Stochastic Modeling of Fatigue Crack Damage for Risk Analysis and Remaining Life Prediction

Abstract

This paper presents a stochastic model of fatigue crack damage in metallic materials that are commonly encountered in structures and machinery components of complex mechanical systems (e.g., aircraft, spacecraft, and power plants). The constitutive equation of the damage model is based on the physics of fracture mechanics and is validated by Karhunen-Loève analysis of test data. The (nonstationary) probability distribution function (PDF) of fatigue crack damage is generated in a closed form without numerically solving stochastic differential equations in the Wiener integral or Itô integral setting. The crack damage model thus allows real-time execution of decision algorithms for risk assessment and life prediction on inexpensive platforms such as a Pentium processor. The model predictions are in close agreement with experimental data of fatigue crack growth statistics for 2024-T3 and 7075-T6 aluminum alloys.