The problem of a crack terminating at an interface between two materials which is governed by Coulomb’s law of friction is studied using Mellin integral transforms. Depending on the relative slip directions of the two wedges that are created by the crack, both the case of the two wedges moving in opposite directions and that of the two wedges moving in the same direction are treated. The characteristic equations which yield the order of the crack-tip singularity are obtained in terms of the Dundurs constants, the inclination of the crack and the coefficient of friction. For the special case when the crack is perpendicular to the interface and the two wedges slip in opposite directions, it is shown that the problem decouples into mode I (symmetric) and mode II (antisymmetric) cracks, and numerical results are presented for this case.

1.
Bogy
D. B.
,
1968
, “
Edge-Bonded Dissimilar Orthogonal Elastic Wedges Under Normal and Shear Loading
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
35
, pp.
460
466
.
2.
Bogy
D. B.
,
1971
, “
On the Plane Elastostatic Problem of a Loaded Crack Terminating at a Material Interface
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
38
, pp.
911
918
.
3.
Comninou
M.
,
1976
, “
Stress Singularity at a Sharp Edge in Contact Problems with Friction
,”
Journal of Applied Mathematics and Physics (ZAMP)
, Vol.
27
, pp.
493
499
.
4.
Dempsey
J. P.
, and
Sinclair
G. B.
,
1979
, “
On the Stress Singularities in the Plane Elasticity of the Composite Wedge
,”
Journal of Elasticity
, Vol.
9
, pp.
373
391
.
5.
Dempsey
J. P.
, and
Sinclair
G. B.
,
1981
, “
On the Singular Behavior at the Vertex of a Bi-Material Wedge
,”
Journal of Elasticity
, Vol.
11
, pp.
317
327
.
6.
Dundurs
J.
,
1969
,
discussion
,
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
36
, pp.
650
652
.
7.
Erdogan, F., Gupta, G. D., and Cook, T. S., 1973, “Numerical Solution of Singular Integral Equations,” Mechanics of Fracture I: Methods of Analysis and Solutions of Crack Problems, G. C. Sih, ed., Noordhoff, Leyden, pp. 368–425.
8.
Evans
A. G.
, and
Marshall
D. B.
,
1989
, “
The Mechanical Behavior of Ceramic Matrix Composites
,”
Acta Metallurgica
, Vol.
37
, pp.
2567
2583
.
9.
Gdoutos
E. E.
and
Theocaris
P. S.
,
1975
, “
Stress Concentrations at the Apex of a Plane Indenter Acting on an Elastic Half Plane
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
42
, pp.
688
692
.
10.
Gharpuray
V. M.
,
Dundurs
J.
, and
Keer
L. M.
,
1991
, “
A Crack Terminating at a Slipping Interface Between Two Materials
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
58
, pp.
960
963
.
11.
Hill
R.
,
1964
, “
Theory of Mechanical Properties of Fiber-Strengthened Materials: I. Elastic Behaviour
,”
Journal of the Mechanics and Physics of Solids
, Vol.
12
, pp.
213
218
.
12.
Lee, J.-W., and Daniel, I. M., 1992, “Deformation and Failure of Longitudinally Loaded Brittle-Matrix Composites,” Composite Materials: Testing and Design, C. M. Glenn, ed., ASTM-STP 1120, pp. 204–221.
13.
Muskhelishvili, N. I., 1953, Singular Integral Equations, Noordhoff, Groningen, Holland.
14.
Wijeyewickrema
A. C.
,
Keer
L. M.
,
Hirashima
K.
, and
Mura
T.
,
1991
, “
The Annular Crack Surrounding an Elastic Fiber in a Tension Field
,”
International Journal of Solids and Structures
, Vol.
27
, pp.
315
328
.
15.
Wijeyewickrema
A. C.
, and
Keer
L. M.
,
1993
, “
Matrix Cracking in a Fiber-Reinforced Composite with Slip at the Fiber-Matrix Interface
,”
International Journal of Solids and Structures
, Vol.
30
, pp.
91
113
.
16.
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.