The accuracy of probabilistic risk assessment of rotor disks is strongly dependent on the accurate description of the size and shape distributions of anomalies in alloys. These size-shape distributions of anomalies are often derived from planar sectioning data measurements using stereological unfolding algorithms. Since it is impossible to accurately predict the shape and orientation parameters of a general ellipsoid based on measurements obtained from two-dimensional sectioning data, the anomaly model should be limited to a spheroid. In this study, an unfolding algorithm was implemented and verified that can be used to estimate the probabilistic dimensions and orientations of 3D spheroids based on 2D section data. It is shown that the accuracy of the predicted spheroid model is dependent on the number of sections and the discretization of the mesh used to characterize the data.
Issue Section:
Gas Turbines: Structures and Dynamics
References
1.
National Transportation Safety Board
, 1990, “Aircraft Accident Report - United Airlines Flight 232 McDonnell Douglas DC-10-10 Sioux Gateway Airport, Sioux City, Iowa, July 19, 1989
,” Report No. NTSB/AAR-90/06
, National Transportation Safety Board
, Washington, DC
.2.
National Transportation Safety Board
, 1996, “Aircraft Accident Report – Uncontained Engine Failure, Delta Air Lines Flight 1288, McDonnell Douglas MD-88, N927DA
,” Report No. NTSB/AAR-98/01
, National Transportation Safety Board
, Washington, DC
.3.
Roth
, P. G.
, 1992, “Probabilistic Rotor Design System (PRDS) Phase I
,” Report No. WL-TR-92-2011, GE Aircraft Engines
.4.
Adamson
, J. D.
, Fox
, E. P.
, and Malone
, J. E.
, 1995, “Probabilistic Design System – Phase I and II Interim Report
,” Pratt & Whitney Report No. FR-24004-1.5.
Leverant
, G. R.
, Littlefield
, D. L.
, McClung
, R. C.
, Millwater
, H. R.
, and Wu
, Y -T.
, 1997, “A Probabilistic Approach to Aircraft Turbine Material Design
,” ASME Paper No. 97-GT-22.6.
Millwater
, H.
, Fitch
, S.
, Wu
, Y -T.
, Riha
, D.
, Enright
, M.
, Leverant
, G.
, McClung
, C.
, Kuhlman
, C.
, Chell
, G.
, and Lee
, Y.
, 2000, “A Probabilistically-Based Damage Tolerance Analysis Computer Program for Hard Alpha Anomalies in Titanium Rotors
,” ASME Paper No. 2000-GT-0421.7.
Leverant
, G. R.
, McClung
, R. C.
, Millwater
, H. R.
, and Enright
, M. P.
, 2003, “A New Tool for Design and Certification of Aircraft Turbine Rotors
,” ASME J. Eng. Gas Turbines Power
, 126
(1
), pp. 155
–159
.8.
McClung
, R. C.
, Enright
, M. P.
, Millwater
, H. R.
, Leverant
, G. R.
, and Hudak
, S.J.
, 2004, “A Software Framework for Probabilistic Fatigue Life Assessment
,” J. ASTM Int., 1
(8
), Paper No. JAI11563.9.
Southwest Research Institute
, 2010, DARWIN® User’s Guide
, Southwest Research Institute
, San Antonio, TX.
10.
Federal Aviation Administration
, 2001, “Advisory Circular - Damage Tolerance for High Energy Turbine Engine Rotors
,” Report No. AC 33.14-1
, U.S. Department of Transportation,
Washington, DC
.11.
Federal Aviation Administration
, 2009, “Advisory Circular - Guidance Material for Aircraft Engine Life-Limited Parts Requirements
,” Report No. AC 33.70-1
, U.S. Department of Transportation
, Washington, DC
.12.
Federal Aviation Administration
, 2009, “Advisory Circular - Damage Tolerance of Hole Features In High-Energy Turbine Engine Rotors
,” Report No. AC 33.70-2
, U.S. Department of Transportation
, Washington, DC
.13.
Wu
, Y.-T.
, Enright
, M. P.
, McClung
, R. C.
, Millwater
, H.
, and Leverant
, G. R.
, 2000, “Probabilistic Methods for Design Assessment of Reliability With Inspection
,” Proceedings, 41st Structures, Structural Dynamics, and Materials Conference, Atlanta, GA, April 3–6.14.
Enright
, M. P.
, and Wu
, Y.-T.
, 2000, “Probabilistic Fatigue Life Sensitivity Analysis of Titanium Rotors
,” Proceedings of the 41st Structures, Structural Dynamics, and Materials Conference, Atlanta, GA, April 3–6, AIAA Paper No. 2000-1647.15.
Wicksell
, S. D.
, 1925, “The Corpuscle Problem I: Case of Spherical Corpuscles
,” Biometrica
, 17
, pp. 84
–99
.16.
Wicksell
, S. D.
, 1926, “The Corpuscle Problem II: Case of Ellipsoidal Corpuscles
,” Biometrica
, 18
, pp. 151
–172
.17.
Moran
, P. A. P.
, 1972, “The Probabilistic Basis of Stereology
,” Suppl. Adv. Appl. Prob.
, 4
, pp. 69
.18.
Cruz-Orive
, L. M.
, 1976, “Particle Size-Shape Distributions: The General Spheroid Problem I: Mathematical Model
,” J. Microsc.
, 107
, pp. 235
–253
.19.
Cruz-Orive
, L. M.
, 1977, “Particle Size-Shape Distributions: The General Spheroid Problem II: Stochastic Model and Practical Guide
,” J. Microsc.
, 112
, pp. 153
–167
.20.
Hilliard
, J. E.
, and Lawson
, L. R.
, 2003, Stereology and Stochastic Geometry
, Kluwer Academic Publishers
, Norwell, MA
, pp. 308
–312
.21.
Saltykov
, S.
, 1967, “The Determination of the Size Distribution of Particles in an Opaque Material from a Measurement of the Size Distribution of Their Sections
,” Stereology, Proceedings of the Second International Congress for Stereology
, H.
Elias
, ed., Springer Verlag
, New York
, pp. 163
–167
.22.
Pope
, S. B.
, 2008, “Algorithms for Ellipsoids
,” Cornell University Report No. FDA 08-01, Cornell University, Ithaca, NY.23.
Ohser
, J.
, and Mücklich
, F.
, 2000, Statistical Analysis of Microstructures in Material Science
, John Wiley & Sons, LTD
, West Sussex, England
.24.
Ohser
, J.
, and Sandau
, K.
, 2000, “Considerations about the Estimation of the Size Distribution in Wicksell’s Corpuscle Problem
,” Statistical Physics and Spatial Statistics
, J.
Mecke
and D.
Stoyan
, eds., Springer-Verlag
, New York
, pp. 185
–202
.25.
Ghosn
, L. J.
, Kantzos
, P. T.
, Barrie
, R. L.
, and Bonacuse
, P. J.
, 2003, “Unfolding the Ceramic Inclusion Size Distribution in a Powder Metallurgy Alloy from Planar Sections
,” Materials Science and Technology 2003, Chicago, IL, November 11, 2003 (presentation only).Copyright © 2012
by American Society of Mechanical Engineers
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