Advertisement

Penny-Shaped Cracks

  • Qing-Hua Qin

Abstract

This chapter applies the formulation presented in the first two chapters to a range of piezoelectric problems containing penny-shaped cracks. It includes a penny-shaped crack in an infinite piezoelectric plate, a piezoelectric strip, a fiber embedded in a matrix, a piezoelectric cylinder with elastic coating, and the fundamental solution for penny-shaped crack problems.

Keywords

Stress Intensity Factor Piezoelectric Material Piezoelectric Layer Versus Versus Versus Versus Versus Normalize Stress Intensity Factor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Yu SW, Qin QH: Damage analysis of thermopiezoelectric properties. 2. Effective crack model. Theoretical and Applied Fracture Mechanics 25(3), 279–288 (1996).CrossRefGoogle Scholar
  2. [2]
    Qin QH, Yu SW: An arbitrarily-oriented plane crack terminating at the interface between dissimilar piezoelectric materials. International Journal of Solids and Structures 34(5), 581–590 (1997).zbMATHCrossRefGoogle Scholar
  3. [3]
    Qin QH, Mai YW: A closed crack tip model for interface cracks in thermopiezoelectric materials. International Journal of Solids and Structures 36(16), 2463–2479 (1999).zbMATHCrossRefGoogle Scholar
  4. [4]
    Narita F, Lin S, Shindo Y: Penny-shaped crack in a piezoceramic cylinder under mode I loading. Archives of Mechanics 55(3), 275–304 (2003).zbMATHGoogle Scholar
  5. [5]
    Yang JH, Lee KY: Penny shaped crack in a piezoelectric cylinder surrounded by an elastic medium subjected to combined in-plane mechanical and electrical loads. International Journal of Solids and Structures 40(3), 573–590 (2003).MathSciNetzbMATHCrossRefGoogle Scholar
  6. [6]
    Lin S, Narita F, Shindo Y: Electroelastic analysis of a piezoelectric cylindrical fiber with a penny-shaped crack embedded in a matrix. International Journal of Solids and Structures 40(19), 5157–5174 (2003).zbMATHCrossRefGoogle Scholar
  7. [7]
    Kogan L, Hui CY, Molkov V: Stress and induction field of a spheroidal inclusion or a penny-shaped crack in a transversely isotropic piezoelectric material. International Journal of Solids and Structures 33(19), 2719–2737 (1996).zbMATHCrossRefGoogle Scholar
  8. [8]
    Karapetian E, Sevostianov I, Kachanov M: Penny-shaped and half-plane cracks in a transversely isotropic piezoelectric solid under arbitrary loading. Archive of Applied Mechanics 70(1-3), 201–229 (2000).zbMATHCrossRefGoogle Scholar
  9. [9]
    Chen WQ, Shioya T: Complete and exact solutions of a penny-shaped crack in a piezoelectric solid: antisymmetric shear loadings. International Journal of Solids and Structures 37(18), 2603–2619 (2000).zbMATHCrossRefGoogle Scholar
  10. [10]
    Yang FQ: General solutions of a penny-shaped crack in a piezoelectric material under opening mode-I loading. Quarterly Journal of Mechanics and Applied Mathematics 57(4), 529–550 (2004).MathSciNetzbMATHCrossRefGoogle Scholar
  11. [11]
    Eriksson K: Energy release rates for the penny-shaped crack in a linear piezoelectric solid. International Journal of Fracture 116(2), L23–L28 (2002).CrossRefGoogle Scholar
  12. [12]
    Yang JH, Lee KY: Penny-shaped crack in a piezoelectric cylinder under electromechanical loads. Archive of Applied Mechanics 73,323–336 (2003).zbMATHCrossRefGoogle Scholar
  13. [13]
    Wang BL, Noda N, Han JC, Du SY: A penny-shaped crack in a transversely isotropic piezoelectric layer. European Journal of Mechanics A:Solids 20(6), 997–1005 (2001).zbMATHCrossRefGoogle Scholar
  14. [14]
    Li XF, Lee KY: Effects of electric field on crack growth for a penny-shaped dielectric crack in a piezoelectric layer. Journal of the Mechanics and Physics of Solids 52(9), 2079–2100 (2004).MathSciNetzbMATHCrossRefGoogle Scholar
  15. [15]
    Feng WJ, Li YS, Ren DL: Transient response of a piezoelectric layer with a penny-shaped crack under electromechanical impacts. Structural Engineering and Mechanics 23(2), 163–175 (2006).Google Scholar
  16. [16]
    Eshelby JD: The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proceedings of the Royal Society of London Series A:Mathematical and Physical Sciences 241(1226), 376–396 (1957).MathSciNetzbMATHCrossRefGoogle Scholar
  17. [17]
    Wang B: 3-dimensional analysis of a flat elliptic crack in a piezoelectric material. International Journal of Engineering Science 30(6), 781–791 (1992).zbMATHCrossRefGoogle Scholar
  18. [18]
    Huang JH: A fracture criterion of a penny-shaped crack in transversely isotropic piezoelectric media. International Journal of Solids and Structures 34(20), 2631–2644 (1997).zbMATHCrossRefGoogle Scholar
  19. [19]
    Chiang CR, Weng GJ: The nature of stress and electric-displacement concentrations around a strongly oblate cavity in a transversely isotropic piezoelectric material. International Journal of Fracture 134(3-4), 319–337 (2005).zbMATHCrossRefGoogle Scholar
  20. [20]
    Lin S, Narita F, Shindo Y: Electroelastic analysis of a penny-shaped crack in a piezoelectric ceramic under mode I loading. Mechanics Research Communications 30(4), 371–386 (2003).zbMATHCrossRefGoogle Scholar
  21. [21]
    Kudryavtsev BA, Parton VZ, Rakitin VI: Breakdown mechanics of piezoelectric materials:axisymmeric crack on boundary with conductor. Prikladnaya Matematika I Mekhanika 39(2), 352–362 (1975).Google Scholar
  22. [22]
    Chen WQ, Shioya T, Ding HJ: Integral equations for mixed boundary value problem of a piezoelectric half-space and the applications. Mechanics Research Communications 26(5), 583–590 (1999).MathSciNetzbMATHCrossRefGoogle Scholar
  23. [23]
    Qin QH, Wang JS, Li XL: Effect of elastic coating on fracture behaviour of piezoelectric fibre with a penny-shaped crack. Composite Structures 75(1-4), 465–471 (2006).CrossRefGoogle Scholar
  24. [24]
    Chen WQ, Shioya T: Fundamental solution for a penny-shaped crack in a piezoelectric medium. Journal of the Mechanics and Physics of Solids 47(7), 1459–1475 (1999).MathSciNetzbMATHCrossRefGoogle Scholar
  25. [25]
    Wang JS, Qin QH: Penny-shaped crack in a solid piezoelectric cylinder with two typical boundary conditions. Journal of Beijing University of Technology 32(SUPPL), 29–34 (2006).Google Scholar
  26. [26]
    Qin QH: Fracture Mechanics of Piezoelectric Materials. WIT Press, Southampton (2001).Google Scholar
  27. [27]
    Yang JH, Lee KY: Penny shaped crack in a three-dimensional piezoelectric strip under in-plane normal loadings. Acta Mechanica 148(1-4), 187–197 (2001).zbMATHCrossRefGoogle Scholar
  28. [28]
    He LH, Lim CW: Electromechanical responses of piezoelectric fiber composites with sliding interface under anti-plane deformations. Composites Part B:Engineering 34(4), 373–381 (2003).CrossRefGoogle Scholar

Copyright information

© Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Qing-Hua Qin
    • 1
  1. 1.Research School of EngineeringAustralian National UniversityCanberraAustralia

Personalised recommendations