Probabilistic Fatigue Life Sensitivity Analysis of Titanium Rotors

The application of probabilistic methods to the life prediction of fatigue vulnerable structures is becoming increasingly important. In-service inspection and repair/replacement can be an effective strategy for decreasing fatigue failure probability. However, inspection introduces additional random variables that must be considered in an overall lifetime reliability assessment. In this study, a methodology is illustrated to assess the influences of changes in the main descriptors of fatigue related random variables on the lifetime failure probability of an aircraft titanium rotor disk. The methodologies can be used for the development of reliability-based optimal design and maintenance strategies for fatigue vulnerable structures subject to in-service inspection. Introduction The need for the use of non-deterministic methods for fatigue life predictions is becoming increasingly important. Variabilities in fatigue strength data and in the relationship between stress range and fatigue life for a given material can be significant. A probabilistic fatigue evaluation can take into account these and other uncertainties associated with fatigue failure of structures and mechanical components. Design-Assessment-of-Reliability-With-Inspection (DARWIN*) is a computer program that integrates finite element stress analysis, fracture mechanics analysis, non-destructive inspection simulation, and probabilistic analysis to assess the risk of rotor fracture with in-service inspection. DARWIN computes the probability-of-fracture versus flight cycles considering random defect occurrence and location, random inspection schedules, multiple inspections, and other random variables. In this study, the influences of changes in the main descriptors of fatigue related random variables on the lifetime failure probability of an aircraft titanium rotor disk is illustrated using the DARWIN computer program. It is shown that, compared to the other random variables considered, the defect size can have a dominant influence on the lifetime reliability of turbine rotor disks. In addition, for the rotor disk considered, inspection time variability does not appear to have a significant effect on lifetime reliability, but does influence the optimum mean inspection time. The results can be used for the development of reliabilitybased optimal design and maintenance strategies for fatigue vulnerable structures subject to in-service inspection. Fatigue Reliability Prediction Using DARWIN The fatigue failure probability is defined as the probability of violating the fatigue limit state g(X, Y, t). Fatigue failure occurs when the stress intensity factor K exceeds the fracture toughness KC : g t = K K t C ( ) ( , ) X, Y, X, Y 0 (1) where X is a vector of input variables unrelated to inspections, Y is a vector of input variables related to inspections, and t is flight hours. A negative or zero value of g(X, Y, t) represents a failure event. Vector X consists of three key random variables: initial defect area, stress, and life. The initial defect area is represented using a defect distribution based on historic data developed by the Rotor Integrity Sub Committee (RISC) of the Aerospace Industries Association. The stress random variable is modeled as the product of deterministic stress and a random variable X1 as follows: = X FEM 1 (2) where X1 is the stress multiplier, a random variable accounting for the errors in geometry and numerical *DARWIN is a registered trademark of Southwest Research Institute. “Copyright © 2000 by Southwest Research Institute. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission.” 2 American Institute of Aeronautics and Astronautics (e.g., finite element) modeling, and σFEM is the deterministic stress obtained from finite element analysis (adjusted to account for residual stresses). The life N is also modeled as the product of a deterministic variable and a random variable: