Analysis of a Crack in a Linear Electrostrictive Ceramic Subjected to Electric Fields

전기장을 받는 선형 전왜세라믹 내의 균열해석

  • Published : 2001.02.01


A crack with electrically conducting surfaces in a linear electrostrictive ceramic subjected to uniform electric fields is analyzed. Complete forms of electric fields and elastic fields for the crack are derived by using the complex function theory. The linear electromechanical theory predicts overlapping of the traction free crack surfaces. It is shown that the surfaces of the crack are contact near the crack tip. The contact zone size obtained on the basis of the linear dielectric theory for the conducting crack does not depend on the electric fields and depends on only the original crack and the material property for the linear electrostrictive ceramic.


Electrostrictive Ceramic;Crack;Electric Field;Elastic Field;Contact;Complex Function Theory;Linear Dielectric Theory


  1. Beom, H. G., 1999, 'Small Scale Nonlinear Analysis of Electrostrictive Crack Problems,' J. Mach. Phys. Solids, Vol. 47, pp. 1379-1395
  2. Knops, R. J., 1963, 'Two-Dimensional Electrostriction,' Quart. J. Mech. Appl. Math., Vol. 16, pp. 377-388
  3. Muskhelishivili, N. I., 1963, Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, Netherlands
  4. England, A. H., 1971, Complex Variable Methods in Elasticity, John Wiley & Sons Ltd., New York
  5. Suo, Z., 1993, 'Models for Breakdown-Resistant Dielectric and Ferroelectric Ceramics,' J. Mech. Phys. Solids, Vol. 41, pp. 1155-1176
  6. Uchino, K., 1986, 'Electrostrictive Actuators: Materials and Applications,' Am. Ceram. Soc. Bulletin, Vol. 65, pp. 647-652
  7. 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
  8. Yang, W. and Suo, Z., 1994, 'Cracking in Ceramic Actors Caused by Electrostriction,' J. Mech. Phys. Solids, Vol. 42, pp. 649-663
  9. 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
  10. 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
  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. McMeeking, R. M., 1987, 'On Mechanical Stresses at Cracks in Dielectric With Application to Dielectric Breakdown,' J. Apple. Phys., Vol. 62, pp. 3116-3122
  14. McMeeking, R. M., 1989, 'Electrostrictive Stresses Near Crack-Like Flaws,' J. Appl. Math. Phys, Vol. 40, pp. 615-627
  15. Beom, H. G., 1999, 'Singular Behaviour Near a Crack Tip in an Electrostrictive Material,' J. Mech. Phys. Solids, Vol. 47, pp. 1027-1049