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Semi-permeable Yoffe-type interfacial crack analysis in MEE composites based on the strip electro-magnetic polarization saturation model

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Abstract

Fracture analysis of a semi-permeable Yoffe-type interfacial crack propagating subsonically in magneto-electro-elastic (MEE) composites is presented based on the strip electromagnetic polarization saturation (SEMPS) model. The electro-magnetic fields inside the crack are considered under the semi-permeable boundary condition. Nonlinear effects near the interfacial crack tip are represented by different electro-magnetic saturation zones. Utilizing the extended Stroh’s method, we derive the moving dislocation densities as well as intensity factor and energy release rate for Yoffe-type MEE interfacial crack. Numerical results through an iterative approach are presented to show the characteristics of fracture-dominant parameters with respect to propagation velocity and boundary condition category. The fracture-dominant parameters under the semi-permeable boundary condition are lower than those under the impermeable one, which implies that the electro-magnetic fields in the crack gap can retard the propagation of MEE interfacial crack.

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References

  1. R. Ramesh, Spaldin, N.A. Multiferroics, Progress and prospects in thin films, Nat. Mater. 6 (2007) 21–29.

    Article  Google Scholar 

  2. N. Ortega, A. Kumar, J.F. Scott, R.S. Katiyar, Multifunctional magnetoelectric materials for device applications, J. Phys.: Condens. Matter 27 (2015) 504002.

    Google Scholar 

  3. S. Dong, J.M. Liu, S.W. Cheong, Z.F. Ren, Multiferroic materials and magnetoelectric physics: symmetry, entanglement, excitation, and topology, Adv. Phys. 64 (2015) 519–626.

    Article  Google Scholar 

  4. Y.F. Cao, Y.Y. Li, Y.Y. Li, G.N. Wei, Y. Ji, K.Y. Wang, Magnetic coupling in ferromagnetic semiconductor GaMnAs/AlGaMnAs bilayer devices, Sci. China Phys. Mech. Astron. 57 (2014) 1471–1475.

    Article  Google Scholar 

  5. P.X. Zhang, G.F. Yin, Y.Y. Wang, B. Cui, F. Pan, C. Song, Electrical control of antiferromagnetic metal up to 15 nm, Sci. China Phys. Mech. Astron. 59 (2016) 687511.

    Article  Google Scholar 

  6. S.X. Dong, J.R. Cheng, J.F. Li, D. Viehland, Enhanced magnetoelectric effects in laminate composites of Terfenol-D/Pb (Zr, Ti) O3 under resonant drive, Appl. Phys. Lett. 83 (2003) 4812–4814.

    Article  Google Scholar 

  7. M.M. Vopson, Fundamentals of multiferroic materials and their possible applications, Crit. Rev. Solid State. Mater. Sci. 40 (2015) 223–250.

    Article  Google Scholar 

  8. W. Eerenstein, N.D. Mathur, J.F. Scott, Multiferroic and magnetoelectric materials, Nature 442 (2006) 759–765.

    Article  Google Scholar 

  9. Z.C. Zhang, X.Z. Wang, Effective multi-field properties of electro-magneto-thermoelastic composites estimated by finite element method approach, Acta Mech. Solida Sin. 28 (2015) 145–155.

    Article  Google Scholar 

  10. C.W. Nan, M.I. Bichurin, S.X. Dong, D. Viehland, G. Srinivasan, Multiferroic magnetoelectric composites: historical perspective, status, and future directions, J. Appl. Phys. 103 (2008) 031101.

    Article  Google Scholar 

  11. T. Taniyama, Electric-field control of magnetism via strain transfer across ferromagnetic/ferroelectric interfaces, J. Phys.: Condens. Matter 27 (2015) 504001.

    Google Scholar 

  12. C. Häusler, H. Jelitto, P. Neumeister, H. Balke, G. Schneider, Interfacial fracture of piezoelectric multilayer actuators under mechanical and electrical loading, Int. J. Fract. 160 (2009) 43–54.

    Article  Google Scholar 

  13. G. Srinivasan, E.T. Rasmussen, J. Gallegos, R. Srinivasan, Y.I. Bokhan, V.M. Laletin, Magnetoelectric bilayer and multilayer structures of magnetostrictive and piezoelectric oxides, Phys. Rev. B 64 (2001) 214408.

    Article  Google Scholar 

  14. M. Ayatollahi, R. Bagheri, Dynamic behavior of several cracks in functionally graded strip subjected to anti-plane time-harmonic concentrated loads, Acta Mech. Solida Sin. 26 (2013) 691–705.

    Article  Google Scholar 

  15. J. Wu, H. Zhang, Y. Zheng, A concurrent multiscale method for simulation of crack propagation, Acta Mech. Solida Sin. 28 (2015) 235–251.

    Article  Google Scholar 

  16. L.B. Freund, Dynamic Fracture Mechanics. Cambridge University Press, 1998.

  17. A.N. Guz, Mechanics of crack propagation in materials with initial (residual) stresses (review), Int. Appl. Mech. 47 (2011) 121–168.

    Article  MathSciNet  Google Scholar 

  18. E.H. Yoffe, The moving griffith crack, Philos. Mag. 42 (1951) 739–750.

    Article  MathSciNet  Google Scholar 

  19. K.B. Broberg, The propagation of a brittle crack, Ark. Fys. 18 (1960) 159–192.

    MathSciNet  Google Scholar 

  20. M. Nourazar, M. Ayatollahi, Multiple moving interfacial cracks between two dissimilar piezoelectric layers under electromechanical loading, Smart Mater. Struct. 25 (2016) 075011.

    Article  Google Scholar 

  21. K.Q. Hu, Y.L. Kang, G.Q. Li, Moving crack at the interface between two dissimilar magnetoelectroelastic materials, Acta Mech. 182 (2006) 1–16.

    Article  Google Scholar 

  22. Y.P. Yue, Y.P. Wan, Multilayered piezomagnetic/piezoelectric composite with periodic interfacial Yoffe-type cracks under magnetic or electric field, Acta Mech. 225 (2014) 1–18.

    Article  MathSciNet  Google Scholar 

  23. B.L. Wang, J.C. Han, Discussion on electromagnetic crack face boundary conditions for the fracture mechanics of magneto-electro-elastic materials, Acta Mech. Sin. 22 (2006) 233–242.

    Article  Google Scholar 

  24. F.X. Li, Y. Sun, R. Rajapakse, Effect of electric boundary conditions on crack propagation in ferroelectric ceramics, Acta Mech. Sin. 30 (2014) 153–160.

    Article  MathSciNet  Google Scholar 

  25. H.S. Nan, B.L. Wang, Influence of residual surface stress on the fracture of nanoscale piezoelectric materials with conducting cracks, Sci. China Phys. Mech. Astron. 57 (2014) 280–285.

    Article  Google Scholar 

  26. V.Z. Parton, Fracture mechanics of piezoelectric materials, Acta Astronaut. 3 (1976) 671–683.

    Article  Google Scholar 

  27. W.F. Deeg, The Analysis of Dislocation, Crack, and Inclusion Problems in Piezoelectric Solids (1980).

  28. G. Schneider, F. Felten, R. McMeeking, The electrical potential difference across cracks in PZT measured by Kelvin Probe Microscopy and the implications for fracture, Acta Mater. 51 (2003) 2235–2241.

    Article  Google Scholar 

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

    Article  Google Scholar 

  30. C.M. Landis, Energetically consistent boundary conditions for electromechanical fracture, Int. J. Solids Struct. 41 (2004) 6291–6315.

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  33. T.H. Hao, Steady propagate crack in a transverse isotropic piezoelectric material considering the permittivity of the medium in the crack gap, Int. J. Fract. 118 (2002) 239–249.

    Article  Google Scholar 

  34. N. Balke, S. Choudhury, S. Jesse, M. Huijben, Y.H. Chu, A.P. Baddorf, L.Q. Chen, R. Ramesh, S.V. Kalinin, Deterministic control of ferroelastic switching in multiferroic materials, Nat. Nanotechnol. 4 (2009) 868–875.

    Article  Google Scholar 

  35. S.M. Wu, S.A. Cybart, P. Yu, M.D. Rossell, J.X. Zhang, R. Ramesh, R.C. Dynes, Reversible electric control of exchange bias in a multiferroic field-effect device, Nat. Mater. 9 (2010) 756–761.

    Article  Google Scholar 

  36. D.M. Evans, A. Schilling, A. Kumar, D. Sanchez, N. Ortega, M. Arredondo, R.S. Katiyar, J.M. Gregg, J.F. Scott, Magnetic switching of ferroelectric domains at room temperature in multiferroic PZTFT, Nat. Commun. 4 (2013) 1534.

    Article  Google Scholar 

  37. X.D. Xia, Z. Zhong, Tuning of non-uniform switch toughening in ferroelectric composites by an electric field, Acta Mech. Sin. 32 (2016) 866–880.

    Article  MathSciNet  Google Scholar 

  38. S.P. Shen, T. Nishioka, Z.B. Kuang, Z.X. Liu, Nonlinear electromechanical interfacial fracture for piezoelectric materials, Mech. Mater. 32 (2000) 57–64.

    Article  Google Scholar 

  39. S.P. Shen, Z.B. Kuang, T. Nishioka, Dynamic mode-III interfacial crack in ferroelectric materials, Int. J. Appl. Electromagn. Mech. 11 (2000) 211–222.

    Google Scholar 

  40. H.S. Chen, J. Ma, Y.M. Pei, D.N. Fang, Anti-plane Yoffe-type crack in ferroelectric materials, Int. J. Fract. 179 (2013) 35–43.

    Article  Google Scholar 

  41. X.D. Xia, Z. Zhong, A mode III moving interfacial crack based on strip magneto-electric polarization saturation model, Smart Mater. Struct. 24 (2015) 085015.

    Article  Google Scholar 

  42. K.Q. Hu, Z.J. Yang, Moving Dugdale type crack along the interface of two dissimilar piezoelectric materials, Theor. Appl. Fract. Mech. 74 (2014) 157–163.

    Article  Google Scholar 

  43. K.Q. Hu, Z.T. Chen, J.W. Fu, Moving Dugdale crack along the interface of two dissimilar magnetoelectroelastic materials, Acta Mech. 226 (2015) 2065–2076.

    Article  MathSciNet  Google Scholar 

  44. A. Stroh, Dislocations and cracks in anisotropic elasticity, Philos. Mag. 3 (1958) 625–646.

    Article  MathSciNet  Google Scholar 

  45. J.M. Qu, Q.Q. Li, Interfacial dislocation and its applications to interface cracks in anisotropic bimaterials, J. Elast. 26 (1991) 169–195.

    Article  Google Scholar 

  46. M.H. Zhao, Q.Y. Zhan, C.Y. Fan, J.N. Jia, Semi-permeable crack analysis in a 2D magnetoelectroelastic medium based on the EMPS model, Mech. Res. Commun. 55 (2014) 30–39.

    Article  Google Scholar 

  47. M.H. Zhao, C.Y. Fan, F. Yang, T. Liu, Analysis method of planar cracks of arbitrary shape in the isotropic plane of a three-dimensional transversely isotropic magnetoelectroelastic medium, Int. J. Solids Struct. 44 (2007) 4505–4523.

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  50. D.A. Hills, Solution of Crack Problems: The Distributed Dislocation Technique. Springer, 1996.

    Chapter  Google Scholar 

  51. C.F. Gao, M.H. Zhao, P. Tong, T.Y. Zhang, The energy release rate and the J-integral of an electrically insulated crack in a piezoelectric material, Int. J. Eng. Sci. 42 (2004) 2175–2192.

    Article  Google Scholar 

  52. T.C.T. Ting, Barnett-Lothe tensors and their associated tensors for monoclinic materials with the symmetry plane at x3=0, J. Elast. 27 (1992) 143–165.

    Article  Google Scholar 

  53. J.H. Huang, Y.H. Chiu, H.K. Liu, Magneto-electro-elastic Eshelby tensors for a piezoelectric-piezomagnetic composite reinforced by ellipsoidal inclusions, J. Appl. Phys. 83 (1998) 5364–5370.

    Article  Google Scholar 

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Xia, X., Zhong, Z. Semi-permeable Yoffe-type interfacial crack analysis in MEE composites based on the strip electro-magnetic polarization saturation model. Acta Mech. Solida Sin. 30, 354–368 (2017). https://doi.org/10.1016/j.camss.2017.07.011

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  • DOI: https://doi.org/10.1016/j.camss.2017.07.011

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