Stochastic measure of fatigue crack damage for health monitoring of ductile alloy structures

This paper models a stochastic measure of fatigue crack damage in ductile alloys that are commonly encountered in structures and machinery components of complex mechanical systems such as land, air, ocean, and space vehicles. The constitutive equations of the damage measure are built upon the physics of fracture mechanics and are substantiated by Karhunen-Loeve decomposition of fatigue test data where statistical orthogonality of the estimated measure and the resulting estimation error is demonstrated in a Hilbert space setting. The non-stationary probability distribution (PDF) function of the damage estimate is generated in a closed form without numerically solving stochastic differential equations in the Wiener integral or Itô integral setting. The model of crack damage measure allows real-time execution of decision algorithms for health monitoring, risk assessment, and life prediction of mechanical structures on inexpensive platforms such as a Pentium processor. The stochastic model of fatigue crack damage measure is in good agreement with experimental data sets for 2024-T3 and 7075-T6 aluminum alloys.