Acta Mechanica Solida Sinica

, Volume 19, Issue 2, pp 167–173 | Cite as

Investigation of the M-integral in crack-damaged piezoelectric ceramics

  • Defa Wang
  • Lifeng Ma
  • Junping Shi
Article

Abstract

The physical interpretation of the M-integral is investigated in the analysis of crack-damaged piezoelectric problems. The relation between the M-integral and the change of the total electric enthalpy (CTEE), i.e., M = 2CTEE, is derived with a theoretical derivation procedure for two-dimensional piezoelectric problems. It is shown that the M-integral may provide a more natural description of electric enthalpy release due to the formation of the pre-existing microcracks associated with the damaged body, rather than the description of the total potential energy release rate as interpreted for conventional brittle solids. For crack-damaged piezoelectric ceramics, numerical calculation of the M-integral is discussed. Based on the pseudo-traction electric displacement method, M = 2CTEE has also been proved by the numerical results.

Key words

M-integral crack piezoelectric ceramics electric enthalpy damage 

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References

  1. [1]
    Rice, J.R., A path-independent integral and the approximate analysis of strain concentration by notch and cracks, ASME Journal of Applied Mechanics, Vol.35, 1968, 279–320.CrossRefGoogle Scholar
  2. [2]
    Knowles, J.K. and Sternberg, E., On a class of conservation laws in linearized and finite elastostatics, Archiv for Rational Mechanics and Analysis, Vol.44, 1972, 187–211.MathSciNetCrossRefGoogle Scholar
  3. [3]
    Budiansky, B. and Rice, J.R., Conservation laws and energy-release rates, ASME Journal of Applied Mechanics, Vol.40, 1973, 201–203.CrossRefGoogle Scholar
  4. [4]
    Herrmann, G.A. and Hermann, G., On energy release rates for plane cracks, ASME Journal of Applied Mechanics, Vol.48, 1981, 525–530.CrossRefGoogle Scholar
  5. [5]
    King, R.B. and Herrmann, G., Nondestructive evaluation of the J- and M-integrals, ASME Journal of Applied Mechanics, Vol.48, 1981, 83–87.CrossRefGoogle Scholar
  6. [6]
    Chen, Y.Z., New path independent integrals in linear elastic fracture mechanics, Engineering Fracture Mechanics, Vol.22, 1985, 673–686.CrossRefGoogle Scholar
  7. [7]
    Freund, L.B., Stress-intensity factor calculations based on a conservation integral, International Journal of Solids and Structures, Vol.14, 1978, 241–250.CrossRefGoogle Scholar
  8. [8]
    Yau, J.F., Wang, S.S. and Corten, H.T., A mixed-mode crack analysis of isotropic solids using conservation laws of elasticity, ASME Journal of Applied Mechanics, Vol.47, 1980, 335–341.CrossRefGoogle Scholar
  9. [9]
    Wang, D.F. and Chen, Y.H., M-integral analysis for a two dimensional metal/ceramic bimaterial solid with extending subinterface microcracks, Archive of Applied Mechanics, Vol.72, 2002, 588–598.Google Scholar
  10. [10]
    Wang, D.F., Chen, Y.H. and Fukui, T., Conservation laws in finite microcracking brittle solids, Acta Mechanica Solida Sinica, Vol.18, No.3, 2005, 189–199.Google Scholar
  11. [11]
    Wang, D.F., Chen, Y.H. and Liu, C.S., Further investigation of the J2-integral in bimaterial solids, Acta Mechanica Solida Sinica, Vol.16, No.2, 2003, 179–188.Google Scholar
  12. [12]
    Sabir, M. and Maugin, G.A., On the fracture paramagnets and soft ferromagnets, International Journal of Non-Linear Mechanics, Vol.31, 1996, 425–440.CrossRefGoogle Scholar
  13. [13]
    Fomethe, A. and Maugin, G.A., On the crack mechanics of hard ferromagnets, International Journal of Non-Linear Mechanics, Vol.33, 1998, 85–95.MathSciNetCrossRefGoogle Scholar
  14. [14]
    Han, J.J. and Chen, Y.H., Multiple parallel cracks interaction problem in piezoelectric ceramics, International Journal of Solids and Structures, Vol.36, 1999, 3375–3390.CrossRefGoogle Scholar
  15. [15]
    Suo, Z., Kuo, C.M., Barnett, D.M. and Willis, J.R., Fracture mechanics for piezoelectric ceramics, Journal of the Mechanics and Physics of Solids, Vol.40, 1992, 739–765.MathSciNetCrossRefGoogle Scholar
  16. [16]
    Sosa, H.A., Plane problems in piezoelectric media with defects, International Journal of Solids and Structures, Vol.28, 1991, 491–505.CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2006

Authors and Affiliations

  • Defa Wang
    • 1
  • Lifeng Ma
    • 2
  • Junping Shi
    • 3
  1. 1.Department of Civil EngineeringXi’an University of TechnologyXi’anChina
  2. 2.Department of Civil EngineeringXi’an JiaoTong UniversityXi’anChina
  3. 3.Department of Engineering MechanicsXi’an University of TechnologyXi’anChina

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