Session: 14-06-01: Developments in Design Theory for Component and System Safety and Reliability

Paper Number: 114109

114109 - Uncertainty of Thermodynamic-Entropy-Based Reliability and Remaining Useful Life Predictions Under Variable Amplitude Fatigue 

Traditionally, engineers have used empirical relationships such as the modified Goodman relation and the Basquin equation to design for fatigue and Miner’s Rule to calculate reliability and to predict the remaining useful life (RUL) of structures subjected to fatigue.  Research has shown the viability of using thermodynamic entropy as an alternative to traditional empirical relationships for fatigue-related design, reliability calculation, and RUL prediction.  This entropy-based approach relies upon fatigue fracture entropy, a material property shown empirically to be connected with an entropy-based Miner’s Rule.

However, practical application of any approach demands that anything used for predictive purposes must account for uncertainty; otherwise, the predictions inherently carry a higher level of risk.  Miner’s Rule as traditionally employed contains a large degree of uncertainty; research has shown that the damage coefficient from Miner’s Rule often does not equal unity at the point of final fracture in a fatigue test specimen.  In addition, entropy-based formulations observed in the literature provide no such accounting.  This work provides an analytically derived formulation for uncertainty in entropy-derived, time-based reliability and RUL calculations.  To test the formulation, we obtained data from a Monte Carlo simulation in Microsoft Excel of an AISI 304 stainless steel rod subjected to variable amplitude fatigue at room temperature.  Constants for traditional empirical fatigue relationships as well as for entropy-derived relationships were taken from the literature.  In addition, the simulation accounts for the mean rise of internal temperature experienced by a test specimen subjected to fatigue loading.  Loading is fully reversed with a maximum stress level selected randomly from a uniform distribution bounded between zero and the ultimate tensile strength.  The amplitude stress for each applied load in the simulation is randomly selected from a uniform distribution bounded by the stress value which 10% below the fatigue limit and the maximum allowable stress back calculated from a randomly selected number of cycles to failure and the Basquin equation.

We used the data from this simulation to calculate time-based reliability using both entropy-derived and empirically derived formulations.  We applied this procedure with both a non-parametric and a parametric approach.  A minimum of 50 simulation runs were executed for each approach.  The results of this procedure show that the entropy-based calculations compare well with their traditional empirically derived counterparts within a certain range.  Using a non-parametric approach, the methods compare well for reliability values above 80%.  Using a parametric approach, the methods compare well for reliability values above 50%.  More investigation to improve the simulation as well as comparing against empirical fatigue tests are recommended.

Presenting Author: Lance Curtis University of Maryland

Presenting Author Biography: Mr. Curtis is a PhD student in the Reliability Engineering Program, Mechanical Engineering Department, at the University of Maryland College Park. He earned a BS in metallurgical engineering and a MS in mechanical engineering from the University of Idaho, after which he spent almost a decade in industry, working first as a materials/mechanical engineer and failure analyst for The M&P Lab (Schenectady, NY and Greenville, SC) and then as a reliability engineer for GE Energy in their natural gas turbine division (Greenville, SC and Seattle, WA). In addition to his research, he teaches engineering as an adjunct professor at Howard Community College (Columbia, MD).

Authors:

Lance R. Curtis University of Maryland
Bilal M. Ayyub University of Maryland