I. Rychlik et al., MARKOV BASED CORRELATIONS OF DAMAGE CYCLES IN GAUSSIAN AND NON-GAUSSIAN LOADS, Probalistic engineering mechanics, 10(2), 1995, pp. 103-115
The sequence of peaks and troughs in a load process acting on a materi
al, 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 load
ing. The moments, in particular the mean and variance, of the load ran
ge are important variables that determine the total damage caused by a
sequence of stress cycles, and they give the parameters in the distri
bution of the time to fatigue failure. However, for many random load p
rocesses, the successive stress ranges can show considerable correlati
on, which affects the failure time distribution. In this paper we deri
ve the modified failure time distribution under correlated stress rang
es, under a realistic approximation that the sequence of peaks and tro
ughs forms a Markov chain. We use the regression method to calculate t
he transition probabilities of the Markov chain for Gaussian load proc
esses with known spectral density. Simulations of Gaussian processes w
ith Pierson-Moscowitz spectrum, and linear and the Duffing oscillators
driven by Gaussian white noise, show very good agreement between obse
rved correlations and those calculated from the Markov approximation.
Also the numerically calculated transition probabilities lead to good
agreement with simulation.