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Generalized 2D problem of piezoelectric media containing collinear cracks

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Abstract

The generalized 2D problem in piezoelectric media with collinear cracks is addressed based on Stroh's formulation and the exact electric boundary conditions on the crack faces. Exact solutions are obtained, respectively, for two special cases: one is that a piezoelectric solid withN collinear cracks is subjected to uniform loads at infinity, and the other is that a piezoelectric solid containing a single crack is subjected to a line load at an arbitrary point. It is shown when uniform loads are applied at infinity or on the crack faces that, the stress intensity factors are the same as those of isotropic materials, while the intensity factor of electric displacement is dependent on the material constants and the applied mechanical loads, but not on the applied electric loads. Moreover, it is found that the electric field inside any crack is not equal to zero, which is related to the material properties and applied mechanical-electric loads.

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References

  1. Parton VZ. Fracture mechanics of piezoelectric materials.Acta Astronautic, 1976, 3: 671–683

    Article  MATH  Google Scholar 

  2. Deeg WF. The analysis of dislocation, crack and inclusion problems in piezoelectric solids. Ph.D. Thesis, Stanford University, 1980

  3. Pak YE. Crack extension force in a piezoelectric material.ASME J Appl Mech, 1990, 57: 647–653

    Article  MATH  Google Scholar 

  4. Sosa HA, Pak YE. Three-dimensional eigenfunction analysis of a crack in a piezoelectric material.Int J Solids Struct, 1990, 26:1–15

    Article  MATH  Google Scholar 

  5. Sosa HA. On the fracture mechanics of piezoelectric solids.Int J Solids Struct, 1992, 28: 2613–2622

    Article  Google Scholar 

  6. Suo Z, Kuo CM, Barnett DM, Willis JR. Fracture mechanics for piezoelectric ceramics.J Mech Phys Solids, 1992, 40: 739–765

    Article  MATH  MathSciNet  Google Scholar 

  7. Wang B. Three-dimensional analysis of a flat elliptical crack in a piezoelectric medium.Int J Eng Sci, 1992, 30:781–791

    Article  MATH  Google Scholar 

  8. Pak YE. Linear electro-elastic fracture mechanics of piezoelectric materials.Int J Fracture, 1992, 54: 79–100

    Google Scholar 

  9. Park SB, Sun CT. Effect of electric field on fracture of piezoelectric ceramic.Int J Fracture, 1995, 70: 203–216

    Article  Google Scholar 

  10. Beom HG, Atluri SN. Near-tip fields and intensity factors for interfacial cracks in dissimilar anisotropic piezoelectric media.Int J Fracture, 1996, 75: 163–183

    Article  Google Scholar 

  11. Qin QH, Yu SW. An arbitrarily-oriented plane crack terminating at the interface between dissimilar piezoelectric materials.Int J Solids Struct, 1997, 34: 581–590

    Article  MATH  Google Scholar 

  12. Zhong Z, Meguid SA. Interfacial debonding of a circular inhomogeneity in piezoelectric materials.Int J Solids Struct, 1997, 34: 1965–1984

    Article  MATH  Google Scholar 

  13. Zhong Z, Meguid SA. Analysis of a circular arc-crack in piezoelectric materials.Int J Fracture, 1997, 84: 143–158

    Article  Google Scholar 

  14. McMeeking RM. Electrostrictive stresses near crack-like flaws.J Appl Math Phys (ZAMM), 1989, 640: 615–627

    Article  Google Scholar 

  15. Dunn ML. The effect of crack face boundary conditions on the fracture mechanics of piezoelectric solids.Eng Frac Mech, 1994, 48: 25–39

    Article  Google Scholar 

  16. Kogan LC, Hui Y, Molkov V. Stress and induction field of a spheroidal inclusion or a pennyshaped crack in a transversely isotropic piezoelectric material.Int J Solids Struct, 1996, 33: 2719–2737

    Article  MATH  Google Scholar 

  17. Sosa HA, Khutoryansky N. New developments concerning piezoelectric materials with defects.Int J Solids Struct, 1996, 33: 3399–3414

    Article  MATH  MathSciNet  Google Scholar 

  18. Zhang TY, Qian CF, Tong P. Linear electro-elastic analysis of a cavity or a crack in a piezoelectric material.Int J Solids Struct, 1998, 35: 2121–2149

    Article  MATH  Google Scholar 

  19. Filŝhtinskii LA, Filŝhtinskii ML. Extension of composite piezoelectric plate weakened with cracks cutting.Prikl Mekh, 1993, 12: 66–71 (in Russian)

    Google Scholar 

  20. Filŝhtinskii LA, Filŝhtinskii ML. Green function for a composite piezoceramic plane with an interfacial crack.Prikl Mat Mekh, 1994, 58: 159–166 (in Russian)

    Google Scholar 

  21. Hou MS. A general solution of the plane stress planes in piezoelectric media with line cracks.Acta Mech Sinica, 1997, 29: 595–599 (in Chinese)

    Google Scholar 

  22. Chung MY, Ting TCT. Piezoelectric solid with an elliptic inclusion or hole.Int J Solids Struct, 1996, 33: 3343–3361

    Article  MATH  MathSciNet  Google Scholar 

  23. Suo Z. Singularities, interfaces and cracks in dissimilar anisotropic media.Proc R Soc Lond, 1990, A427: 331–358

    MathSciNet  Google Scholar 

  24. Muskhelishvili NI. Some basic problems of mathematical theory of elasticity. Noordhoof, leyden, 1975

    MATH  Google Scholar 

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The project supported by the National Natural Science Foundation of China (19772004)

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Cunfa, G., Minzhong, W. Generalized 2D problem of piezoelectric media containing collinear cracks. Acta Mech Sinica 15, 235–244 (1999). https://doi.org/10.1007/BF02486151

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  • DOI: https://doi.org/10.1007/BF02486151

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