Skip to main content

Advertisement

SpringerLink
Log in

Surface free energy effect on electro-mechanical behavior of piezoelectric thin film with square nanofibers under anti-plane shear

  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

For a nano-sized piezoelectric film, the surface free energy at the surface/interface will exert great effect on the behavior of nano-sized piezoelectric structures. This paper concerns the effect of surface free energy at the surface/interface of square nanofibers on the electro-mechanical behavior of a piezoelectric thin film under anti-plane shear. Combining the electro-elastic surface/interface theory, the mapping method and the generalized self-consistent method, a closed-form solution of the effective electro-elastic moduli is obtained. Numerical examples are given to illustrate quantitatively the macro-effective electro-elastic moduli under different surfaces/interfaces when the size of the square nanofibers is on the order of nanometer. The effect of shape of square nanofibers on the effective electro-elastic moduli is also examined.

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. Wang Z.L., Song J.H.: Piezoelectric nanogenerators based on zinc oxide nano-wire arrays. Science 312, 242–246 (2006)

    Article  Google Scholar 

  2. Wang Z.L.: The new field of nanopiezotronics. Mater. Today. 10, 20–28 (2007)

    Article  Google Scholar 

  3. Dai S., Park H.S.: Surface effects on the piezoelectricity of ZnO nanowires. J. Mech. Phys. Solids 61, 385–397 (2013)

    Article  Google Scholar 

  4. Agrawal R., Espinosa H.D.: Giant piezoelectric size effects in zinc oxide and gallium nitride nanowires. A first principles investigation. Nano. Lett. 11, 786–790 (2011)

    Article  Google Scholar 

  5. Guitin M.E., Murdoch A.I.: Surface stress in solids. Int. J. Solids Struct. 14, 431–440 (1978)

    Article  Google Scholar 

  6. Sharma P., Ganti S.: Interfacial elasticity corrections to size-dependent strain-state of embedded quantum dots. Phys. Status Solidi B. 234, R10–R12 (2002)

    Article  Google Scholar 

  7. Wu H.A., Liu G.R., Wang J.S.: Atomistic and continuum simulation on extension behavior of single crystal with nano-holes. Model. Simul. Mater. Sci. Eng. 12, 225 (2004)

    Article  Google Scholar 

  8. Duan H.L., Wang J., Huang Z.P., Luo Z.Y.: Stress concentration tensors of inhomogeneities with interface effects. Mech. Mater. 37, 723–736 (2005)

    Article  Google Scholar 

  9. Dingreville R., Qu J., Cherkaoui M.: Surface free energy and its effect on the elastic behavior of nano-sized particles, wires and films. J. Mech. Phys. Solids 53, 1827–1854 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  10. Duan H.L., Yi X., Huang Z.P., Wang J.: A unified scheme for prediction of effective moduli of multiphase composites with interface effects: Part II—application and scaling laws. Mech. Mater. 39, 94–103 (2007)

    Article  Google Scholar 

  11. Chen T., Dvorak G.J., Yu C.C.: Solids containing spherical nano-inclusions with interface stresses: effective properties and thermal–mechanical connections. Int. J. Solids Struct. 44, 941–955 (2007)

    Article  MATH  Google Scholar 

  12. Pan X.H., Yu S.W., Feng X.Q.: A continuum theory of surface piezoelectricity for nanodielectrics. Sci. China Phys. Mech. 54, 564–573 (2011)

    Article  Google Scholar 

  13. Chen T.: Exact size-dependent connections between effective moduli of fibrous piezoelectric nanocomposites with interface effects. Acta. Mech. 196, 205–217 (2008)

    Article  MATH  Google Scholar 

  14. Yang S.S., Hu S.L., Shen S.P.: Local electroelastic field and effective electro-elastic moduli of piezoelectric nanocomposites with interface effect. CMC Comput. Mater. Con. 29, 279–298 (2012)

    Google Scholar 

  15. Yoon M.S., Khansur N.H., Choi B.K., Lee Y.G., Ur. S.C.: The effect of nano-sized BNBT on microstructure and dielectric/piezoelectric properties. Ceram. Int. 35, 3027–3036 (2009)

    Article  Google Scholar 

  16. Ramos-Cano J., Miki-Yoshida M., Goncalves A.M., Eiras J.A., Gonzalez-Hernandez J., Rodriguez-Lopez J.A., Amezaga-Madrid P., urtado-Macias A.: Characterization of nanomechanical, ferroelectric, and piezoelectric properties by nanoindentation and piezoresponse force microscopy of PbTiO3 thin films. Int. Eng. Chem. Res. 52, 14328–14334 (2013)

    Article  Google Scholar 

  17. Jafari A., Khatibi A.A., Mashhadi M.M.: Comprehensive investigation on hierarchical multiscale homogenization using representative volume element for piezoelectric nanocomposites. Compos. Part B. 42, 553–561 (2011)

    Article  Google Scholar 

  18. He L., Xia G., Sun J., Zhao Q., Song R., Ma Z.: Unzipped multiwalled carbon nanotubes-incorporated poly (vinylidene fluoride) nanocomposites with enhanced interface and piezoelectric β phase. J. Colloid. Interf. Sci. 393, 97–103 (2013)

    Article  Google Scholar 

  19. Nili H., Cheng G., Venkatesh T.A., Sriram S., Bhaskaran M.: Correlation between nanomechanical and piezoelectric properties of thin films: An experimental and finite element study. Mater. Lett. 90, 148–151 (2013)

    Article  Google Scholar 

  20. Wang P., Du H., Shen S., Zhangc M., Liu B.: Deposition, characterization and optimization of zinc oxide thin film for piezoelectric cantilevers. Appl. Surf. Sci. 258, 9510–9517 (2012)

    Article  Google Scholar 

  21. Xia X., Yuan Y., Du H., Chow K.S., Zhang M., Yu S., Liu B.: Study of piezoelectric ZnO thin films for contact sensing and head actuation. IEEE Trans. Magn. 49, 2539–2543 (2013)

    Article  Google Scholar 

  22. Mishra D., Park C.Y., Yoo S.H., Pak Y.E.: Closed-form solution for elliptical inclusion problem in antiplane piezoelectricity with far-field loading at an arbitrary angle. Eur. J. Mech. A/Solid 40, 186–197 (2013)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Xue-Qian Fang, Ming-Juan Huang & Jin-Xi Liu

  2. School of Mathematics and Science, Xiamen University, Xiamen, 361005, China

    Zi-Tao Zhu

Authors
  1. Xue-Qian Fang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ming-Juan Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zi-Tao Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jin-Xi Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xue-Qian Fang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fang, XQ., Huang, MJ., Zhu, ZT. et al. Surface free energy effect on electro-mechanical behavior of piezoelectric thin film with square nanofibers under anti-plane shear. Acta Mech 226, 149–156 (2015). https://doi.org/10.1007/s00707-014-1174-5

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-014-1174-5

Keywords

Search

Navigation