Abstract

A methodology for assessing structural reliability of railroad tank cars undergoing fatigue crack growth is being developed. A three-degree-of freedom (3-dof) surface crack is employed to account for an asymmetric stress field existing at a fatigue critical location in tank car structures. A fatigue life prediction program using the Walker equation to account for stress ratio effects is developed for the 3-dof surface crack model. A component reliability problem is formulated as a limit state function and solved using a first-order reliability method along with importance sampling method within the commercial reliability software, STRUREL. The methodology is demonstrated using illustrative railroad tank car examples. The results show that: (a) failure probability, Pf, increases as tank car mileage increases; (b) welding residual stresses in the tank structure can significantly increase Pf; (c) uncertainty in the stress amplitude also has a significant effect on Pf; and (d) the correlation between initial crack depth and initial crack aspect ratio is an important parameter.

References

1.
Cardinal
,
J. W.
,
McKeighan
,
P. C.
, and
Hudak
, ,
S. J.
 Jr.
, “
Damage Tolerance Analysis of Tank Car Stub Sill Cracking
,” Final Report, SwRI Project No. 06-6965,
1998
.
2.
Zhao
,
W.
,
Sutton
,
M. A.
,
Pena
,
J.
,
Hattery
,
B. K.
,
Wang
,
D. Q.
, and
Hubbard
,
C. R.
, “
Damage Tolerance Analysis of Railroad Tank Cars
,”
ASME Rail Transportation Division RTD
, Vol.
19
,
2000
, pp.
37
-
48
.
3.
Sutharshana
,
S.
,
Creager
,
M.
,
Ebbeler
,
D.
, and
Moore
,
N.
, “
A Probabilistic Fracture Mechanics Approach for Structural Reliability Assessment of Space Flight Systems
,” ASTM STP 1122,
M. R.
Mitchell
and
R. W.
Landgraf
, Eds.,
ASTM International
,
West Conshohocken, PA
,
1992
, pp.
234
-
246
.
4.
Manning
,
S. D.
,
Yang
,
J. N.
,
Pretzer
,
F. L.
, and
Marter
J. E.
, “
Reliability Centered Maintenance for Metallic Airframes Based on a Stochastic Crack Growth Approach
,” ASTM STP 1122,
M. R.
Mitchell
and
R. W.
Landgraf
, Eds.,
ASTM International
,
West Conshohocken, PA
,
1992
, pp.
422
-
434
.
5.
Harkness
,
H. H.
,
Belytschko
,
T.
, and
Liu
,
W. K.
, “
Finite Element Reliability Analysis of Fatigue Life
,”
Nuclear Engineering and Design
 0029-5493 https://doi.org/10.1016/0029-5493(92)90181-T
133
,
1992
, pp.
209
-
224
.
6.
Paris
,
P. C.
and
Erdogan
,
F.
, “
A Critical Analysis of Crack Propagation Laws
,”
Transactions of ASME, Journal of Basic Engineering
, Series D,
85
,
3
,
1963
, pp.
528
-
534
.
7.
Millwater
,
H. R.
,
Wu
,
Y. T.
, and
Cardinal
,
J. R.
, “
Probabilistic Structural Analysis of Fatigue and Fracture
,”
AIAA-94-1507-CP
.
8.
Tryon
,
R. G.
,
Cruse
,
T. A.
, and
Mahadevan
,
S.
, “
Development of a Reliability-Based Fatigue Life Model for Gas Turbine Engine Structures
,”
Engineering Fracture Mechanics
 0013-7944 
53
,
5
,
1996
, pp.
807
-
828
.
9.
Berens
,
A. P.
, “
Applications of Risk Analysis to Aging Military Aircraft
,”
41st International SAMPLE Symposium
, 24–28 March, 1996, pp.
99
-
107
.
10.
Cardinal
J. W.
and
Enright
,
M. P.
, “
Tank Car Stub Sill Damage Tolerance Analysis (DTA) Sensitivity Studies
,”
43rd Mechanical Working and Steel Processing Conference Proceedings
,
The Iron & Steel Society
,
Charlotte, NC
, 28–31 Oct., 2001, pp.
895
-
906
.
11.
Forman
,
R. G.
, et al
, “
Fatigue Crack Growth Computer Program NASGRO Version 3.0.5
,” JSC-22267B, NASA-JSC,
03
2000
.
12.
Riha
,
D. S.
,
Thacker
,
B. H.
,
Millwater
,
H. R.
,
Wu
,
Y. T.
, and
Enright
,
M. P.
, “
Probabilistic Engineering Analysis Using the NESSUS Software
,” AIAA-2000-1512.
13.
Zhao
,
W.
,
Newman
,
J. C.
, Jr.
, and
Sutton
,
M. A.
A Three-Dimensional Weight Function Method — Evaluation and Applications
,” ASTM STP 1296,
ASTM International
,
West Conshohocken, PA
,
1997
, pp.
563
-
579
.
14.
Zhao
,
W.
,
Sutton
,
M. A.
, and
Newman
,
J. C.
, Jr.
, “
K3D — A Program for Determining Stress Intensity Factors of Surface and Corner Cracks from a Hole
,” ASTM STP 1321,
ASTM International
,
West Conshohocken, PA
,
1997
, pp.
656
-
670
.
15.
Walker
,
E. K.
, “
Effects of Environments and Complex Load History on Fatigue Life
,” ASTM STP 462,
ASTM International
,
West Conshohocken, PA
,
1970
, pp.
1
-
14
.
16.
STRUREL
, “
A Structural Reliability Analysis Program System
,” URL: http://www.strurel.de, Reliability Consulting Programs, RCP GmbH,
2000
.
17.
Sutton
,
M. A.
and
Zhao
,
W.
, “
A Study of Load Spectrum Issues for Railroad Tank Cars
,”
43rd Mechanical Working and Steel Processing Conference Proceedings
,
The Iron & Steel Society
,
Charlotte, NC
, 28–31 Oct., 2001, pp.
863
-
872
.
18.
Sutton
,
M. A.
,
Abdelmajid
,
I.
,
Zhao
,
W.
,
Wang
,
D.
, and
Hubbard
,
C.
, “
Welds Characterization and Residual Stress Measurement for TC128-B Steel Plate
,”
ASME Journal of Pressure Vessel Technology
 0094-9930 https://doi.org/10.1115/1.1487878, Vol.
124
,
2002
, pp.
405
-
414
.
19.
Newman
,
J. C.
, Jr.
, “
FASTRAN-II — A Fatigue Crack Growth Structural Analysis Program
,” NASA TM-104159,
1992
.
20.
Suresh
,
S.
and
Ritchie
,
R. O.
, “
Mechanistic Dissimilarities Between Environmentally Influenced Fatigue-Crack Propagation at Near-Threshold and Higher Growth Rates in Lower Strength Steels
,”
Metal Science
 0306-3453 
16
,
1982
, pp.
529
-
538
.
21.
Hudak
, ,
S. J.
 Jr.
,
Burnside
,
O. H.
, and
Chan
,
K. S.
, “
Analysis of Corrosion Fatigue Crack Growth in Welded Tubular Joints
,”
Journal of Energy Resources Technology
 0195-0738, Transactions of the ASME, Vol.
107
,
06
1985
, pp.
212
-
219
.
22.
Rackwitz
,
R.
and
Fiessler
,
B.
, “
Structural Reliability Under Combined Random Load Sequences
,”
Computers and Structures
9
, No.
5
,
1978
, pp.
489
-
494
.
23.
Chen
,
X.
and
Lind
,
N. C.
, “
Fast Probability Integration by Three-Parameter Normal Tail Approximation
,”
Structural Safety
1
,
1983
, pp.
269
-
276
.
24.
Wu
,
Y. T.
and
Wirsching
,
P. H.
, “
A New Algorithm for Structural Reliability Estimation
,”
Journal of Engineering Mechanics
 0733-9399, ASCE,
113
,
9
,
1987
, pp.
1319
-
1336
.
25.
Der Kiureghian
,
A.
and
Liu
,
P. L.
, “
Structural Reliability Under Incomplete Probability Information
,”
Journal of Engineering Mechanics
 0733-9399, ASCE,
112
,
1
,
1986
, pp.
85
-
104
.
26.
Hohenbichler
,
M.
and
Rackwitz
,
R.
, “
Improvement of Second-Order Reliability Estimates by Importance Sampling
,”
Journal of Engineering Mechanics
 0733-9399, ASCE,
114
,
12
,
1988
, pp.
2195
-
2199
.
27.
Wu
,
X. R.
and
Carlsson
,
A. J.
, “
Weight Functions and Stress Intensity Factor Solutions
,”
Pergamon Press plc
,
1991
.
This content is only available via PDF.
You do not currently have access to this content.