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Interface crack problem of functionally graded piezoelectric materials: effects of the position of electromechanical impact and gradient

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Abstract

This paper analyzes the transient response of the dynamic stress intensity factor for an interfacial crack of a functionally graded piezoelectric material (FGPM) coated on the surface of a homogeneous piezoelectric substrate. Different from previous analyses, this study mainly considers a realistic situation when electromechanical loadings are suddenly applied at the material surface. Obtained results are compared with those when the crack surfaces are directly loaded by the same impacts. By using the integral transform method, the problem is reduced to solving two singular integral equations. It is found that dynamic stress intensity factors are significantly amplified and reduced depending on the negative and positive gradient for electromechanical impacts at the material surface. Positive or negative electric impact also decreases or increases the overshoot of the dynamic stress intensity factor. It is suggested that designing an FGPM with a positive gradient index is safer than a negative gradient index.

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References

  1. Furuta A., Uchino K.: Dynamic observation of crack propagation in piezoelectric multilayer actuators. J. Am. Ceram. Soc. 76, 1615–1617 (1993)

    Article  Google Scholar 

  2. Lucato S.L.S., Bahr H.-A., Pham V.-B., Lupascua D.C., Balke H., Rodel J., Bahr U.: Electrically driven cracks in piezoelectric ceramics: experiments and fracture mechanics analysis. J. Mech. Phys. Solids 50, 2333–2353 (2002)

    Article  MATH  Google Scholar 

  3. Chen Z.-T., Karihaloo B.L.: Dynamic response of a cracked piezoelectric ceramic under arbitrary electro-mechanical impact. Int. J. Solids Struct. 36, 5125–5133 (1999)

    Article  MATH  Google Scholar 

  4. Wang X.D., Meguid S.A.: Effect of electromechanical coupling on the dynamic interaction of cracks in piezoelectric materials. Acta Mech. 143, 1–15 (2000)

    Article  MATH  Google Scholar 

  5. Li X.-F.: Transient response of a piezoelectric material with a semi-infinite mode-III crack under impact loads. Int. J. Fract. 111, 119–130 (2001)

    Article  Google Scholar 

  6. Wang B.L., Mai Y.W.: A cracked piezoelectric material strip under transient thermal loading. ASME J. Appl. Mech. 69, 539–546 (2002)

    MATH  Google Scholar 

  7. Li X.-F., Tang G.J.: Transient response of a piezoelectric ceramic strip with an eccentric crack under electromechanical impacts. Int. J. Solids Struct. 40, 3571–3588 (2003)

    Article  MATH  Google Scholar 

  8. Wang X.Y., Yu S.W.: Transient response of a crack in piezoelectric strip subjected to the mechanical and electrical impacts: mode-I problem. Mech. Mater. 33, 11–20 (2001)

    Article  Google Scholar 

  9. Garcia-Sanchez F., Zhang C., Sladek J. et al.: 2D transient dynamic crack analysis in piezoelectric solids by BEM. Comput. Mater. Sci. 39, 179–186 (2007)

    Article  Google Scholar 

  10. Qiu J.H., Tani J., Ueno T., Morita T., Takahashi H., Du H.J.: Fabrication and high durability of functionally graded piezoelectric bending actuators. Smart Mater. Struct. 12, 115–121 (2003)

    Article  Google Scholar 

  11. Takagi K., Li J.-F., Yokoyama S., Watanabe R.: Fabrication and evaluation of PZT/Pt piezoelectric composites and functionally graded actuators. J. Eur. Ceram. Soc. 23, 1577–1583 (2003)

    Article  Google Scholar 

  12. Li C., Weng G.J.: Antiplane crack problem in functionally graded piezoelectric materials. ASME J. Appl. Mech. 69, 481–488 (2002)

    MATH  Google Scholar 

  13. Wang B.L.: A mode III crack in a functionally graded piezoelectric material. Mech. Res. Commun. 30, 151–159 (2003)

    Article  MATH  Google Scholar 

  14. Li C.Y., Weng G.J.: Yoffe-type moving crack in a functionally graded piezoelectric material. Proc. R. Soc. Lond. A 458, 381–399 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  15. Jin B., Zhong Z.: A moving mode-III crack in functionally graded piezoelectric material: permeable problem. Mech. Res. Comm. 29, 217–224 (2002)

    Article  MATH  Google Scholar 

  16. Kwon S.M., Lee K.Y.: An anti-plane propagating crack in a functionally graded piezoelectric strip bonded to a homogeneous piezoelectric strip. Arch. Appl. Mech. 73, 348–366 (2003)

    Article  MATH  Google Scholar 

  17. Chen J., Liu Z., Zou Z.: Dynamic response of a crack in a functionally graded interface of two dissimilar piezoelectric half-planes. Arch. Appl. Mech. 72, 686–696 (2003)

    Article  MATH  Google Scholar 

  18. Yong H.D., Zhou Y.H.: Transient anti-plane crack problem for two bonded functionally graded piezoelectric materials. Arch. Appl. Mech. 76, 497–509 (2006)

    Article  MATH  Google Scholar 

  19. Chen J., Soh A.K., Liu J., Liu Z.X.: Transient anti-plane crack problem of a functionally graded piezoelectric strip bonded to elastic layers. Acta. Mech. 169, 87–100 (2004)

    Article  MATH  Google Scholar 

  20. Li X.-F., Fan T.-Y.: Dynamic analysis of a crack in a functionally graded material sandwiched between two elastic layers under anti-plane loading. Compos. Struct. 79, 211–219 (2007)

    Article  Google Scholar 

  21. Erdogan F.: The crack problem for bonded nonhomogeneous materials under antiplane shear loading. ASME J. Appl. Mech. 52, 823–828 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  22. Fildis H., Yahsi O.S.: The axisymmetric crack problem in a nonhomogeneous interfacial region between homogeneous half-spaces. Int. J. Fract. 78, 139–163 (1996)

    Article  Google Scholar 

  23. Crump K.S.: Numerical inversion of Laplace transforms using a Fourier series approximation. J. Assoc. Comp. Mach. 23, 89–96 (1976)

    MATH  MathSciNet  Google Scholar 

  24. Li X.-F., Lee K.Y.: Dynamic behavior of a piezoelectric ceramic layer with two surface cracks. Int. J. Solids Struct. 41, 3193–3209 (2004)

    Article  MATH  Google Scholar 

  25. Li X.-F., Duan X.-Y.: Comparison of dynammic response of a piezoelectric ceramic containing two parallel cracks via two methods of Laplace inversion. Int. J. Fract. 122, L131–L136 (2003)

    Article  Google Scholar 

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Authors and Affiliations

  1. Institute of Mechanics and Sensor Technology, School of Civil Engineering and Architecture, Central South University, Changsha, Hunan, 410083, China

    Xu-Long Peng & Xian-Fang Li

  2. School of Mechanical Engineering, Yonsei University, Seoul, 120-749, South Korea

    Kang Yong Lee

Authors
  1. Xu-Long Peng
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  2. Xian-Fang Li
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Correspondence to Xian-Fang Li.

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Peng, XL., Li, XF. & Lee, K.Y. Interface crack problem of functionally graded piezoelectric materials: effects of the position of electromechanical impact and gradient. Acta Mech 207, 69–82 (2009). https://doi.org/10.1007/s00707-008-0108-5

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  • DOI: https://doi.org/10.1007/s00707-008-0108-5

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