Abstract

One of the difficulties in using fracture mechanics is in determining stress intensity factors of cracked structural and mechanical components. The cracks are often subjected to complex stress fields induced by external loads and residual stresses resulting from the surface treatment. Both stress fields are characterized by non-uniform distributions, and handbook stress intensity factor solutions are seldom available in such cases. The method presented below is based on the generalized weight function technique enabling the stress intensity factors to be calculated for any Mode I loading applied to a planar semi-elliptical surface crack. The stress intensity factor can be determined at any point on the crack tip contour by using the general weight function. The calculation is carried out by integrating the product of the stress field and the weight function over the crack area.

Several examples of point-load weight functions and resulting stress intensity factors are presented in the paper. The method is particularly suitable for modeling fatigue crack growth in the presence of complex stress fields.

Issue Section:
Research Papers
Keywords:
stress intensity factor, weight function, nonlinear stress field

References

1.
Bueckner
,
H. F.
, “
A Novel Principle for the Computation of Stress Intensity Factors
,”
Zeitschrift fur Angewandte Mathematik Und Mechanik
, Vol.
50
,
1970
, pp.
529
-
546
.
2.
Rice
,
J. R.
, “
Some Remarks on Elastic Crack-Tip Stress Field
,”
International Journal of Solids and Structures
 0020-7683 https://doi.org/10.1016/0020-7683(72)90040-6, Vol.
8
,
1972
, pp.
751
-
758
.
Google Scholar
Crossref
Search ADS
 
3.
Tada
,
H.
,
Paris
,
P.
, and
Irwin
,
G.
,
The Stress Analysis of Cracks Handbook
, 2nd ed.,
Paris Production Inc.
,
1985
,
St. Louis, MO
.
4.
Wu
,
X. R.
 and
Carlsson
,
A. J.
,
Weight Functions and Stress Intensity Factor Solutions
,
1991
,
Pergamon Press
,
Oxford, UK
.
5.
Fett
,
T.
 and
Munz
,
D.
, “
Stress Intensity Factors and Weight Functions for One-Dimensional Cracks
,” Report No. KfK 5290, Kernforschungszentrum Karlsruhe, Institut fur Materialforschung, December, 1994, Karlsruhe, Germany.
6.
Glinka
,
G.
 and
Shen
,
G.
, “
Universal Features of Weight Functions for Cracks in Model I
,”
Engineering Fracture Mechanics
 0013-7944 https://doi.org/10.1016/0013-7944(91)90177-3, Vol.
40
, No.
6
,
1991
, pp.
1135
-
1146
.
Google Scholar
Crossref
Search ADS
 
7.
Shen
,
G.
 and
Glinka
 
G.
, “
Determination of Weight Functions from Reference Stress Intensity Factors
,”
Theoretical and Applied Fracture Mechanics
 0167-8442 https://doi.org/10.1016/0167-8442(91)90022-C, Vol.
15
, No.
2
,
1991
, pp.
237
-
245
.
8.
Shen
,
G.
 and
Glinka
 
G.
, “
Weight Functions for a Surface Semi-Elliptical Crack in a Finite Thickness Plate
,”
Theoretical and Applied Fracture Mechanics
 0167-8442 https://doi.org/10.1016/0167-8442(91)90023-D, Vol.
15
, No.
2
,
1991
, pp.
247
-
255
.
9.
Zheng
,
X. J.
,
Glinka
,
G.
, and
Dubey
,
R.
, “
Calculation of Stress Intensity Factors for Semi-Elliptical Surface Cracks in a Thick-Wall Cylinder
,”
International Journal of Pressure Vessels and Piping
 0308-0161 https://doi.org/10.1016/0308-0161(94)00017-D, Vol.
62
,
1995
, pp.
249
-
258
.
Google Scholar
Crossref
Search ADS
 
10.
Newman
,
J. C.
,
Raju
,
I. S.
, “
Stress-Intensity Factor Equations for Cracks in Three-Dimensional Finite Bodies Subjected to Tension and Bending Loads
,”
NASA Technical Memorandum
 85793,
NASA Langley Research Center
,
Hampton, VA
,
1989
.
11.
Lena
 
Nilsson
,
SAQ/FoU-Report 98/10, Stress Intensity Factors for Half-Elliptical Surface Cracks in Plates Subjected to a Complex Stress Field
, ISSN 1401-5331.
12.
Rice
,
J.
, “
Weight Function Theory for Three-Dimensional Elastic Crack Analysis
,”
Fracture Mechanics Perspectives and Directions (20th Symposium)
, ASTM STP 1020,
ASTM International
,
West Conshohocken, PA
,
1989
, pp.
29
-
57
.
13.
Oore
,
M.
 and
Burns
,
D. J.
, “
Estimation of Stress Intensity Factors for Embedded Irregular Cracks Subjected to Arbitrary Normal Stress Fields
,”
Journal of Pressure Vessel Technology, ASME
, Vol.
102
,
1980
, pp.
201
-
211
.
Google Scholar
Crossref
Search ADS
 
14.
Glinka
,
G.
 and
Reinhardt
,
W.
, “
Calculation of Stress Intensity Factors for Cracks of Complex Geometry and Subjected to Arbitrary Nonlinear Stress Fields
,”
Fatigue and Fracture Mechanics
, Vol.
31
, ASTM STP 1389,
G. R.
 
Halford
 and
J. P.
 
Gallagher
, Eds.,
ASTM International
,
West Conshohocken, PA
,
2000
, pp.
348
-
370
15.
Murakami
,
Y.
,
Stress Intensity Factors Handbook
, Vol.
2
,
1987
,
Pergamon Press
,
Oxford
.
This content is only available via PDF.
All rights reserved. This material may not be reproduced or copied, in whole or in part, in any printed, mechanical, electronic, film, or other distribution and storage media, without the written consent of ASTM International.
You do not currently have access to this content.