Markov based correlations of damage cycles in Gaussian and non-Gaussian loads

The sequence of peaks and troughs in a load process acting on a material, contains important information about the damage caused by the load, e.g. on the growth rate of a widening crack. The stress range, i.e. the difference between a peak and the following trough, is one of the variables that is used to describe e.g. fatigue life under random loading. The moments, in particular the mean and variance, of the load range are important variables that determine the total damage caused by a sequence of stress cycles, and they give the parameters in the distribution of the time to fatigue failure. However, for many random load processes, the successive stress ranges can show considerable correlation, which affects the failure time distribution. In this paper we derive the modified failure time distribution under correlated stress ranges, under a realistic approximation that the sequence of peaks and troughs forms a Markov chain. We use the regression method to calculate the transition probabilities of the Markov chain for Gaussian load processes with known spectral density. Simulations of Gaussian processes with Pierson-Moscowitz spectrum, and linear and the Duffing oscillators driven by Gaussian white noise, show very good agreement between observed correlations and those calculated from the Markov approximation. Also the numerically calculated transition probabilities lead to good agreement with simulation.