Stochastic continuum approach to high-cycle fatigue: Modelling stress history as a stochastic process

In this article, the continuum-based high-cycle fatigue analysis method, introduced by Ottosen, Stenstrom and Ristinmaa in 2008, is extended to cases where the stress history is a stochastic process. The basic three parameter Ornstein-Uhlenbeck process is chosen for stress description. As a practical example, the theory is applied in both finite and infinite life cases. A definition for the safety factor is introduced, which is reduced to a minimization problem of the value for the endurance surface. In the stochastic case, the values of the endurance surface form a stochastic process and the cumulative distribution function can be constructed for its maximum values.