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Influence of inclined electric fields on the effective fracture toughness of piezoelectric ceramics

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Abstract

Electric fields effectuate the fracture behavior of ferroelectrics on different scales. On the atomic scale, forces in covalent bonds are influenced. On the mesoscopic scale, the ferroelectric domain wall motion shields the crack tip or leads to an additional loading. Based on classical approaches, on the macroscopic scale, the electric field has a major impact on the energy release rate and the electric displacement intensity factor; however, it scarcely influences the mechanical stress intensity factors. The situation is different if Maxwell stresses at crack faces, as a consequence of the jump of dielectric properties, are incorporated in the crack tip loading analysis. First, general considerations deal with the question how a fracture criterion has to be formulated, incorporating all three scales. On the macroscopic scale, the influence of an arbitrarily inclined electric field on the critical mechanical crack loading is investigated. The extended model, in particular, reveals the significance of electric fields parallel to the crack faces. A combined analytical–numerical approach is applied to solve the coupled two-domains problem of solid and crack dielectric, supporting the well-established capacitor approach even for inclined electric fields.

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References

  1. Wang H., Singh R.N.: Crack propagation in piezoelectric ceramics: effects of applied electric fields. J. Appl. Phys. 81, 7471–7479 (1997)

    Article  Google Scholar 

  2. Förderreuther A., Thurn G., Zimmermann A., Aldinger F.: R-curve effect, influence of electric field and process zone in BaTiO3 ceramics. J. Eur. Ceram. Soc. 22, 2023–2031 (2002)

    Article  Google Scholar 

  3. Westram I., Ricoeur A., Emrich A., Rödel J., Kuna M.: Fatigue crack growth law for ferroelectrics under cyclic electrical and combined electromechanical loading. J. Eur. Ceram. Soc. 27, 2485–2494 (2007)

    Article  Google Scholar 

  4. Pak Y.E.: Linear electro-elastic fracture mechanics of piezoelectric materials. Int. J. Fract. 54, 79–100 (1992)

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  6. Park S.B., Sun C.T.: Effect of electric field on fracture of piezoelectric ceramics. Int. J. Fract. 70, 203–216 (1995)

    Article  Google Scholar 

  7. Kuna M.: Finite element analyses of crack problems in piezoelectric structures. Comput. Mater. Sci. 13, 67–80 (1998)

    Article  Google Scholar 

  8. Abendroth M., Groh U., Kuna M., Ricoeur A.: Finite element-computation of the electromechanical J-integral for 2-D and 3-D crack analysis. Int. J. Fract. 114, 359–378 (2002)

    Article  Google Scholar 

  9. Hwang S.C., McMeeking R.M.: A finite element model of ferroelectric polycrystals. Ferroelectrics 211, 177–194 (1998)

    Article  Google Scholar 

  10. Kamlah M., Liskowsky A.C., McMeeking R.M., Balke H.: Finite element simulation of a polycrystalline ferroelectric based on a multidomain single crystal switching model. Int. J. Solids Struct. 42, 2949–2964 (2005)

    Article  MATH  Google Scholar 

  11. Li F., Fang D.: Simulations of domain switching in ferroelectrics by a three-dimensional finite element model. Mech. Mater. 36, 959–973 (2004)

    Article  Google Scholar 

  12. Yang W., Zhu T.: Switch-toughening of ferroelectrics subjected to electric fields. J. Mech. Phys. Solids 46, 291–311 (1998)

    Article  MATH  Google Scholar 

  13. Ricoeur A., Kuna M.: A micromechanical model for the fracture process zone in ferroelectrics. Comput. Mater. Sci. 27, 235–249 (2003)

    Article  Google Scholar 

  14. Xu B.-X., Schrade D., Gross D., Müller R.: Phase field simulation of domain structures in cracked ferroelectrics. Int. J. Fract. 165, 163–173 (2010)

    Article  MATH  Google Scholar 

  15. Li Q., Kuna M.: Evaluation of electromechanical fracture behavior by configurational forces in cracked ferroelectric polycrystals. Comput. Mater. Sci. 57, 91–101 (2012)

    Google Scholar 

  16. Janski L., Kuna M.: Adaptive finite element modeling of stationary and propagating cracks in piezoelectric structures. Arch. Appl. Mech. 63, 599–619 (2011)

    MathSciNet  Google Scholar 

  17. Linder C., Rosato D., Miehe C.: New finite elements with embedded strong discontinuities for the modeling of failure in electromechanical coupled solids. Comput. Methods Appl. Mech. 200, 141–161 (2011)

    Article  MathSciNet  Google Scholar 

  18. Abdollahi A., Arias I.: Phase-field modelling of crack propagation in piezoelectric and ferroelectric materials with different electromechanical crack conditions. J. Mech. Phys. Solids 60, 21002126 (2012)

    Article  MathSciNet  Google Scholar 

  19. Wilson Z.A., Borden M.J., Landis C.M.: A phase-field model for fracture in piezoelectric ceramics. Int. J. Fract. 183, 135–153 (2013)

    Article  Google Scholar 

  20. Kuna, M., Ricoeur, A.: Theoretical investigation of fracture behavior in ferroelectric ceramics. In: Bradt, R.C., et al. (eds.) Fracture Mechanics of Ceramics, vol. 13, pp. 63–82 (2002)

  21. Gellmann R., Ricoeur A.: Some new aspects of boundary conditions at cracks in piezoelectrics. Arch. Appl. Mech. 82, 841–852 (2012)

    Article  MATH  Google Scholar 

  22. Gellmann R., Ricoeur A.: Extended semi-analytical investigations of crack growth resistance behavior in ferroelectric materials. Acta Mech. 223, 2357–2368 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  23. Barenblatt G.I.: The mathematical theory of equilibrium cracks in brittle fracture. Adv. Appl. Mech. 7, 55–129 (1962)

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  25. Kemmer G., Balke H.: Kraftwirkung auf die Flanken nichtleitender Risse in Piezoelektrika. ZAMM 79, 509–510 (1999)

    Google Scholar 

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

    Article  MATH  Google Scholar 

  27. Ricoeur A., Kuna M.: Electrostatic tractions at dielectric interfaces and their implication for crack boundary conditions. Mech. Res. Commun. 36, 330–335 (2009)

    Article  MATH  Google Scholar 

  28. Ricoeur A., Kuna M.: Electrostatic tractions at crack faces and their influence on the fracture mechanics of piezoelectrics. Int. J. Fract. 157, 3–12 (2009)

    Article  MATH  Google Scholar 

  29. Brandt S., Dahmen H.D.: Elektrodynamik—Eine Einfhrung in Experiment und Theorie. Springer, Berlin (2004)

    Google Scholar 

  30. Wippler K., Ricoeur A., Kuna M.: Towards the computation of electrically permeable cracks in piezoelectrics. Eng. Fract. Mech. 71, 2567–2587 (2004)

    Article  Google Scholar 

  31. Ricoeur A., Kuna M.: Influence of electric fields on the fracture of ferroelectric ceramics. J. Eur. Ceram. Soc. 23, 1313–1328 (2003)

    Article  Google Scholar 

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Authors and Affiliations

  1. Institute of Mechanics, University of Kassel, Mönchebergstraße 7, 34125, Kassel, Germany

    A. Ricoeur, R. Gellmann & Z. Wang

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  1. A. Ricoeur
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  2. R. Gellmann
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  3. Z. Wang
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Correspondence to A. Ricoeur.

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Ricoeur, A., Gellmann, R. & Wang, Z. Influence of inclined electric fields on the effective fracture toughness of piezoelectric ceramics. Acta Mech 226, 491–503 (2015). https://doi.org/10.1007/s00707-014-1190-5

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  • DOI: https://doi.org/10.1007/s00707-014-1190-5

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