An exact elastic solution is derived in a decoupled manner for the interaction problem between an edge dislocation and a three-phase circular inclusion with circumferentially homogeneous sliding interface. In the three-phase composite cylinder model, the inner inclusion and the intermediate matrix phase form a circumferentially homogeneous sliding interface, while the matrix and the outer composite phase form a perfect interface. An edge dislocation acts at an arbitrary point in the intermediate matrix. This three-phase cylinder model can simultaneously take into account the damage taking place in the circumferential direction at the inclusion-matrix interface and the interaction effect between the inclusions. As an application, we then investigate a crack interacting with the slipping interface.

Issue Section:
Technical Papers
Keywords:
edge dislocations, inclusions, composite materials, composite material interfaces, cracks
Topics:
Boundary-value problems, Composite materials, Cylinders, Dislocations, Fracture (Materials), Stress, Damage
1.
Christensen
,
R. M.
, and
Lo
,
K. H.
,
1979
, “
Solution for Effective Shear Properties in Three Phase Sphere and Cylinder Models
,”
J. Mech. Phys. Solids
,
27
, pp.
315
–
330
.
2.
Luo
,
H. A.
, and
Chen
,
Y.
,
1991
, “
An Edge Dislocation in a Three-Phase Composite Cylinder Model
,”
ASME J. Appl. Mech.
,
58
, pp.
75
–
86
.
3.
Qaissaunee
,
M. T.
, and
Santare
,
M. H.
,
1995
, “
Edge Dislocation Interacting With an Elliptical Inclusion Surrounded by an Interfacial Zone
,”
Q. J. Mech. Appl. Math.
,
48
, pp.
465
–
482
.
4.
Ru
,
C. Q.
,
1999
, “
Three-Phase Elliptical Inclusions with Internal Uniform Hydrostatic Stresses
,”
J. Mech. Phys. Solids
,
47
, pp.
259
–
273
.
5.
Xiao
,
Z. M.
, and
Chen
,
B. J.
,
2000
, “
A Screw Dislocation Interacting With a Coated Fiber
,”
Mech. Mater.
,
32
, pp.
485
–
494
.
6.
Xiao
,
Z. M.
, and
Chen
,
B. J.
,
2001
, “
On the Interaction Between an Edge Dislocation and a Coated Inclusion
,”
Int. J. Solids Struct.
,
38
, pp.
2533
–
2548
.
7.
Ru
,
C. Q.
,
1999
, “
A New Method for an Inhomogeneity With Stepwise Graded Interphase Under Thermomechanical Loadings
,”
J. Elast.
,
56
, pp.
107
–
127
.
8.
Dundurs
,
J.
, and
Gangadharan
,
A. C.
,
1969
, “
Edge Dislocation Near an Inclusion With a Slipping Interface
,”
J. Mech. Phys. Solids
,
17
, pp.
459
–
471
.
9.
Mura
,
T.
, and
Furuhashi
,
R.
,
1984
, “
The Elastic Inclusion With a Sliding Interface
,”
ASME J. Appl. Mech.
,
51
, pp.
308
–
310
.
10.
Mura
,
T.
,
Jasiuk
,
I.
, and
Tsuchida
,
E.
,
1985
, “
The Stress Field of a Sliding Inclusion
,”
Int. J. Solids Struct.
,
21
, pp.
1165
–
1179
.
11.
Jasiuk
,
I.
,
Tsuchida
,
E.
, and
Mura
,
T.
,
1987
, “
The Sliding Inclusion Under Shear
,”
Int. J. Solids Struct.
,
23
, pp.
1373
–
1385
.
12.
Lee
,
M.
,
Jasiuk
,
I.
, and
Tsuchida
,
E.
,
1992
, “
The Sliding Circular Inclusion in an Elastic Half-Space
,”
ASME J. Appl. Mech.
,
59
, pp.
57
–
64
.
13.
Gharpuray
,
V. M.
,
Dundurs
,
J.
, and
Keer
,
L. M.
,
1991
, “
A Crack Terminating at a Slipping Interface Between Two Materials
,”
ASME J. Appl. Mech.
,
58
, pp.
960
–
963
.
14.
Ru
,
C. Q.
,
1998
, “
A Circular Inclusion With Circumferentially Inhomogeneous Sliding Interface in Plane Elastostatics
,”
ASME J. Appl. Mech.
,
65
, pp.
30
–
38
.
15.
Lubarda
,
V. A.
, and
Markenscoff
,
X.
,
1999
, “
Energies of Circular Inclusions: Sliding Versus Bonded Interfaces
,”
Proc. R. Soc. London, Ser. A
,
455
, pp.
961
–
974
.
16.
Muskhelishvili, N. I., 1953, Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, Groningen.
17.
England, A. H., 1971, Complex Variable Method in Elasticity, John Wiley and Sons, New York.
18.
Honein
,
T.
, and
Herrmann
,
G.
,
1990
, “
On Bonded Inclusions With Circular or Straight Boundaries in Plane Elastostatics
,”
ASME J. Appl. Mech.
,
57
, pp.
850
–
856
.
19.
Worden
,
R. E.
, and
Keer
,
L. M.
,
1991
, “
Green’s Functions for a Point Load and Dislocation in an Annular Region
,”
ASME J. Appl. Mech.
,
58
, pp.
954
–
959
.
20.
Chao
,
C. K.
, and
Tan
,
C. J.
,
2000
, “
On the General Solution for Annular Problems With a Point Heat Source
,”
ASME J. Appl. Mech.
,
67
, pp.
511
–
518
.
21.
Erdogan
,
F.
, and
Gupta
,
G. D.
,
1972
, “
On the Numerical Solution of Singular Integral Equations
,”
Q. Appl. Math.
,
29
, pp.
525
–
534
.
22.
Erdogan
,
F.
,
Gupta
,
G. D.
, and
Ratwani
,
M.
,
1974
, “
Interaction Between a Circular Inclusion and an Arbitrarily Oriented Crack
,”
ASME J. Appl. Mech.
,
41
, pp.
1007
–
1013
.
23.
Luo
,
H. A.
, and
Chen
,
Y.
,
1991
, “
Matrix Cracking in Fiber-Reinforced Composite Materials
,”
ASME J. Appl. Mech.
,
58
, pp.
846
–
848
.
Copyright © 2002
 by ASME
You do not currently have access to this content.