The problem of a point dislocation interacting with an elliptical hole located on a bimaterial interface is examined. Analytical solution is obtained by employing the techniques of complex variables and conformal mapping. A rational mapping function is used to map a half-plane with a semielliptical notch onto a unit circle. In the first part of this paper, complex potentials for the bimaterial system with an elliptical hole on the interface is derived when a point dislocation is present in the upper half-plane without loss of generality. The solution derived can be used as Green’s function to study internal cracks interacting with an elliptical interfacial cavity.

1.
Williams
,
M. L.
, 1959, “
The Stress Around a Fault or Crack in Dissimilar Media
,”
Bull. Seismol. Soc. Am.
0037-1106,
49
, pp.
199
204
.
2.
Rice
,
J. R.
, and
Sih
,
G. C.
, 1965, “
Plane Problems in Dissimilar Media
,”
J. Appl. Mech.
0021-8936,
32
, pp.
418
423
.
3.
England
,
A. H.
, 1965, “
A Crack Between Dissimilar Media
,”
J. Appl. Mech.
0021-8936,
32
, pp.
400
402
.
4.
Erdogan
,
F.
, 1965, “
Stress Distribution in Bonded Dissimilar Materials with Cracks
,”
J. Appl. Mech.
0021-8936,
32
, pp.
403
410
.
5.
Rice
,
J. R.
, 1988, “
Elastic Fracture Mechanics Concepts for Interfacial Cracks
,”
J. Appl. Mech.
0021-8936,
55
, pp.
98
103
.
6.
Comninou
,
M.
, 1977, “
The Interface Crack
,”
J. Appl. Mech.
0021-8936,
44
, pp.
631
636
.
7.
Comninou
,
M.
, 1990, “
An Overview of Interface Cracks
,”
Eng. Fract. Mech.
0013-7944,
37
, pp.
197
208
.
8.
Erdogan
,
F.
, 1970, “
Fracture Problems in Composite Materials
,”
Eng. Fract. Mech.
0013-7944,
4
, pp.
811
840
.
9.
Hutchinson
,
J. W.
,
Mear
,
M. E.
, and
Rice
,
J. R.
, 1987, “
Crack Paralleling an Interface Between Dissimilar Elastic Materials
,”
J. Appl. Mech.
0021-8936,
54
, pp.
828
832
.
10.
Murakami
,
Y.
,
et al.
, 1992,
Stress Intensity Factors Handbook
,
Elsevier Science
, New York.
11.
Oda
,
K.
,
Noda
,
N.
, and
Arita
,
S.
, 2003, “
Stress Intensity Factors for Interaction between Interface Crack and Internal Crack and for Kinked Interface Crack in Bonded Semi-Infinite Planes
,”
Key Eng. Mater.
1013-9826,
243–244
, pp.
375
380
.
12.
Hasebe
,
N.
,
Okumura
,
M.
, and
Nakamura
,
T.
, 1992, “
Bonded Bi-material Half-Planes With Semi-elliptical Notch Under Tension Along the Interface
,”
J. Appl. Mech.
0021-8936,
59
, pp.
77
83
.
13.
Okumura
,
M.
,
Hasebe
,
N.
, and
Nakamura
,
T.
, 1995, “
Bi-material Plane with Elliptic Hole under Uniform Tension Normal to the Interface
,”
Int. J. Fract.
0376-9429,
71
, pp.
293
310
.
14.
Hasebe
,
N.
, and
Inohara
,
S.
, 1980, “
Stress Analysis of a Semi-infinite Plate with an Oblique Edge Crack
,”
Ingenieurs
0020-1197,
49
, pp.
51
62
.
15.
Hasebe
,
N.
,
Qian
,
J.
, and
Chen
,
Y. Z.
, 1996, “
Fundamental Solutions for Half Plane with an Oblique Edge Crack
,”
Eng. Anal. Boundary Elem.
0955-7997,
17
, pp.
263
267
.
16.
Muskhelishvili
,
N. I.
, 1963,
Some Basic Problems of the Mathematical Theory of Elasticity
,
4th ed.
,
Noordhoff
, The Netherlands.
17.
Hasebe
,
N.
,
Irikura
,
H.
,
Nakamura
,
T.
, 1991, “
A Solution of the Mixed Boundary Value Problem for an Infinite Plate with a Hole under Uniform Heat Flux
,”
J. Appl. Mech.
0021-8936,
113
, pp.
996
1000
.
18.
Hasebe
,
N.
, and
Iida
,
J.
, 1978, “
A Crack Originating from a Triangular Notch on a Rim of a Semi-infinite Plate
,”
Eng. Fract. Mech.
0013-7944,
10
, pp.
773
782
.
You do not currently have access to this content.