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
.Copyright © 2005
by American Society of Mechanical Engineers
You do not currently have access to this content.
