This paper deals with linear elastic fracture problems for a planar crack on an interface between two dissimilar elastic half-space solids bonded together. The finite-part integral concept is used to derive hypersingular integro-differential equations for the interfacial crack from the point-force solutions for a bimaterial space. Investigations on the singularities and the singular stress fields in the vicinity of the crack are made by the dominant-part analysis of the two-dimensional hypersingular integrals. Thereafter the stress intensity factor K-fields and the energy release rate G are exactly obtained by using the definitions of stress intensity factors and the principle of virtual work, respectively. The results show that, unlike the homogenous case, the asymptotic fields always consist of all three modes of fracture. Finally, some numerical examples of various aspects of elliptical cracks subjected to constant pressures are given.

1.
Brebbia, C. A., 1981, Progress in Boundary Element Methods, Vol. 1, Pentech Press, London.
2.
Chen, M.-C., 1997, “A Hypersingular Integral Equation Method of Three-Dimensional Crack Problems Near and on an Interface of Bimaterials,” Ph.D dissertation, Shanghai Jiao Tong University, Shanghai, P.R. China.
3.
Chen
 
M.-C.
, and
Tang
 
R.-J.
,
1997
, “
An Explicit Tensor Expressions of Fundamental Solutions of a Space Problem of Bimaterials
,”
Chinese Appl. Math. Mech.
, Vol.
18
, pp.
331
340
.
4.
Erdogan
 
F.
, and
Arin
 
K.
,
1972
, “
Penny-Shaped Interface Crack Between an Elastic Layer and a Half-space
,”
Int. J. Solids Struct.
, Vol.
8
, pp.
93
109
.
5.
Hadamard, J., 1952, Lectures on Cauchy's Problem in Linear Partial Differential Equations, Dover, New York.
6.
Hutchinson
 
J. W.
,
Mear
 
M. E.
, and
Rice
 
J. R.
,
1987
, “
Crack Paralleling an Interface Between Dissimilar Materials
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
54
, pp.
828
832
.
7.
Kassir
 
M. K.
, and
Bregman
 
A. M.
,
1972
, “
The Stress Intensity Factor for a Penny-Shaped Crack Between Two Dissimilar Materials
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
39
, pp.
308
301
.
8.
Nakamura
 
T.
,
1991
, “
Three-Dimensional Stress Fields of Elastic Interface Cracks
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
58
, pp.
939
946
.
9.
Parton, V. Z., and Perlin, P. I., 1984, Mathematical Methods of the Theory of Elasticity, Moscow.
10.
Qin
 
T.-Y.
, and
Tang
 
R.-J.
,
1993
, “
Finite-Pan Integral and Boundary Element Method to Solve Embedded Planar Crack Problems
,”
Int. J. Fracture
, Vol.
60
, pp.
373
381
.
11.
Rice
 
J. R.
,
1988
, “
Elastic Fracture Mechanics Concepts for Interfacial Cracks
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
55
, pp.
98
103
.
12.
Shibuya
 
T.
, et al.,
1989
, “
Stress Analysis of the Vicinity of an Elliptical Crack at the Interface of Two Bounded Half-Spaces
,”
JSME Int. J.
, Vol.
32
, pp.
485
491
.
13.
Takakuda
 
K.
,
Koizumi
 
T.
, and
Shibuya
 
T.
,
1985
, “
On Integral Equation Methods for Cracks
,”
Bulletin of JSME
, Vol.
28
, pp.
217
224
.
14.
Tang
 
R.-J.
, and
Qin
 
T.-Y.
,
1993
, “
A Hypersingular Integral Method for Three-Dimensional Crack Problems
,”
Acta Mechanica Sinica
, Vol.
25
, pp.
665
675
.
15.
Williams
 
M. L.
,
1959
, “
The Stresses Around a Fault or Crack in Dissimilar Media
,”
Bull. Seis. Soc. America
, Vol.
49
, pp.
199
204
.
16.
Willis
 
J. R.
,
1972
, “
The Penny-Shaped Crack on an Interface
,”
Q. J. Mech. & Appl. Math.
, Vol.
25
, pp.
367
385
.
17.
Yuuki
 
R.
, and
Xu
 
J.-Q.
,
1992
, “
A BEM Analysis of a Three-Dimensional Interfacial Crack of Bimaterials
,”
Transactions of JSME
, Series A Vol.
58
, No.
545
, pp.
19
46
(in Japanese).
18.
Zak
 
A. R.
, and
Williams
 
M. L.
,
1963
, “
Crack Point Stress Singularities at a Bimaterial Interface
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
30
, pp.
142
143
.
This content is only available via PDF.
You do not currently have access to this content.