For a sharp notch with curved edges and subjected to surface tractions along the edges, the fracture parameters (in particular, the stress intensity factors and the size of a singular-dominant zone) are significantly affected by the near-tip geometric and loading conditions. In this paper, a pair of contour integrals termed $JkR$ is presented for calculating the mixed-mode stress intensity factors at such a sharp notch-tip. Furthermore, by proper use of the integrals, the extent of the singular-dominant zone can be effectively characterized. Since no a priori auxiliary (or, complementary) solutions are required in its formulation, the approach appears to be feasible for problems of arbitrary notch angles and curved shapes. Also, no special treatments are required for the modeling of the near-tip singular behavior so that the integration can be performed by direct use of numerical schemes such as finite element method.

1.
Williams
,
M. L.
, 1952, “
Stress Singularities Resulting From Various Boundary Conditions in Angular Corners of Plates in Extension
,”
ASME J. Appl. Mech.
,
19
, pp.
526
528
. 0021-8936
2.
Bogy
,
D. B.
, 1972, “
The Plane Solution for Anisotropic Elastic Wedges Under Normal and Shear Loading
,”
ASME J. Appl. Mech.
,
39
, pp.
1103
1109
. 0021-8936
3.
Awaji
,
H.
,
Toshimitsu
,
Y. A.
, and
Yokobori
,
T.
, 1986, “
The Variation of the Stress Singularity at the Notch Tip as Notch Angle and Radius of Curvature
,”
Compos. Struct.
,
22
(
1
), pp.
25
30
. 0263-8223
4.
Peng
,
X.
, 1986, “
On Stress Singularities at Tips of Plane Notches
,”
Mech. Res. Commun.
,
13
, pp.
173
178
. 0093-6413
5.
Carpenter
,
W. C.
, 1984, “
Calculation of Fracture Parameters for a General Corner
,”
Int. J. Fract.
0376-9429,
24
, pp.
45
58
.
6.
Sinclair
,
G. B.
,
Okajima
,
M.
, and
Griffin
,
J. H.
, 1984, “
Path Independent Integrals for Computing Stress Intensity Factors at Sharp Corners in Elastic Plates
,”
Int. J. Numer. Methods Eng.
0029-5981,
20
, pp.
999
1008
.
7.
Babuska
,
I.
, and
Miller
,
A.
, 1984, “
The Post-Processing Approach in the Finite Element Method, Part 2: The Calculation of Stress Intensity Factors
,”
Int. J. Numer. Methods Eng.
0029-5981,
20
, pp.
1111
1129
.
8.
Labossiere
,
P. E. W.
, and
Dunn
,
M. L.
, 1998, “
Calculation of Stress Intensities at Sharp Notches in Anisotropic Media
,”
Eng. Fract. Mech.
0013-7944,
61
, pp.
635
654
.
9.
Chang
,
J. H.
, and
Kang
,
L. K.
, 2002, “
Evaluation of the Stress Field Around a Notch Tip Using Contour Integrals
,”
Int. J. Eng. Sci.
,
40
, pp.
569
586
. 0020-7225
10.
Sih
,
G. C.
,
Paris
,
P. C.
, and
Erdogan
,
F.
, 1962, “
Crack Tip, Stress Intensity Factors for Plane Extension and Plate Bending Problems
,”
ASME J. Appl. Mech.
,
29
, pp.
306
312
. 0021-8936
11.
Dreilich
,
L.
, and
Gross
,
D.
, 1985, “
The Curved Crack
,”
Z. Angew. Math. Mech.
,
65
, pp.
132
134
. 0044-2267
12.
Chen
,
Y. Z.
, 2004, “
Singular Integral Equation Method for the Solution of Multiple Curved Crack Problems
,”
Int. J. Solids Struct.
,
41
, pp.
3505
3519
. 0020-7683
13.
Chang
,
J. H.
, 1994, “
On the Calculation of Energy Release Rate for Curved Cracks of Rubbery Materials
,”
Finite Elem. Anal. Design
,
17
, pp.
323
338
. 0168-874X
14.
Beom
,
H. G.
,
Earmme
,
Y. Y.
, and
Choi
,
S. Y.
, 1994, “
Energy Release Rates for an Arbitrarily Curved Interface Crack
,”
Mech. Mater.
,
18
, pp.
195
204
. 0167-6636
15.
Lorentzon
,
M.
, and
Eriksson
,
K.
, 2000, “
A Path Independent Integral for the Crack Extension Force of the Circular Arc Crack
,”
Eng. Fract. Mech.
,
66
, pp.
423
439
. 0013-7944
16.
Rice
,
J. R.
, 1968, “
Mathematical Analysis in the Mechanics of Fracuture
,”
Fracture
, Vol.
2
,
H.
Liebowitz
, ed.,
,
New York
, pp.
191
213
.
17.
Eshelby
,
J. D.
, 1974, “
Calculation of Energy Release Rate
,”
Prospects of Fracture Mechanics
,
G. C.
Sih
,
H. C.
Van Elst
, and
D.
Broek
, eds.,
Noordhoff
,
Groningen
, pp.
69
84
.
18.
Chen
,
Y. H.
, and
Lu
,
T. J.
, 2004, “
On the Path Dependence of the J-Integral in Notch Problems
,”
Int. J. Solids Struct.
,
41
, pp.
607
618
. 0020-7683
19.
Zhang
,
Z.
, and
Suo
,
Z.
, 2007, “
Split Singularities and the Competition Between Crack Penetration and Debond at a Bimaterial Interface
,”
Int. J. Solids Struct.
0020-7683,
44
, pp.
4559
4573
.