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A periodic array of cracks in a transversely isotropic magnetoelectroelastic material

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Abstract

Magnetoelectroelastic materials are inherently brittle and prone to fracture. Therefore, it is important to evaluate the fracture behavior of these advanced materials. In this paper, a periodic array of cracks in a transversely isotropic magnetoelectroelastic material is investigated. Hankel transform is applied to solve elastic displacements, electric potential and magnetic potential. The problem is reduced into a system of integral equations. Both impermeable and permeable crack-face electromagnetic boundary conditions assumptions are investigated. Quantities of the stress, electric displacement and magnetic induction and their intensity factor are obtained. Effect of the crack spacing on these quantities is investigated in details.

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References

  1. Vandenbo J., Terrell D.R., Born R. and Giller H.F.J.I. (1974). In situ grown eutectic magnetoelectric composite-material.1. Composition and unidirectional solidification. J. Mater. Sci. 9(10): 1705–1709

    Article  Google Scholar 

  2. Van run A.M.J.G., Terrell D.R. and Scholing J.H. (1974). In situ grown eutectic magnetoelectric composite-material.2. Physical Properties. J. Mater. Sci. 9(10): 1710–1714

    Article  Google Scholar 

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

    Google Scholar 

  4. Nan C.-W. (1994). Magnetoelectric effect in composites of piezoelectric and piezomagnetic phases. Phys. Rev. B 50: 6082–6088

    Article  Google Scholar 

  5. Harshe G., Dougherty J.P. and Newnham R.E. (1993). Theoretical modeling of multilayer magnetoelectric composites. Int. J. Appl. Electromagn. Mater. 4(2): 145–159

    Google Scholar 

  6. Harshe G., Dougherty J.P. and Newnham R.E. (1993). Theoretical modeling of 3–0/0–3 magnetoelectric composites. Int. J. Appl. Electromagn. Mater. 4(2): 161–171

    Google Scholar 

  7. Aboudi J. (2001). Micromechanical analysis of fully coupled electro-magneto-thermo-elastic multiphase composites. Smart Materi. Struct. 10: 867–877

    Article  Google Scholar 

  8. Carman G.P., Cheung K.S. and Wang D. (1995). Micro-mechanical model of a composite containing a conservative nonlinear electro-magneto-thermo-mechanical material. J. Intell. Mater. Syst. Struct. 6: 691–698

    Google Scholar 

  9. Zhang Z.K. and Soh A.K. (2005). Micromechanics predictions of the effective moduli of magnetoelectroelastic composite materials. Euro. J. Mech. A/Solids 24: 1054–1067

    Article  MATH  Google Scholar 

  10. Li, J.Y., Dunn, M.L.: Micromechanics of magnetoelectroelastic composite materials: average field and effective behavior. J. Intell. Mater. Syst. Struct. 404–416 (1998)

  11. Fiebig, M.: Revival of the magnetoelectric effect. J. Phys. D 38 R123 (2005)

  12. Huang J.H. and Kuo W.S. (1997). The analysis of piezoelectric/piezomagnetic composite materials containing an ellipsoidal inclusion. J Appl. Phys. 81: 1378–1386

    Article  Google Scholar 

  13. Li J.Y. and Dunn M.L. (1998). Anisotropic coupled field inclusion and inhomogeneity problems. Philos. Mag. A 77: 1341–1350

    Article  Google Scholar 

  14. Liu J.-X., Liu X. and Zhao Y. (2001). Green’s functions for anisotropic magnetoelectroelastic solids with an elliptical cavity or a crack. Inte. J. Eng. Sci. 39(12): 1405–1418

    Article  Google Scholar 

  15. Wu X.-H., Shen Y.-P. and Wang X. (2004). Stress concentration around a hyperboloidal notch under tension in a magnetoelectroelastic material. ZAMM J Appl Math Mech Z Angewa Math Mech 84: 818–824

    Article  MATH  Google Scholar 

  16. Qin Q.H. (2004). Green’s functions of magnetoelasic solids with a half-plane boundary or biomaterial interface. Philoso. Maga. Lett. 84: 771–779

    Google Scholar 

  17. Feng W.J., Xue Y. and Zou Z.Z. (2005). Crack growth of an interface crack between two dissimilar magneto-electro-elastic materials under anti-plane mechanical and in-plane electric magnetic impact. Theore. Appl. Fracture Mech. 43: 376–394

    Article  Google Scholar 

  18. Hu G.-Q. and Li K.-Q. (2005). Electro-magneto-elastic analysis of a piezoelectromagnetic strip with a finite crack under longitudinal shear. Mecha. Mater. 37: 925–934

    Google Scholar 

  19. Tian W.-Y. and Rajapakse R.K.N.D. (2005). Theoretical modelling of a conducting crack in a magnetoelectroelastic solid. Int. J. Appl. Electromagn Mecha 22: 141–158

    Google Scholar 

  20. Zhou Z.-G., Wu L.-Z. and Wang B. (2005). The behavior of a crack in functionally graded piezoelectric/piezomagnetic materials under anti-plane shear loading. Arch. Appl. Mech. 74: 526–535

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  23. Chue C.H. and Liu T.J.C. (2005). Magneto-electro-elastic antiplane analysis of a biniaterial BaTiO3–CoFe2O4 composite wedge with an interface crack. Theor. Appl. Fracture Mech. 44(3): 275–296

    Article  Google Scholar 

  24. Hao R.J. and Liu J.X. (2006). Interaction of a screw dislocation with a semi-infinite interfacial crack in a magneto-electro-elastic bi-material. Mech. Res. Commun. 33: 415–424

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MATH  Google Scholar 

  27. Wang X.M. and Shen Y.P. (1996). The conservation laws and path-independent integrals for linear electro-magneto-elastic media with an application. Inte. J. Solids Struct. 33: 865–878

    Article  MATH  Google Scholar 

  28. Han J.C. and Wang B.L. (2006). Crack spacing effect for a piezoelectric cylinder under electromechanical loading or transient heating. Inte. J. Solids and Struct. 43(7/8): 2126–2145

    Article  MATH  Google Scholar 

  29. Huang J.H. (1998). Magneto-electro-elastic Eshelby tensors for a piezoelectric-piezomagnetic composite reinforced by elliptical inclusions. J. Appl. Phys. 83: 5364–5370

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Graduate School at Shenzhen, Harbin Institute of Technology, Harbin, 150001, People’s Republic of China

    Bao-Lin Wang, Hua-Yu Zhang & Jie-Cai Han

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  1. Bao-Lin Wang
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  2. Hua-Yu Zhang
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Correspondence to Hua-Yu Zhang.

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Wang, BL., Zhang, HY. & Han, JC. A periodic array of cracks in a transversely isotropic magnetoelectroelastic material. Arch Appl Mech 77, 541–558 (2007). https://doi.org/10.1007/s00419-006-0104-y

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  • DOI: https://doi.org/10.1007/s00419-006-0104-y

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