Skip to main content
SpringerLink
Log in

A magnetically impermeable and electrically permeable interface crack with a contact zone in a magnetoelectroelastic bimaterial under concentrated magnetoelectromechanical loads on the crack faces

  • Research Paper
  • Published:
Science China Physics, Mechanics and Astronomy Aims and scope Submit manuscript

Abstract

An interface crack with a frictionless contact zone at the right crack-tip between two dissimilar magnetoelectroelastic materials under the action of concentrated magnetoelectromechanical loads on the crack faces is considered. The open part of the crack is assumed to be magnetically impermeable and electrically permeable. The Dirichlet-Riemann boundary value problem is formulated and solved analytically. Stress, magnetic induction and electrical displacement intensity factors as well as energy release rate are thus found in analytical forms. Analytical expressions for the contact zone length have been derived. Some numerical results are presented and compared with those based on the other crack surface conditions. It is shown clearly that the location and magnitude of the applied loads could significantly affect the contact zone length, the stress intensity factor and the energy release rate.

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. New York: Gordon and Breach Science Publishers, 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, 2004, 42: 1155–1167

    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, 2004, 41: 6613–6629

    Article  MATH  Google Scholar 

  4. Chue C H, Liu T J C. Magneto-electro-elastic antiplane analysis of a bimaterial BaTiO3-CoFe2O4 composite wedge with an interface crack. Theor Appl Fract Mech, 2005, 44: 275–296

    Article  Google Scholar 

  5. Hu K Q, Li G Q. Constant moving crack in a magnetoelectroelastic material under anti-plane shear loading. Int J Solids Struct, 2005, 42: 2823–2835

    Article  MathSciNet  MATH  Google Scholar 

  6. Feng W J, Xue Y, Zou Z Z. Crack growth of an interface crack between two dissimilar magneto-electro-elastic materials under antiplane mechanical and in-plane electromagnetic impact. Theor Appl Fract Mech, 2005, 43: 376–394

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  9. Li Y D, Lee K Y. Anti-plane crack intersecting the interface in a bonded smart structure with graded magnetoelectroelastic properties. Theor Appl Fract Mech, 2008, 50: 235–242

    Article  Google Scholar 

  10. Zhou Z G, Wang J Z, Wu L Z. The behavior of two parallel non-symmetric interface cracks in a magneto-electro-elastic material strip under an anti-plane shear stress loading. Int J Appl Electromagn Mech, 2009, 29: 163–184

    Google Scholar 

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

    Article  MATH  Google Scholar 

  12. 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, 2006, 139: 27–38

    Article  MATH  Google Scholar 

  13. Zhao M H, Yang F, Liu T. Analysis of a penny-shaped crack in a magneto-electro-elastic medium. Philos Mag, 2006, 86: 4397–4416

    Article  ADS  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  16. Wang B L, Sun Y G, Zhang H Y. Analysis of a penny-shaped crack in magnetoelectroelastic materials. J Appl Phys, 2008, 103: 083530-1-8

    Google Scholar 

  17. 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, 2010, 29: 242–252

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  19. 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-Solids, 2009, 28: 599–609

    Article  MATH  Google Scholar 

  20. Liu J X, Liu X L, Zhao Y B. Green’s functions for anisotropic magnetoelectroelastic solids with an elliptical cavity or a crack. Int J Eng Sci, 2001, 39: 1405–1418

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  24. 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, 2003, 40: 161–186

    Article  Google Scholar 

  25. Tian W Y, Gabbert U. Multiple crack interaction problem in magnetoelectroelastic solids. Eur J Mech A-Solids, 2004, 23: 599–614

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  28. Zhong X C, Li X F. T-stress analysis for a Griffith crack in a magnetoelectroelastic solid. Arch Appl Mech, 2007, 78: 117–125

    Article  Google Scholar 

  29. 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, 2007, 44: 419–435

    Article  MATH  Google Scholar 

  30. Zhou Z G. Wang J Z, Wu L Z. Two collinear Mode-I cracks in piezoelectric/piezomagnetic materials. Struct Eng Mech, 2008, 29: 55–75

    Google Scholar 

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

    Article  MATH  Google Scholar 

  32. 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, 2009, 46: 2950–2958

    Article  MATH  Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

  35. Gao C F, Tong P, Zhang T Y. Interfacial crack problems in magneto-electric solids. Int J Eng Sci, 2003, 41: 2105–2121

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  38. Feng W J, Su R K L, Liu J X, et al. Fracture analysis of bounded magnetoelectroelastic layers with interfacial cracks under magnetoelectromechanical loads: Plane Problem. J Intell Mater Syst Struct, 2010, 21: 581–594

    Article  Google Scholar 

  39. Feng W J, Li Y S, Xu Z H. Transient response of an interfacial crack between dissimilar magnetoelectroelastic layers under magnetoelectromechanical impact loadings: mode-I problem. Int J Solids Struct, 2009, 46: 3346–3356

    Article  MATH  Google Scholar 

  40. Li X F, Liu G L, Lee K Y. Magnetoelectroelastic field induced by a crack terminating at the interface of a bi-magnetoelectric material. Philos Mag, 2009, 89: 449–463

    Article  ADS  Google Scholar 

  41. Zhao M H, Li N, Fan CY, et al. Analysis method of planar interface cracks of arbitrary shape in three-dimensional transversely isotropic magnetoelectroelastic bimaterials. Int J Solids Struct, 2008, 45: 1804–1824

    Article  MATH  Google Scholar 

  42. Zhu B J, Shi Y L, Qin T Y, et al. Mixed-mode stress intensity factors of 3D interface crack in fully coupled electromagnetothermoelastic multiphase composites. Int J Solids Struct, 2010, 46: 2669–2679

    Article  Google Scholar 

  43. Comninou M. The interface crack. ASME J Appl Mech, 1977, 44: 631–636

    Article  MATH  Google Scholar 

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

    Google Scholar 

  45. Simonov I V. The interface crack in homogeneous field of stresses. Mech Compos Mater, 1985, 46: 969–976

    Google Scholar 

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

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  48. 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, 2000, 70: 127–143

    Article  ADS  MATH  Google Scholar 

  49. 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, 2001, 111: 203–227

    Article  Google Scholar 

  50. Herrmann K P, Loboda V V, Khodanen T V. An interface crack with contact zones in a piezoelectric/piezomagnetic bimaterial. Arch Appl Mech, 2010, 80: 651–670

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  52. Muskhelishvili N I. Some Basic Problems of the Mathematical Theory of Elasticity. Noordhoff, Leyden, 1975

    MATH  Google Scholar 

  53. Wang S S, Choi I. The interface crack between two dissimilar anisotropic composite materials. ASME J Appl Mech, 1983, 50: 169–178

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  55. Papas C H. Theory of Electromagnetic Wave Propagation. New York: Dover, 1988

    Google Scholar 

  56. Alshits V I, Barnett D M, Darinskii A N, et al. On the existence problem for localized acoustic waves on the interface between two piezocrystals. Wave Motion, 1994, 20: 233–244

    Article  MathSciNet  MATH  Google Scholar 

  57. Volakis J L, Chatterjee A, Kempel L C. Finite Element Method for Electromagnetics. New York: IEEE Press, 1998

    Book  MATH  Google Scholar 

  58. Pan E. Some new three-dimensional Green’s functions in anisotropic piezoelectric biomaterials. Electron J Bound Elem, 2003, 1: 236–269

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Engineering Mechanics, Shijiazhuang Tiedao University, Shijiazhuang, 050043, China

    WenJie Feng, Peng Ma & JinXi Liu

  2. Department of Civil Engineering, The University of Akron, Akron, OH, 44329, USA

    ErNian Pan

Authors
  1. WenJie Feng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Peng Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. ErNian Pan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. JinXi Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to WenJie Feng.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Feng, W., Ma, P., Pan, E. et al. 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 (2011). https://doi.org/10.1007/s11433-011-4403-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11433-011-4403-0

Keywords

Search

Navigation