Using a body force method and the finite-part integral concepts, a set of hypersingular integral equations for a vertical crack terminating at an interface in a three-dimensional infinite bimaterial subjected to arbitrary loads are derived. The stress singularity orders and singular stress fields around the crack front terminating at the interface are obtained by the main-part analytical method of hypersingular integral equations. Then, a numerical method for the solution of the hypersingular integral equations in case of a rectangular crack is proposed, in which the crack displacement discontinuities are approximated by the product of basic density functions and polynomials. Numerical solutions for the stress intensity factors of some examples are given.

Issue Section:
Technical Papers
Keywords:
interface phenomena, crack-edge stress field analysis, integral equations
Topics:
Fracture (Materials), Integral equations, Stress
1.
Cook
,
T. S.
, and
Erdogan
,
F.
,
1972
, “
Stresses in Bonded Materials With a Crack Perpendicular to the Interface
,”
Int. J. Solids Struct.
,
10
, pp.
677
–
697
.
2.
Erdogan
,
F.
, and
Cook
,
T. S.
,
1974
, “
Antiplane Shear Crack Terminating at and Going Through a Bimaterial Interface
,”
Int. J. Fract.
,
10
, pp.
227
–
240
.
3.
Lee
,
J. C.
, and
Keer
,
L. M.
,
1986
, “
Study of a Three-Dimensional Crack Terminating at an Interface
,”
ASME J. Appl. Mech.
,
53
, pp.
311
–
316
.
4.
Chen
,
D. H.
, and
Nisitani
,
H.
,
1993
, “
Stress Intensity Factors of a Crack Meeting the Bimaterial Interface
,”
Trans. Jpn. Soc. Mech. Eng., Ser. A
,
59
, pp.
47
–
53
(in Japanese).
5.
Xu
,
G.
, and
Ortiz
,
M.
,
1993
, “
A Variational Boundary Integral Method for the Analysis of 3-D Cracks of Arbitrary Geometry Modeled as Continuous Distributions of Dislocation Loops
,”
Int. J. Numer. Methods Eng.
,
36
, pp.
3675
–
3701
.
6.
Xu
,
Y.
,
Moran
,
B.
, and
Belytschko
,
T.
,
1997
, “
Self-Similar Crack Expansion Method for Three-Dimensional Crack Analysis
,”
ASME J. Appl. Mech.
,
64
, pp.
729
–
737
.
7.
Guo
,
Q.
, and
Wang
,
J.-J.
, et al.,
1995
, “
Elastic Analyses of Planar Cracks Arbitrary Shape
,”
ASME J. Appl. Mech.
,
62
, pp.
108
–
115
.
8.
Dai
,
D. N.
,
Hills
,
D. A.
, and
Nowell
,
D. N.
,
1997
, “
Modeling of Growth of Three-Dimensional Cracks by a Continuous Distribution of Dislocation Loops
,”
Computational Mech., Berlin
,
19
, pp.
538
–
544
.
9.
Noda
,
N. A.
,
Kobayashi
,
K.
, and
Yagishita
,
M.
,
1999
, “
Variation of Mixed Modes Stress Intensity Factors of an Inclined Semi-Elliptical Surface Cracks
,”
Int. J. Fract.
,
100
, pp.
207
–
225
.
10.
Wang
,
Q.
, et al.,
2000
, “
Solution of the Distribution of Stress Intensity Factor Along the Front of a 3D Rectangular Crack by Using a Singular Integral Equation Method
,”
Trans. Jpn. Soc. Mech. Eng., Ser. A
,
66
(
650
), pp.
1922
–
1927
(in Japanese).
11.
Chen
,
M. C.
, and
Tang
,
R. J.
,
1997
, “
An Explicit Tensor Expression for the Fundamental Solutions of a Bimaterial Space Problem
,”
Appl. Math. Mech.
,
18
(
4
), pp.
331
–
340
.
12.
Erdogan F., 1978, “Mixed Boundary Value Problems,” Mechanics Today, S. Nemat-Nasser ed., Pergamon Press, New York, 4, pp. 1–86.
13.
Tang
,
R. J.
, and
Qin
,
T. Y.
,
1993
, “
Method of Hypersingular Integral Equations in Three-Dimensional Fracture Mechanics
,”
Acta Mech. Sin.
,
25
, pp.
665
–
675
.
14.
Qin
,
T. Y.
, and
Tang
,
R. J.
,
1993
, “
Finite-Part Integral and Boundary Element Method to Solve Embedded Planar Crack Problems
,”
Int. J. Fract.
,
60
, pp.
191
–
202
.
15.
Noda, N. A., and Wang, Q., 2000, “Application of Body Force Method to Fracture and Interface Mechanics of Composites,” Research Report of the JSPS Postdoctoral Fellowship for Foreign Researchers, No. 98187.
16.
Isida
,
M.
,
Yoshida
,
T.
, and
Noguchi
,
H.
,
1991
, “
A Rectangular Crack in an Infinite Solid, a Semi-Infinite Solid and a Finite-Thickness Plate Subjected to Tension
,”
Int. J. Fract.
,
52
, pp.
79
–
90
.  
Copyright © 2002
 by ASME
You do not currently have access to this content.