DEVELOPMENT OF A STOCHASTIC MODEL FOR FATIGUE CRACKS IN AIRCRAFT STRUCTURES

The mechanism of fatigue damage involves the changing probability distribution for crack lengths with increasing number of cycles and is generally in three stages from a macroscopic point of view. Crack growth time from microsize to detectable size can be lumped into the first stage of the following three stages comprising the fatigue process (1) crack initiation, (2) crack growth, and (3) failure. The inadequacy of the present probabilistic methods that use a single random variable to characterize fatigue is that they do not encompass all of the above stages of the fatigue phenomenon. The development of a methodology for the reliability based optimum design of aircraft structures necessitates a model that encompasses all stages of progressive damage from mircosize to cracks of critical lengths. This is in turn helpful for the proper prescription of inspection and maintenance schedule also. This can be accomplished by developing a stochastic model for fatigue that describes the changing probability distribution of cracks with increasing flight hours or cycles. In this paper, a stochastic model for fatigue crack propagation under random loading is derived. Parameter estimation of the derived fatigue model from observed fatigue crack data is presented. Also, a methodology is proposed for the application of the model for the optimum selection of design variables and inspection schedule.