Markov Fatigue in Single Crystal Airfoils

Abstract

This paper considers the influence of microstructure on macrobehavior in single crystal airfoils by treating the micromechanics of damage accumulation as a Markov process. Single Crystal Fatigue (SCF) is a result of several, simultaneous (competing), damage mechanisms, which are selectively favored by particular combinations of external conditions. As with any real physical process, SCF is also influenced by a stochastic component. This probabilistic influence can be exploited to help explain the macrobehavior. We begin with a description of single crystal materials and how they differ from more conventional (isotropic) alloys. Relationships are suggested among the more probable of several competing microstructural damage mechanisms and specific rate-controlling parameters. The states of microstructural damage are then described and catalogued, and the various avenues of damage accumulation are investigated. Next, the Markov paradigm is reviewed as it applies to these materials. Finally, a Markov model is presented to describe the rather complex behavior observed in single crystals, and its use in lifing gas turbine engine airfoils is discussed.