack in an interlayer between piezoelectric materials with different zones of electrical saturation and mechanical yielding. Int. J. Solids Struct. 47, 1795–1806 (2010)

    Article  MATH  Google Scholar 

  35. Loboda, V., Lapusta, Y., Sheveleva, A.: Electro-mechanical pre-fracture zones for an electrically permeable interface crack in a piezoelectric biomaterial. Int. J. Solids Struct. 44, 5538–5553 (2007)

    Article  MATH  Google Scholar 

  36. Lapusta, Y., Loboda, V.: Electro-mechanical yielding for a limited permeable crack in an interlayer between piezoelectric materials. Mech. Res. Commun. 36, 183–192 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  37. Tvergaard, V., Hutchinson, J.W.: On the toughness of ductile adhesive joints. J. Mech. Phys. Solids 44, 789–800 (1996)

    Article  Google Scholar 

  38. Wang, T.C.: Analysis of strip electric saturation model of crack problem in piezoelectric materials. Int. J. Solids Struct. 37, 6031–6049 (2000)

    Article  MATH  Google Scholar 

  39. Fan, C.Y., Zhao, Y.F., Zhao, M.H., Pan, E.: Analytical solution of a semi-permeable crack in a 2D piezoelectric medium based on the PS model. Mech. Res. Commun. 40, 34–40 (2012)

    Article  Google Scholar 

  40. Gao, H., Zhang, T.Y., Tong, P.: Local and global energy release rates for an electrically yielded crack in a piezoelectric ceramic. J. Mech. Phys. Solids. 45, 491–510 (1997)

    Article  Google Scholar 

  41. Sih, G.C., Song, Z.F.: Magnetic and electric poling effects associated with crack growth in BaTiO3–CoFe2O4 composite. Theor. Appl. Fract. Mech. 39, 209–227 (2003)

    Article  Google Scholar 

  42. Tian, W.Y., Rajapakse, R.K.N.D.: Fracture analysis of magnetoelectroelastic solids by using path independent integrals. Int. J. Fract. 131, 311–335 (2005)

    Article  MATH  Google Scholar 

  43. Annigeri, A.R., Ganesan, N., Swarnamani, S.: Free vibration behaviour of multiphase and layered magneto-electro-elastic beam. J. Sound Vib. 299, 44–63 (2007)

    Article  Google Scholar 

  44. Wang, B.L.: Fracture and effective properties of finite magnetoelectroelastic media. J. Intell. Mater. Syst. Struct. 23, 1699–1712 (2012)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Civil Engineering, The University of Hong Kong, Hong Kong, People’s Republic of China

    P. Ma & R. K. L. Su

  2. Department of Engineering Mechanics, Shijiazhuang Tiedao University, Shijiazhuang, 050043, People’s Republic of China

    W. J. Feng

Authors
  1. P. Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. K. L. Su
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. W. J. Feng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to R. K. L. Su.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ma, P., Su, R.K.L. & Feng, W.J. A new extended pre-fracture zone model for a limited permeable crack in an interlayer between magnetoelectroelastic materials. Acta Mech 226, 1045–1065 (2015). https://doi.org/10.1007/s00707-014-1235-9

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-014-1235-9

Keywords

Search

Navigation