On the relationship of the cumulative jump model for random fatigue to empirical data

The cumulative jump model, consisting of a random sum of random increments, has previously been proposed, in a general format, to model the fatigue crack growth process. In this paper the cumulative jump process for random fatigue is used to model the constant-load amplitude Virkler fatigue crack growth data. It is shown, through the proper choice of the intensity function of the underlying birth process, that the mean crack growth behavior of the model may be specified to match any desired functional form. This assures reasonable agreement with experiments. For fatigue crack growth the intensity function is characterized by a constant and a random variable (this makes the underlying birth process a so-called doubly stochastic counting process). For the case of the `simplifiedʹ jump model (constant elementary crack increments), the constant and the random variable characterizing the intensity function may be estimated by matching approximate formulae for the mean and the variance of the model with the data. Simulations of the jump model show trajectories which behave qualitatively like the data and yield distribution functions for the crack length which match well the data.