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Interaction of parallel dielectric cracks in functionally graded piezoelectric materials

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Abstract

In this paper, the problem of two interacting parallel cracks in functionally graded piezoelectric materials under in-plane electromechanical loads is studied. The formulation is based on using Fourier transforms and modeling the cracks as distributed dislocations, and the resulting singular integral equations are solved with Chebyshev polynomials. A dielectric crack model considering the crack filling effect is adopted to describe the electric boundary conditions along crack surfaces. Numerical simulations are made to show the effect of material gradient, the geometry of interacting cracks, and crack position upon fracture parameters such as stress intensity factors, electric displacement intensity factor, and COD intensity factor. By considering the effect of a dielectric medium inside the crack and crack deformation, the results obtained from the dielectric crack model are always between those from the traditional crack models with physical limitation.

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References

  1. Wu C.M., Kahn M., Moy W.: Piezoelectric ceramics with functional gradients: a new application in material design. J. Am. Ceram. Soc. 79, 809–812 (1996)

    Google Scholar 

  2. Hudnut S., Almajid A., Taya M.: Functionally gradient piezoelectric bimorph type actuator. Pro. SPIE 3992, 376–386 (2000)

    Article  Google Scholar 

  3. Zhu X.H., Xu J., Meng Z.Y., Zhu J.M., Zhou S.H., Li Q., Liu Z.G., Ming N.B.: Microdisplacement characteristics and microstructures of functionally graded piezoelectric ceramic actuator. Mater. Des. 21, 561–566 (2000)

    Google Scholar 

  4. Takagi K., Li J.F., Yokoyama S., Watanabe R., Almajid A., Taya M.: Design and fabrication of functionally graded PZT/Pt piezoelectric bimorph actuator. Sci. Tech. Adv. Mater. 3, 217–224 (2002)

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  6. Deeg, W.F.J.: The analysis of dislocation, crack, and inclusion problems in piezoelectric solids. PhD thesis, Stanford University (1980)

  7. McMeeking R.M.: Electrostrictive stresses near crack-like flaws. Z. Angew. Math. Phys. 40, 615–627 (1989)

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  10. Sosa H., Khutoryansky N.: New developments concerning piezoelectric materials with defects. Int. J. Solids Struct. 33, 3399–3414 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  11. Zhang T.Y., Tong P.: Fracture mechanics for a mode III crack in a piezoelectric material. Int. J. Solids Struct. 33, 343–359 (1996)

    Article  MATH  Google Scholar 

  12. 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 (1998)

    Article  MATH  Google Scholar 

  13. Parton V.Z., Kudryavtsev B.A.: Electromagnetoelasticity: Piezoelectrics and Electrically Conductive Solids. Gordon and Breach Science Publishers, New York (1988)

    Google Scholar 

  14. Dascalu C., Homentcovschi D.: An intermediate crack model for flaws in piezoelectric solids. Acta Mech. 154, 85–100 (2002)

    Article  MATH  Google Scholar 

  15. Chiang C.R., Weng G.J.: Nonlinear behavior and critical state of a penny-shaped dielectric crack in a piezoelectric solid. J. Appl. Mech. T ASME 74, 852–860 (2007)

    Article  Google Scholar 

  16. 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 

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

    Article  MATH  Google Scholar 

  18. Wang X.D., Jiang L.Y.: Fracture behaviour of cracks in piezoelectric media with electromechanically coupled boundary conditions. Proc. R. Soc. Lond. A 458, 2545–2560 (2002)

    Article  MATH  Google Scholar 

  19. Wang X.D., Jiang L.Y.: The nonlinear fracture behavior of an arbitrarily oriented dielectric crack in piezoelectric materials. Acta Mech. 172, 195–210 (2004)

    Article  MATH  Google Scholar 

  20. Meguid S.A., Wang X.D.: Dynamic antiplane behaviour of interacting cracks in a piezoelectric medium. Int. J. Fract. 91, 391–403 (1998)

    Article  Google Scholar 

  21. Zhou Z.G., Wang B., Sun Y.G.: Investigation of the dynamic behavior of two parallel symmetric cracks in piezoelectric materials use of non-local theory. Int. J. Solids Struct. 40, 747–762 (2003)

    Article  MATH  Google Scholar 

  22. Han J.J., Chen Y.H.: Multiple parallel cracks interaction problem in piezoelectric ceramics. Int. J. Solids Struct. 36, 3375–3390 (1999)

    Article  MATH  Google Scholar 

  23. Han X.L., Wang T.C.: Interacting multiple cracks in piezoelectric materials. Int. J. Solids Struct. 36, 4183–4202 (1999)

    Article  MATH  Google Scholar 

  24. Wang X.D., Jiang L.Y.: Nonlinear behaviour of interacting dielectric cracks in piezoelectric materials. Int. J. Solids Struct. 39, 585–600 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  25. Zhou Z.G., Zhang P.W., Wu L.Z.: Two parallel limited-permeable mode-I cracks or four parallel limited-permeable mode-I cracks in the piezoelectric materials. Int. J. Solids Struct. 44, 4184–4205 (2007)

    Article  MATH  Google Scholar 

  26. 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 

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

    MATH  Google Scholar 

  28. Ma L., Wu L.Z., Zhou Z.G., Guo L.C., Shi L.P.: Scattering of harmonic anti-plane shear waves by two collinear cracks in functionally graded piezoelectric materials. Eur. J. Mech. A Solid 23, 633–643 (2004)

    Article  MATH  Google Scholar 

  29. Zhou Z.G., Wu L.Z.: Non-local theory solution for the anti-plane shear of two collinear permeable cracks in functionally graded piezoelectric materials. Int. J. Eng. Sci. 44, 1366–1379 (2006)

    Article  MathSciNet  Google Scholar 

  30. Zhang P.W., Zhou Z.G., Chen Z.T.: Basic solution of two parallel mode-I permeable cracks in functionally graded piezoelectric materials. Arch. Appl. Mech. 78, 411–430 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  31. Zhou Z.G., Chen Z.T.: The interaction of two parallel Mode-I limited-permeable cracks in a functionally graded piezoelectric material. Eur. J. Mech. A Solid 27, 824–846 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  32. Konda N., Erdogan F.: The mixed mode crack problem in a nonhomogeneous elastic medium. Eng. Fract. Mech. 47, 533–545 (1994)

    Article  Google Scholar 

  33. Ding H.J., Chen B., Liang J.: General solutions for coupled equations for piezoelectric media. Int. J. Solids. Struct. 33, 2283–2298 (1996)

    Article  MATH  Google Scholar 

  34. Wang X.D., Jiang L.Y.: Coupled behaviour of interacting dielectric cracks in piezoelectric materials. Int. J. Fract. 132, 115–133 (2005)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical and Materials Engineering, The University of Western Ontario, London, ON, N6A 5B9, Canada

    Z. Yan & L. Y. Jiang

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  1. Z. Yan
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  2. L. Y. Jiang
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Correspondence to L. Y. Jiang.

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Yan, Z., Jiang, L.Y. Interaction of parallel dielectric cracks in functionally graded piezoelectric materials. Acta Mech 211, 251–269 (2010). https://doi.org/10.1007/s00707-009-0229-5

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  • DOI: https://doi.org/10.1007/s00707-009-0229-5

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