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Research Papers: Gas Turbines: Structures and Dynamics

Estimating the Probabilistic Size and Shape Distributions of 3D Anomalies From Sectioning Measurements Using the Stereological Unfolding Approach

[+] Author and Article Information
Wuwei Liang, Michael P. Enright

 Southwest Research Institute® , San Antonio, TX 78238

J. Eng. Gas Turbines Power 134(5), 052506 (Feb 29, 2012) (7 pages) doi:10.1115/1.4004727 History: Received May 19, 2011; Revised May 19, 2011; Published February 29, 2012; Online February 29, 2012

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.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

General sphere and associated circular profile at a random planar section

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Figure 2

Probability density function of the radii of circular profiles f(r) generated by sectioning a sphere at random locations

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Figure 3

A unit volume with randomly placed spheres intersected by an arbitrary plane

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Figure 4

PDF of the radii of circular profiles associated with spheres of one or two deterministic radii (a) R/2, (b) R, and (c) combination of R/2 and R

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Figure 5

Bivariate histograms (stereograms) of anomaly size and shape parameters associated with anomalies in the fictitious material: (a) original population of spheroids, and (b) predicted population of spheroids based on sectioning data transformed using the Cruz-Orive unfolding algorithm

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Figure 6

Influence of the number of section plane measurements on predicted spheroid size parameter values: (a) 10 × 10 bin grid, and (b) 5 × 5 bin grid

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Figure 7

Influence of the number of section plane measurements on predicted spheroid shape parameter values: (a) 10 × 10 bin grid, and (b) 5 × 5 bin grid

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