Analysis of a Conducting Crack in an Electrostrictive Ceramic Under Combined Electric and Mechanical Loading

  • Beom, Hyeon-Gyu (Department of Mechanical Engineering, Chonnam National University) ;
  • Jeong, Kyoung-Moon (Department of Mechanical Engineering, Chonnam National University) ;
  • Jeong, Eun-Do (Department of Mechanical Engineering, Chonnam National University)
  • Published : 2002.08.01

Abstract

A conducting crack in an electrostrictive ceramic under combined electric and mechanical loading is investigated. Analysis based on linear dielectric model predicts that the surfaces of the crack are not open completely but they are contact near the crack tip. The complete solution for the crack with a contact zone in a linear electrostrictive ceramic under combined electric and mechanical loading is obtained by using the complex variable formula. The asymptotic problems for a semi-infinite crack with a partial opening zone as well as for a fully open semi-infinite crack in a nonlinear electrostrictive ceramic are analyzed in order to investigate the effect of the electrical nonlinearity on the stress intensity factor under small scale nonlinear conditions. Particular attention is devoted to a finite crack in the nonlinear electrostrictive ceramic subjected to combined electric and mechanical loading. The stress intensity factor for the finite crack under small scale nonlinear conditions is obtained from the asymptotic analysis.

References

  1. Beom, H. G., 1999a, 'Singular Behaviour Near a Crack Tip in an Electrostrictive Material,' J. Mech. Phys. Solids, Vol. 47, pp. 1027-1049 https://doi.org/10.1016/S0022-5096(98)00098-2
  2. Beom, H. G., 1999b, 'Small Scale Nonlinear Analysis of Electrostrictive Crack Problems,' J. Mech. Phys. Solids, Vol. 47, pp. 1379-1395 https://doi.org/10.1016/S0022-5096(98)00099-4
  3. Hao, T. H., Gong, X. and Suo, Z., 1996, 'Fracture Mechanics for the Design of Ceramic Multilayer Actuators,' J. Mech. Phys. Solids, Vol. 44, pp. 23-48 https://doi.org/10.1016/0022-5096(95)00068-2
  4. Knops, R. J., 1963, 'Two-Dimensional Electrostriction,' Qt. J. Mech. Appl. Math., Vol. 16, pp. 377-388 https://doi.org/10.1093/qjmam/16.3.377
  5. McMeeking, R. M., 1987, 'On Mechanical Stresses at Cracks in Dielectric with Application to Dielectric Breakdown,' J. Appl Phys., Vol. 62, pp. 3116-3122 https://doi.org/10.1063/1.339361
  6. McMeeking, R. M., 1989, 'Electrostrictive Stresses Near Crack-Like Flaws,' J. Appl. Math. Phys., Vol. 40, pp. 615-627 https://doi.org/10.1007/BF00945867
  7. McMeeking, R. M., 1990, 'A J-Integral for the Analysis of Electrically Induced Mechanical Stress at Cracks in Elastic Dielectrics,' Int. J. Engng Sci., Vol. 28, pp. 605-613 https://doi.org/10.1016/0020-7225(90)90089-2
  8. Murakami, Y., 1987, Stress Intensity Factors Handbook, Pergamon
  9. Muskhelishivili, N. I., 1963, Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, Netherlands
  10. Ru, C. Q., Mao, X. and Epstein, M., 1998, 'Electric-Field Induced Interfacial Cracking in Multilayer Electrostrictive Actuators,' J. Mech. Phys. Solids, Vol. 46, pp. 1301-1318 https://doi.org/10.1016/S0022-5096(98)00038-6
  11. Smith, T. E. and Warren, W. E, 1966, 'Some Problems in Two-Dimensional Electrostriction,' J. Math. Phys., Vol. 45, pp. 45-51
  12. Smith, T. E. and Warren, W. E, 1968, 'Corrigenda to Some Problems in Two-Dimensional Electrostriction,' J. Math. Phys., Vol. 47, pp. 109-110
  13. Suo, Z., 1993, 'Models for Breakdown-Resistant Dielectric and Ferroelectric Ceramics,' J. Mech. Phys. Solids, Vol. 41, pp. 1155-1176 https://doi.org/10.1016/0022-5096(93)90088-W
  14. Winzer, S. R., Shankar, N. and Ritter, A. P., 1989, 'Designing Cofired Multilayer Electrostrictive Actuators for Reliability,' J. Am. Ceram. Soc., Vol. 72, pp. 2246-2257 https://doi.org/10.1111/j.1151-2916.1989.tb06069.x
  15. Yang, W. and Suo, Z., 1994, 'Cracking in Ceramic Actuators Caused by Electrostriction,' J. Mech. Phys. Solids, Vol. 42, pp. 649-663 https://doi.org/10.1016/0022-5096(94)90056-6