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.
Similar content being viewed by others
References
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.
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.
Budiansky, B. and Rice, J.R., Conservation laws and energy-release rates, ASME Journal of Applied Mechanics, Vol.40, 1973, 201–203.
Herrmann, G.A. and Hermann, G., On energy release rates for plane cracks, ASME Journal of Applied Mechanics, Vol.48, 1981, 525–530.
King, R.B. and Herrmann, G., Nondestructive evaluation of the J- and M-integrals, ASME Journal of Applied Mechanics, Vol.48, 1981, 83–87.
Chen, Y.Z., New path independent integrals in linear elastic fracture mechanics, Engineering Fracture Mechanics, Vol.22, 1985, 673–686.
Freund, L.B., Stress-intensity factor calculations based on a conservation integral, International Journal of Solids and Structures, Vol.14, 1978, 241–250.
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.
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.
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.
Wang, D.F., Chen, Y.H. and Liu, C.S., Further investigation of the J 2 -integral in bimaterial solids, Acta Mechanica Solida Sinica, Vol.16, No.2, 2003, 179–188.
Sabir, M. and Maugin, G.A., On the fracture paramagnets and soft ferromagnets, International Journal of Non-Linear Mechanics, Vol.31, 1996, 425–440.
Fomethe, A. and Maugin, G.A., On the crack mechanics of hard ferromagnets, International Journal of Non-Linear Mechanics, Vol.33, 1998, 85–95.
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.
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.
Sosa, H.A., Plane problems in piezoelectric media with defects, International Journal of Solids and Structures, Vol.28, 1991, 491–505.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Wang, D., Ma, L. & Shi, J. Investigation of the M-integral in crack-damaged piezoelectric ceramics. Acta Mech. Solida Sin. 19, 167–173 (2006). https://doi.org/10.1007/s10338-006-0620-x
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10338-006-0620-x