The interface crack problem of bonded piezoelectric and elastic half-space under transient electromechanical loads is considered. Both the permeable and impermeable boundary conditions are examined and discussed. Based on the use of integral transform techniques, the problem is reduced either to a singular integral equation for the permeable boundary condition or to two coupled singular integral equations for the impermeable boundary condition, which can be solved using Chebyshev polynomial expansions. Numerical results are provided to show the effect of the applied electric fields, the electric boundary conditions along the crack faces and a free surface on the resulting dynamic stress intensity factor and electric displacement intensity factor.

Issue Section:
Technical Papers
Keywords:
crack-edge stress field analysis, piezoelectric materials, mechanical contact, integral equations, Chebyshev approximation, polynomial approximation
Topics:
Boundary-value problems, Fracture (Materials), Stress, Transients (Dynamics), Elastic half space, Integral equations, Electric fields, Displacement
1.
Shindo, Y., and Ozawa, E., 1990, “Dynamic Analysis of a Cracked Piezoelectric Material,” Mechanical Modeling of New Electromagnetic Materials, R. K. T. Hsieh, ed., Elsevier, Amsterdam, pp. 297–304.
2.
Norris
,
A. N.
,
1994
, “
Dynamic Green’s Functions in Anisotropic Piezoelectric, Thermoelastic and Poroelastic Solids
,”
Proc. R. Soc. London, Ser. A
,
447
, pp.
175
–
186
.
3.
Khutoryyansky
,
N. M.
, and
Sosa
,
H.
,
1995
, “
Dynamic Representation Formulas and Fundamental Solutions for Piezoelectricity
,”
Int. J. Solids Struct.
,
32
, pp.
3307
–
3325
.
4.
Shindo
,
Y.
,
Katsura
,
H.
, and
Yan
,
W.
,
1996
, “
Dynamic Stress Intensity Factor of a Cracked Dielectric Medium in a Uniform Electric Fields
,”
Acta Mech.
,
117
, pp.
1
–
10
.
5.
Narita
,
F.
, and
Shindo
,
Y.
,
1998
, “
Dynamic Anti-Plane Shear of a Cracked Piezoelectric Ceramic
,”
Theor. Appl. Fract. Mech.
,
29
, pp.
169
–
180
.
6.
Narita
,
F.
, and
Shindo
,
Y.
,
1998
, “
Scattering of Love Waves by a Surface-Breaking Crack in Piezoelectric Layered Media
,”
JSME Int. J., Ser. A
,
41
, pp.
40
–
48
.
7.
Meguid
,
S. A.
, and
Wang
,
X. D.
,
1998
, “
Dynamic Anti-Plane Behavior of Interacting Cracks in a Piezoelectric Material
,”
Int. J. Fract.
,
91
, pp.
391
–
403
.
8.
Wang
,
X. D.
,
2001
, “
On the Dynamic Behavior of Interacting Interfacial Cracks in Piezoelectric Media
,”
Int. J. Solids Struct.
,
38
, pp.
815
–
831
.
9.
Li
,
S.
, and
Mataga
,
P. A.
,
1996
, “
Dynamic Crack Propagation in Piezoelectric Materials. Part 1: Electrode Solution
,”
J. Mech. Phys. Solids
,
44
, pp.
1799
–
1830
.
10.
Li
,
S.
, and
Mataga
,
P. A.
,
1996
, “
Dynamic Crack Propagation in Piezoelectric Materials. Part 2: Vacuum Solution
,”
J. Mech. Phys. Solids
,
44
, pp.
1831
–
1866
.
11.
Chen
,
Z. T.
, and
Yu
,
S. W.
,
1997
, “
Crack Tip Field of Piezoelectric Materials Under Anti-Plane Impact
,”
Chin. Sci. Bull.
,
42
, pp.
1613
–
1617
.
12.
Chen
,
Z. T.
, and
Karihaloo
,
B. L.
,
1999
, “
Dynamic Response of a Cracked Piezoelectric Ceramic Under Arbitrary Electro-Mechanical Impact
,”
Int. J. Solids Struct.
,
36
, pp.
5125
–
5133
.
13.
Chen
,
Z. T.
, and
Meguid
,
S. A.
,
2000
, “
The Transient Response of a Piezoelectric Strip With a Vertical Crack Under Electro-Mechanical Impact Load
,”
Int. J. Solids Struct.
,
37
, pp.
6051
–
6062
.
14.
Wang
,
X.
, and
Yu
,
S.
,
2000
, “
Transient Response of a Crack in a Piezoelectric Strip Subjected to the Mechanical and Electrical Impacts
,”
Int. J. Solids Struct.
,
37
, pp.
5795
–
5808
.
15.
Shin
,
J. W.
,
Kwon
,
S. M.
, and
Lee
,
K. Y.
,
2001
, “
An Eccentric Crack in a Piezoelectric Strip Under Anti-Plane Shear Impact Loading
,”
Int. J. Solids Struct.
,
38
, pp.
1483
–
1494
.
16.
Wang
,
B. L.
,
Han
,
J. C.
, and
Du
,
S. Y.
,
2000
, “
Electroelastic Fracture Dynamics for Multi-layered Piezoelectric Materials Under Dynamic Anti-Plane Shearing
,”
Int. J. Solids Struct.
,
37
, pp.
5219
–
5231
.
17.
Narita
,
F.
, and
Shindo
,
Y.
,
1999
, “
Scattering of Antiplane Shear Waves by a Finite Crack in Piezoelectric Laminates
,”
Acta Mech.
,
134
, pp.
27
–
43
.
18.
Narayanan
,
G. V.
, and
Beskos
,
D. E.
,
1982
, “
Numerical Operational Methods for Time-Dependent Linear Problems
,”
Int. J. Numer. Methods Eng.
,
18
, pp.
1829
–
1854
.
19.
Durbin
,
F.
,
1974
, “
Numerical Inversion of Laplace Transforms: An Efficient Improvement to Duber and Abate’s Method
,”
Comput. J.
,
17
, pp.
371
–
376
.
20.
Miller
,
M. K.
, and
Guy
,
W. T.
,
1966
, “
Numerical Inversion of the Laplace Transform by Using Jocabi Polynomials
,”
SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal.
,
3
, pp.
624
–
635
.
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