Abstract

Probabilistic failure risk analysis is frequently used in the airworthiness area, while efficient stress intensity factor (SIF) solutions are vital in its process. Universal weight function (UWF) is a method that has remarkable computational efficiency and high accuracy in SIF calculation. However, the concrete coefficients in the UWF for different geometries remain unknown, which hinders the subsequent application of the method. This article focuses on general off-center embedded cracks. The response surface method is used to construct the UWF database. The accuracy of the database is confirmed by comparing it with existing literature and the finite element method, although large errors are identified to be inevitable for certain stress. Gaussian process regression is further adopted for better fitting, and the R-square is over 0.96. In addition, the effect of the offset distance on SIFs is discussed for embedded cracks in a given plate. Results show that SIF changes are dependent on the plate boundary in the uniform stress field, while stress predominates the SIF changes in nonuniform stress fields.

References

1.
Leverant
,
G. R.
,
Littlefield
,
D. L.
,
McClung
,
R. C.
,
Millwater
, H. R.
, and
Wu
, J. Y.
,
1997
, “
A Probabilistic Approach to Aircraft Turbine Rotor Material Design
,”
ASME
Paper No. 97-GT-022. 10.1115/97-GT-022
2.
McClung
,
R. C.
,
Leverant
,
G. R.
, and
Wu
,
Y. T.
,
1999
, “
Development of a Probabilistic Design System for Gas Turbine Rotor Integrity
,”
The Seventh International Fatigue Conference
, Beijing, China, June 8–12, pp.
4
5
.
3.
Advisory Circular,
2009
, “
Damage Tolerance of Hole Features in High-Energy Turbine Engine Rotors
,”
FAA
,
Washington, DC
, Paper No. 33.70-2.
4.
Paris
,
P. C.
,
Gomez
,
M. P.
, and
Anderson
,
W. E.
,
1961
, “
A Rational Analytic Theory of Fatigue
,”
Trend Eng.
,
13
, pp.
9
14
.
5.
Murakami
,
Y.
,
2002
,
Metal Fatigue: Effects of Small Defects and Nonmetallic Inclusions
,
Elsevier Ltd
.,
Oxford, UK
.
6.
Al Laham
,
S.
, and
Ainsworth
,
R. A.
,
1998
,
Stress Intensity Factor and Limit Load Handbook
,
British Energy Generation Ltd
.,
London
.
7.
Tada
,
H.
,
Paris
,
P. C.
, and
Irwin
,
G. R.
,
2000
,
The Stress Analysis of Cracks Handbook
, Vol.
34
,
Del Research Corporation
,
Hellertown, PA
.
8.
Tsai
,
C. H.
, and
Ma
,
C. C.
,
1989
, “
Weight Functions for Cracks in Finite Rectangular Plates
,”
Int. J. Fract.
,
40
(
1
), pp.
43
63
.10.1007/BF01150865
9.
Aliabadi
,
M. H.
,
Rooke
,
D. P.
, and
Cartwright
,
D. J.
,
1987
, “
An Improved Boundary Element Formulation for Calculating Stress Intensity Factors: Application to Aerospace Structures
,”
J. Strain Anal. Eng. Des.
,
22
(
4
), pp.
203
207
.10.1243/03093247V224203
10.
Gladwell
,
G. M. L.
,
2005
,
Fracture Mechanics
,
Democritus University of Thrace
,
Xanthi, Greece
, pp.
153
160
.
11.
Raju
,
I. S.
, and
Newman
,
J. C.
, Jr.
,
1977
, “Three-Dimensional Finite-Element Analysis of Finite-Thickness Fracture Specimens,” Langley Research Center, Hampton, VA, Report No. NASA TN D-8414.
12.
McClung
,
R. C.
,
Enright
,
M. P.
,
Lee
,
Y.-D.
,
Huyse
,
L. J.
, and
Fitch
,
S. H. K.
,
2004
, “
Efficient Fracture Design for Complex Turbine Engine Components
,”
ASME
Paper No. GT2004-53323.10.1115/GT2004-53323
13.
Raju
,
I. S.
, and
Newman
,
J. C.
, Jr.
,
1988
, “
Stress Intensity Factors for Corner Cracks in Rectangular Bars
,”
Fracture Mechanics: Nineteenth Symposium
,
ASTM STP
, Vol. 969,
Philadelphia, PA, Feb.,
pp.
43
55
.
14.
Bueckner
,
H. F.
,
1970
, “
A Novel Principle for the Amputation of Stress Intensity Factors
,”
Z. Angew. Math. Mech.
,
50
, pp.
529
546
.
15.
Rice
,
J.
,
1972
, “
Some Remarks on Elastic Crack-Tip Stress Fields
,”
Int. J. Solids Struct.
,
8
(
6
), pp.
751
758
.10.1016/0020-7683(72)90040-6
16.
Anderson
,
T. L.
,
2017
,
Fracture Mechanics: Fundamentals and Applications
,
CRC Press
,
Boca Raton, FL
.
17.
Glinka
,
G.
, and
Shen
,
G.
,
1991
, “
Universal Features of Weight Functions for Cracks in Mode I
,”
Eng. Fract. Mech.
,
40
(
6
), pp.
1135
1146
.10.1016/0013-7944(91)90177-3
18.
Millwater
,
H. R.
,
Fitch
,
S. H. K.
,
Wu
,
Y.-T.
,
Riha
,
D. S.
,
Enright
,
M. P.
,
Leverant
,
G. R.
,
McClung
,
R. C.
,
Kuhlman
,
C. J.
,
Chell
,
G. G.
, and
Lee
,
Y.-D.
,
2000
, “
A Probabilistically-Based Damage Tolerance Analysis Computer Program for Hard Alpha Anomalies in Titanium Rotors
,”
ASME
Paper No. 2000-GT-0421.10.1115/2000-GT-0421
19.
Shen
,
G.
, and
Glinka
,
G.
,
1991
, “
Determination of Weight Functions From Reference Stress Intensity Factors
,”
Theor. Appl. Fract. Mech.
,
15
(
3
), pp.
237
245
.10.1016/0167-8442(91)90022-C
20.
Dassault Systems
,
Abaqus theory Guide, Abaqus6.14 Documentation, 2.16.1
,
Dassault Systems
, Vélizy-Villacoublay, France.
21.
Montgomery
,
D. C.
,
2003
,
Design and Analysis of Experiments
,
Wiley
,
New York
.
22.
Myers
,
R. H.
,
Montgomery
,
D. C.
, and
Anderson-Cook
,
C. M.
,
2009
,
Response Surface Methodology: Process and Product Optimization Using Designed Experiments
,
Wiley
,
Hoboken, NJ
.
23.
Ebden
,
M.
,
2015
, “
Gaussian Processes for Regression and Classification: A Quick Introduction
,” arXiv preprint, arXiv: 1505.02965
24.
Patrick
,
D.
, and
Bruno
,
B.
,
2002
, “
Influence Coefficients to Calculate Stress Intensity Factors for an Elliptical Crack in a Plate
,”
ASME
Paper No. PVP2002-1335.10.1115/PVP2002-1335
25.
Wu
,
X.
,
2019
, “
A Review and Verification of Analytical Weight Function Methods in Fracture Mechanics
,”
Fatigue Fract. Eng. Mater. Struct.
,
42
(
9
), pp.
2017
2042
.10.1111/ffe.13073
26.
Mathworks
,
2019
,
Toolbox User's Guide
,
Mathworks
, Massachusetts, NA.
27.
Pan
,
J.
, and
Lin
,
S. H.
,
2005
, “
Fracture Mechanics and Fatigue Crack Propagation
,”
Fatigue Test. Anal.
,
12
(
1
), pp.
237
284
.
28.
Southwest Research Institute
,
2020
,
DARWIN 9.2 Theory
,
Southwest Research Institute
, San Antonio, TX.
You do not currently have access to this content.