Research Papers

Effects of Maxwell Stress on Interfacial Crack Between Two Dissimilar Piezoelectric Solids

[+] Author and Article Information
Yi-Ze Wang

School of Astronautics,
Harbin Institute of Technology,
P. O. Box 137,
Harbin 150001, China
e-mail: wangyize@126.com

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received July 6, 2014; final manuscript received July 21, 2014; accepted manuscript posted July 28, 2014; published online August 5, 2014. Assoc. Editor: Pradeep Sharma.

J. Appl. Mech 81(10), 101003 (Aug 05, 2014) (6 pages) Paper No: JAM-14-1294; doi: 10.1115/1.4028090 History: Received July 06, 2014; Revised July 21, 2014; Accepted July 28, 2014

In this study, the effects of the Maxwell stress on the interfacial crack between two dissimilar piezoelectric solids are investigated. With the Stroh form and Muskhelishvili theory, the explicit expressions of generalized stresses are presented and the closed forms of the stress and electric displacement intensity factors are derived. Results show that the generalized stress field has singularities and oscillatory properties near the crack tip and the Maxwell stress has influences on the fracture characteristics. For the piezoelectric composites with the Maxwell stress, the normalized stress intensity factor KI* can be changed by both the remote stress and electric load. Such phenomenon cannot be found for the piezoelectric system without the Maxwell stress. Furthermore, the electric displacement intensity factor is more sensitive to the electric load than that to the remote stress.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.


Melkumyan, A., and Mai, Y. W., 2009, “Electroelastic Gap Waves Between Dissimilar Piezoelectric Materials in Different Classes of Symmetry,” Int. J. Solids Struct., 46(21), pp. 3760–3770. [CrossRef]
Yan, P., Jiang, C. P., and Song, F., 2011, “An Eigenfunction Expansion-Variational Method for the Anti-Plane Electroelastic Behavior of Three-Phase Fiber Composites,” Mech. Mater., 43(10), pp. 586–597. [CrossRef]
Huang, Y., and Li, X. F., 2011, “Interfacial Waves in Dissimilar Piezoelectric Cubic Crystals With an Imperfect Bonding,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 58(6), pp. 1261–1265. [CrossRef]
Feng, W. J., Wang, L. Q., Jiang, Z. Q., and Zhao, Y. M., 2004, “Shear Wave Scattering From a Partially Debonded Piezoelectric Cylindrical Inclusion,” Acta Mech. Solida Sin., 17(3), pp. 258–269. [CrossRef]
Gao, C. F., Tong, P., and Zhang, T. Y., 2005, “Interaction of a Dipole With an Interfacial Crack in Piezoelectric Media,” Compos. Sci. Technol., 65(9), pp. 1354–1362. [CrossRef]
Sladek, J., Sladek, V., Wünsche, M., and Zhang, C., 2012, “Analysis of an Interface Crack Between Two Dissimilar Piezoelectric Solids,” Eng. Fract. Mech., 89, pp. 114–127. [CrossRef]
Zhao, Y. F., Zhao, M. H., Pan, E. N., and Fan, C. Y., 2014, “Analysis of an Interfacial Crack in a Piezoelectric Bi-Material Via the Extended Green's Functions and Displacement Discontinuity Method,” Int. J. Solids Struct., 51(6), pp. 1456–1463. [CrossRef]
Li, S., 2003, “On Global Energy Release Rate of a Permeable Crack in a Piezoelectric Ceramic,” ASME J. Appl. Mech., 70(2), pp. 246–252. [CrossRef]
Chen, Z. T., 2006, “Dynamic Fracture Mechanics Study of an Electrically Impermeable Mode III Crack in a Transversely Isotropic Piezoelectric Material Under Pure Electric Load,” Int. J. Fract., 141(3–4), pp. 395–402. [CrossRef]
Li, Y. D., and Lee, K. Y., 2009, “The Shielding Effect of the Imperfect Interface on a Mode III Permeable Crack in a Layered Piezoelectric Sensor,” Eng. Fract. Mech., 76(7), pp. 876–883. [CrossRef]
Zhou, Z. G., Guo, Y., and Wu, L. Z., 2009, “The Behavior of Three Parallel Non-Symmetric Permeable Mode-III Cracks in a Piezoelectric Material Plane,” Mech. Res. Commun., 36(6), pp. 690–698. [CrossRef]
Hao, T. H., and Shen, Z. Y., 1994, “A New Electric Boundary Condition of Electric Fracture Mechanics and Its Applications,” Eng. Fract. Mech., 47(6), pp. 793–802. [CrossRef]
Bustamante, R., and Rajagopal, K. R., 2013, “On a New Class of Electroelastic Bodies. I,” Proc. R. Soc. London, Ser. A, 469(2149), p. 20120521. [CrossRef]
Bustamante, R., and Rajagopal, K. R., 2013, “On a New Class of Electro-Elastic Bodies. II. Boundary Value Problems,” Proc. R. Soc. London, Ser. A, 469(2149), p. 20130106. [CrossRef]
Jiang, Q., and Kuang, Z. B., 2004, “Stress Analysis in Two Dimensional Electrostrictive Material With an Elliptic Rigid Conductor,” Eur. J. Mech. A–Solid., 23(6), pp. 945–956. [CrossRef]
Jiang, Q., Gao, C. F., and Kuang, Z. B., 2010, “Electroelastic Stress in an Electrostrictive Material With Charged Surface Electrodes,” Int. J. Eng. Sci., 48(12), pp. 2066–2080. [CrossRef]
Zhang, A. B., and Wang, B. L., 2014, “The Influence of Maxwell Stresses on the Fracture Mechanics of Piezoelectric Materials,” Mech. Mater., 68, pp. 64–69. [CrossRef]
Stroh, A. N., 1958, “Dislocations and Cracks in Anisotropic Elasticity,” Philos. Mag., 3(30), pp. 625–646. [CrossRef]
Suo, Z., Kuo, C. M., Barnett, D. M., and Willis, J. R., 1992, “Fracture Mechanics of Piezoelectric Ceramics,” J. Mech. Phys. Solids, 40(4), pp. 739–765. [CrossRef]
Gao, C. F., and Mai, Y. W., 2010, “Fracture of Electrostrictive Solids Subjected to Combined Mechanical and Electric Loads,” Eng. Fract. Mech., 77(10), pp. 1503–1515. [CrossRef]
Gao, C. F., Mai, Y. W., and Zhang, N., 2010, “Solution of Collinear Cracks in an Electrostrictive Solid,” Philos. Mag., 90(10), pp. 1245–1262. [CrossRef]
Muskhelishvili, N. I., 1975, Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff International Publishing, Leyden, Netherlands.
England, A. H., 1965, “A Crack Between Dissimilar Media,” ASME J. Appl. Mech., 32(2), pp. 400–402. [CrossRef]
Li, Q., and Chen, Y. H., 2008, “Why Traction–Free? Piezoelectric Crack and Coulombic Traction,” Arch. Appl. Mech., 78(7), pp. 559–573. [CrossRef]
Zhang, T. Y., Zhao, M. H., and Gao, C. F., 2005, “The Strip Dielectric Breakdown Model,” Int. J. Fract., 132(4), pp. 311–327. [CrossRef]
Gao, C. F., Noda, N., and Zhang, T. Y., 2006, “Dielectric Breakdown Model for a Conductive Crack and Electrode in Piezoelectric Materials,” Int. J. Eng. Sci., 44(3–4), pp. 256–272. [CrossRef]


Grahic Jump Location
Fig. 1

An interfacial crack between dissimilar piezoelectric solids with the dielectric constants κc for the crack and κ for the surrounding medium

Grahic Jump Location
Fig. 2

Relation between the normalized stress intensity factor (KI* = KI/100 × 106πa) and the electric load (D2∞) with the effects of the Maxwell stress

Grahic Jump Location
Fig. 3

Normalized stress intensity factor (KI* = KI/100 × 106πa) with different remote stresses (σ22∞) and electric loads (D2∞) for: (a) κ= κc= κ0, (b) κ= κc= 3 κ0, (c) κ= κc= 5 κ0, and (d) no Maxwell stress

Grahic Jump Location
Fig. 4

Normalized electric displacement intensity factor (KD* = KD/0.1πa) with different remote stresses (σ22∞) and electric loads (D2∞) for κ= κc= κ0




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In