Considered in this paper is a piezoelectric material strip containing an embedded crack or an edge crack perpendicular to its boundaries. The problem is solved for a strip that is suddenly heated or cooled from the top surface. The bottom surface is assumed to be zero temperature or thermally insulated. First the transient temperature and the stress distributions in an uncracked strip are calculated. Then, these stresses are used as the crack surface traction with opposite sign to formulate the mixed boundary value problem. This leads to a singular integral equation of Cauchy-type, which is then solved numerically. The numerically results for stress intensity factor are computed as a function of the normalized time and the crack size. The temperature and the thermal stress distributions for the uncracked problem are also included.

Issue Section:
Technical Papers
Keywords:
crack-edge stress field analysis, piezoelectric materials, thermal stresses, temperature distribution, boundary-value problems, integral equations
Topics:
Boundary-value problems, Fracture (Materials), Piezoelectric materials, Strips, Thermal stresses, Transients (Dynamics), Stress, Temperature
1.
Rizk
,
A. A.
, and
Radwan
,
S. F.
,
1992
, “
Transient Thermal Stress Problem for a Cracked Semi-infinite Medium
,”
J. Therm. Stresses
,
15
, pp.
451
–
468
.
2.
Rizk
,
A. A.
, and
Radwan
,
S. F.
,
1993
, “
Fracture of a Plate Under Transient Thermal Stresses
,”
J. Therm. Stresses
,
16
, pp.
79
–
102
.
3.
Rizk
,
A. A.
, and
Erdogan
,
F.
,
1989
, “
Cracking of Coated Materials Under Transient Thermal Stresses
,”
J. Therm. Stresses
,
12
, pp.
125
–
168
.
4.
Erdogan
,
F.
, and
Wu
,
B. H.
,
1996
, “
Crack Problem in FGM Layers Under Thermal Stresses
,”
J. Therm. Stresses
,
19
, pp.
237
–
265
.
5.
Noda
,
N.
,
1997
, “
Thermal Stresses Intensity Factor for Functionally Gradient Plate With an Edge Crack
,”
J. Therm. Stresses
,
20
, pp.
373
–
387
.
6.
Shindo
,
Y.
,
Watanabe
,
K.
, and
Narita
,
F.
,
2000
, “
Electroelastic Analysis of a Piezoelectric Ceramic Strip With a Central Crack
,”
Int. J. Eng. Sci.
,
38
, pp.
1
–
19
.
7.
Wang
,
T. C.
,
2000
, “
Analysis of Strip Electric Saturation Model of Crack Problem in Piezoelectric Materials
,”
Int. J. Solids Struct.
,
37
, pp.
6031
–
6049
.
8.
Chao
,
L.-P.
, and
Huang
,
J. H.
,
2000
, “
On a Piezoelectric Material Containing a Permeable Elliptical Crack
,”
Int. J. Solids Struct.
,
37
, pp.
5161
–
5176
.
9.
Pak
,
Y. E.
,
1990
, “
Crack Extension Force in a Piezoelectric Material
,”
J. Appl. Mech.
,
57
, pp.
647
–
653
.
10.
Kwon
,
S. M.
, and
Lee
,
K. Y.
,
2000
, “
Analysis of Stress and Electric Fields in a Rectangular Piezoelectric Body With a Center Crack Under Anti-plane Shear Loading
,”
Int. J. Solids Struct.
,
37
, pp.
4859
–
4869
.
11.
Lee
,
K. Y.
,
Lee
,
W. G.
, and
Pak
,
Y. E.
,
2000
, “
Interaction Between a Semi-infinite Crack and a Screw Dislocation in a Piezoelectric Material
,”
ASME J. Appl. Mech.
,
67
, pp.
165
–
170
.
12.
Calderon-Moreno
,
J. M.
,
2001
, “
Stress Induce Domain Switching of PZT in Compression Tests
,”
Mater. Sci. Eng., Ser. A.
,
315
, pp.
227
–
230
.
13.
Wang
,
B. L.
, and
Noda
,
N.
,
2000
, “
Mixed Mode Crack Initiation in Piezoelectric Ceramic Strip
,”
Theor. Appl. Fract. Mech.
,
34
, pp.
34
–
47
.
14.
Lu
,
P.
,
Tan
,
M. J.
, and
Liew
,
K. M.
,
1998
, “
Piezothermoelastic Analysis of a Piezoelectric Material With an Elliptic Cavity Under Uniform Heat Flow
,”
Arch. Appl. Mech.
,
68
, pp.
719
–
733
.
15.
Gradshteyn, I. S., and Ryzhik, I. M., eds., 1980, Tables of Integral, Series, and Products, Academic Press, San Diego, CA, p. 406.
Copyright © 2002
 by ASME
You do not currently have access to this content.