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The effective electroelastic property of cracked piezoelectric media

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This paper presents a study on the effective electroelastic property of piezoelectric media with parallel or randomly distributed cracks. The theoretical formulation is derived using the dilute model of distributed cracks and the solution of a single dielectric crack problem, in which the electric boundary condition along the crack surfaces is governed by the crack opening displacement. It is observed that the effective electroelastic property of such cracked piezoelectric media is nonlinear and sensitive to loading conditions. Numerical simulations are conducted to show the effects of crack distribution and electric boundary condition upon the effective electroelastic property. The transition between the commonly used electrically permeable and impermeable crack models is studied.

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References

  • Kachanov, M.: Effective elastic properties of cracked solids: critical review of some basic concepts. Appl. Mech. Rev. 39, 304–335 (1992).

    Google Scholar 

  • Kachanov, M.: Elastic solids with many cracks and related problems. Adv. Appl. Mech. 30, 259–428 (1993).

    Google Scholar 

  • Budiansky, Y., O’Connell, R. J.: Elastic moduli of a cracked solid. Int. J. Solids Struct. 12, 81–92 (1976).

    Google Scholar 

  • Hori, H., Nemat-Nasser, S.: Overall moduli of solids with microcracks: load-induced anisotropy. J. Mech. Phys. Solids 33, 155–171 (1983).

    Google Scholar 

  • Norris, A. N.: A differential scheme of the effective moduli of composites. Mech. Mater. 4, 1–16 (1985).

    Google Scholar 

  • Hashin, Z.: The differential scheme and its application to cracked materials. J. Mech. Phys. Solids 36, 719–734 (1988).

    Google Scholar 

  • Zimmerman, R. W.: Elastic moduli of a solid containing spherical inclusions. Mech. Mater. 12, 17–24 (1991).

    Google Scholar 

  • Mori, T., Tanaka, K.: Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall. 21, 571–574 (1973).

    Google Scholar 

  • Benveniste, Y.: On the Mori-Tanaka’s method in cracked bodies. Mech. Res. Comm. 13, 193–201 (1986).

    Google Scholar 

  • Weng, G.: The theoretical connection between Mori-Tanaka’s theory and the Hashin-Shtrikman-Walpole bounds. Int. J. Eng. Sci. 28, 1111–1120 (1990).

    Google Scholar 

  • Aboudi, J., Benveniste, Y.: The effective moduli of cracked bodies in plane deformations. Eng. Fract. Mech. 26, 171–184 (1987).

    Google Scholar 

  • Huang, Y., Hu, K. X., Chandra, A.: A generalized self-consistent mechanics method for microcracked solids. J. Mech. Phys. Solids 42, 1273–1291 (1994).

    Google Scholar 

  • Grekov, A. A., Kramarov, S. O., Kuprienko, A. A.: Effective properties of a transversely isotropic piezocomposite with cylindrical inclusions. Ferroelectrics 99, 115–126 (1989).

    Google Scholar 

  • Dunn, M. L., Taya, M.: MicroMechanics predictions of the effective electro-elastic moduli of piezoelectric composites. Int. J. Solids Struct. 30, 161–175 (1993).

    Google Scholar 

  • Chen, T.: Micromechanical estimates of the overall thermoelectricelastic moduli of multiple fibrous composites. Int. J. Solids Struct. 31, 3099–3111 (1994).

    Google Scholar 

  • Dunn, M. L., Taya, M.: Electromechanical properties of porous piezo-electric ceramics. J. Amer. Ceramics Soc. 76, 1697–1706 (1993).

    Google Scholar 

  • Yu, S. W., Qin, Q. H.: Damage analysis of thermopiezoelectric properties: Part II. Effective crack model. Theor. Appl. Fract. Mech. 25, 279–288 (1996).

    Google Scholar 

  • Qin, Q., Mai, Y., Yu, S.: Effective moduli for thermopiezoelectric materials with microcracks. Int. J. Fract. 91, 359–371 (1998).

    Google Scholar 

  • Parton, V. Z.: Fracture Mechanics piezoelectric materials. Acta Astronaut. 3, 671–683 (1976).

    Google Scholar 

  • Wang, X. D.: On the dynamic behavior of interacting interfacial cracks in piezoelectric media. Int. J. Solids Struct. 38, 815–831 (2001).

    Google Scholar 

  • Deeg, W. E. F.: The analysis of dislocation, crack, and inclusion problems in piezoelectric solids. Ph.D thesis, Stanford University, 1980.

  • Pak, Y. E.: Crack extension force in a piezoelectrical material. J. Appl. Mech. 57, 647–653 (1990).

    Google Scholar 

  • Suo, Z., Kuo, C. M., Barnett, D. M., Willis, J. R.: Fracture mechanics for pieozoelectric ceramics. J. Mech. Phys. Solids 40, 739–765 (1992).

    Google Scholar 

  • Park, S., Sun, C. T.: Fracture criteria for piezoelectric ceramics. J. Amer. Ceramic Soc. 78, 1475–1480 (1995).

    Google Scholar 

  • McMeeking, R. M.: Electrostrictive stresses near crack-like flaws. J. Appl. Math. Phys. 40, 615–627 (1989).

    Google Scholar 

  • Sosa, H.: Plane problems in piezoelectric media with defects. Int. J. Solids Struct. 28, 491–505 (1991).

    Google Scholar 

  • Dunn, M. L.: The effects of crack face boundary conditions on the fracture mechanics piezoelectric solids. Eng. Fract. Mech. 48, 25–39 (1994).

    Google Scholar 

  • Zhang, T. Y., Qian, C. F., Tong, P.: Linear electro-elastic analysis of a cavity or a crack in a piezoelectric material. Int. J. Solids Struct. 35, 2121–2149 (1996).

    Google Scholar 

  • Wang, X. D., Jiang, L. Y.: Fracture behavior of cracks in piezoelectric media with electromechanically coupled boundary conditions. Proc. Royal Soc. London A 458, 2545–2560 (2002).

    Google Scholar 

  • Xu, X. L., Rajapakse, R. K. N. D.: On a plane crack in piezoelectric solids. Int. J. Solids Struct. 38, 7643–7658 (2001).

    Google Scholar 

  • Wang, X. D., Jiang, L. Y.: The effective electroelastic property of piezoelectric media with parallel dielectric cracks. Int. J. Solids Struct. 40, 5287–5303 (2003).

    Google Scholar 

  • Nemat-Nasser, S., Hori, M.: MicroMech: overall properties of heterogeneous materials. Amsterdam: North-Holland 1993.

  • Tsukrov, I., Kachanov, M.: Effective moduli of an anisotropic material with elliptical holes of arbitrarily orientational distribution. Int. J. Solids Struct. 37, 5919–5941 (2000).

    Google Scholar 

  • Bristow, J. R.: Microcracks and the static and dynamic elastic constants of annealed and heavily cold-worked metals. Brit. J. Appl. Phys. 11, 81–85 (1960).

    Google Scholar 

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Wang, X.D., Jiang, L.Y. The effective electroelastic property of cracked piezoelectric media. Acta Mechanica 177, 97–113 (2005). https://doi.org/10.1007/s00707-005-0226-2

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