Research Papers

M-Integral for Calculating Intensity Factors of Cracked Piezoelectric Materials Using the Exact Boundary Conditions

[+] Author and Article Information
Yael Motola

The Dreszer Fracture Mechanics Laboratory, School of Mechanical Engineering, Faculty of Engineering, Tel Aviv University, 69978 Ramat Aviv, Israelymotola@eng.tau.ac.il

Leslie Banks-Sills

The Dreszer Fracture Mechanics Laboratory, School of Mechanical Engineering, Faculty of Engineering, Tel Aviv University, 69978 Ramat Aviv, Israel

J. Appl. Mech 76(1), 011004 (Oct 31, 2008) (9 pages) doi:10.1115/1.2998485 History: Received August 21, 2007; Revised May 11, 2008; Published October 31, 2008

In this paper, the M-integral is extended for calculating intensity factors for cracked piezoelectric ceramics using the exact boundary conditions on the crack faces. The poling direction is taken at an angle to the crack faces within the plane. Since an analytical solution exists, the problem of a finite length crack in an infinite body subjected to crack face traction and electric flux density is examined. In this case, poling is taken parallel to the crack faces. Numerical difficulties resulting from multiplication of large and small numbers were treated by normalizing the variables. This problem was solved with the M-integral and displacement-potential extrapolation methods. With this example, the superiority of the conservative integral is observed. The values for the intensity factor obtained with the M-integral are found to be more accurate than those found by means of the extrapolation method. In addition, a crack parallel to the poling direction in a four-point bend specimen subjected to both an applied load and an electric field was analyzed and different electric permittivity values in the crack gap were assumed. It is seen that the electric permittivity greatly influences the stress intensity factor KII and the electric flux density intensity factor KIV. The absolute value of these intensity factors increases with an increase in the value of the electric permittivity in the crack. The influence of the permittivity on KI is rather small.

Copyright © 2009 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.



Grahic Jump Location
Figure 1

Crack tip and material coordinates

Grahic Jump Location
Figure 2

Integration paths for J-integral calculation

Grahic Jump Location
Figure 3

Mesh and integration paths about the crack tip

Grahic Jump Location
Figure 4

Griffith crack problem

Grahic Jump Location
Figure 5

Meshes for the plate in Fig. 4: (a) coarse and (b) fine meshes

Grahic Jump Location
Figure 6

Meshes in the neighborhood of the crack tip for the infinite plate: (a) coarse and (b) fine meshes

Grahic Jump Location
Figure 7

Four-point bend specimen

Grahic Jump Location
Figure 8

Mesh in the vicinity of the crack for both meshes of the four-point bend specimen shown in Fig. 7 with a/W=0.2

Grahic Jump Location
Figure 9

Normalized intensity factors as a function of normalized crack length a/W as obtained from the fine mesh for the specimen in Fig. 7: (a) K̃I, (b) K̃II, and (c) K̃IV



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