Research Papers: Gas Turbines: Structures and Dynamics

A Robust Optimization Technique for Calculating Scaling Coefficients in an Energy-Based Fatigue Life Prediction Method

[+] Author and Article Information
Todd Letcher

e-mail: letcher.7@osu.edu

John Wertz

e-mail: wertz.46@osu.edu

M.-H. Herman Shen

e-mail: shen.1@osu.edu
Mechanical and Aerospace Engineering
The Ohio State University,
Building 148,
201 West 19th Avenue,
Columbus, OH 43210

Contributed by the Structures and Dynamics Committee of ASME for publication in the Journal of Engineering for Gas Turbines and Power. Manuscript received May 29, 2013; final manuscript received August 28, 2013; published online September 20, 2013. Editor: David Wisler.

J. Eng. Gas Turbines Power 135(12), 122502 (Sep 20, 2013) (7 pages) Paper No: GTP-13-1151; doi: 10.1115/1.4025315 History: Received May 29, 2013; Revised August 28, 2013

The energy-based lifing method is based on the theory that the cumulative energy in all hysteresis loops of a specimens' lifetime is equal to the energy in a monotonic tension test. Based on this theory, fatigue life can be calculated by dividing monotonic tensile energy by a hysteresis energy model, which is a function of stress amplitude. Due to variations in the empirically measured hysteresis loops and monotonic fracture area, fatigue life prediction with the energy-based method shows some variation as well. In order to account for these variations, a robust design optimization technique is employed. The robust optimization procedure uses an interval uncertainty technique, eliminating the need to know an exact probability density function for the uncertain parameters. The robust optimization framework ensures that the difference between the predicted lifetime at a given stress amplitude and the corresponding experimental fatigue data point is minimized and within a specified tolerance range while accounting for variations in hysteresis loop energy and fracture diameter measurements. Accounting for these experimental variations will boost confidence in the energy-based fatigue life prediction method despite a limited number of test specimens.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.


Stowell, E., 1966, “A Study of the Energy Criterion for Fatigue,” Nucl. Eng. Des., 3, pp. 32–40. [CrossRef]
Scott-Emuakpor, O., Shen, M.-H. H., George, T., and Cross, C., 2008, “An Energy-Based Uniaxial Fatigue Life Prediction Method for Commonly Used Gas Turbine Engines Materials,” ASME J. Eng. Gas Turbines Power, 130, pp. 1–15. [CrossRef]
Scott-Emuakpor, O., Shen, M.-H. H., George, T., and Cross, C., 2010, “Multi-Axial Fatigue-Life Prediction Via a Strain-Energy Method,” AIAA J., 48(1), pp. 63–72. [CrossRef]
Scott-Emuakpor, O., George, T., Cross, C., and Shen, M.-H. H., 2010, “Hysteresis Loop Representation for Strain Energy Calculation and Fatigue Assessment,” J. Strain Anal. Eng. Des., 45(4), pp. 275–282. [CrossRef]
Wertz, J., Letcher, T., Shen, M.-H. H., Scott-Emuakpor, O., George, T., and Cross, C., 2012, “An Energy-Based Axial Isothermal-Mechanical Fatigue Lifing Method,” ASME Paper No. GT2012-68889. [CrossRef]
Gunawan, G., and Azarm, S., 2004, “Non-Gradient Based Parameter Sensitivity Estimation for Single Objective Robust Design Optimization,” ASME J. Mech. Des., 126, pp. 395–402. [CrossRef]
American Society of Test and Materials, 2007, “ASTM E466: Standard Practice for Conducting Force Controlled Constant Amplitude Axial Fatigue Tests of Metallic Materials,” Book of Standards, Vol. 03.01, ASTM, West Conshohocken, PA.
Aerospace Material Specifications, 2008, “SAE AMS 2772-E: Heat Treatment of Aluminum Alloy Raw Materials,” SAE, Warrendale, PA.
American Society for Test and Materials, 2008, “ASTM B211-03-M: Standard Specification for Aluminum and Aluminum-Alloy Bar Rod and Wire,” Book of Standards, Vol. 02.02, ASTM, West Conshohocken, PA.
American Society for Test and Materials, 2008, “ASTM E8/E8M-08: Standard Test Methods for Tension Testing of Metallic Materials,” Book of Standards, Vol. 03.01, ASTM, West Conshohocken, PA.
MTS, 1998, TestStar IIs Software Manual, MTS Systems Corp., Eden Prairie, MN.
The MathWorks Inc., 2011, MATLAB Version2011a, MathWorks, Natick, MA.


Grahic Jump Location
Fig. 1

Hysteresis loop in generalized coordinates

Grahic Jump Location
Fig. 2

Scaling coefficients that produce 0.014 MJ/m3 at 227.5 MPa fatigue loading

Grahic Jump Location
Fig. 3

Fatigue life predictions using two sets of scaling coefficients

Grahic Jump Location
Fig. 4

Sensitivity region in Δp space

Grahic Jump Location
Fig. 5

Single objective robust optimization framework

Grahic Jump Location
Fig. 6

Specimen dimensions

Grahic Jump Location
Fig. 7

Typical monotonic specimen after fracture

Grahic Jump Location
Fig. 8

Difference in monotonic curves when using maximum and minimum fracture diameters

Grahic Jump Location
Fig. 9

Cyclic energy variation throughout fatigue life

Grahic Jump Location
Fig. 10

Minimum and maximum SN predictions based on variations in measured parameters

Grahic Jump Location
Fig. 11

Robust life prediction framework

Grahic Jump Location
Fig. 12

Fatigue life predictions using both MSE and robust techniques



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In