A New Probabilistic Approach for Describing Fatigue Crack Growth under Random Overloads

A new probabilistic model describing the fatigue crack growth with retardation due to random overloads is developed. First, a crack growth equation is formulated based upon the Flber law, where a concept of retardation factor is introduced to quantify the retardation effect. Next, a new approach is discussed for describing the temporal variation of the retardation factor by the use of a system of differential equations. The validity of the obtained crack growth model is then shown by comparing with experimental results by cMaster et. al. Next, the discussion is made on an extension of the proposed crack growth model to a probabilistic model, in which the overload process is mathematically modeled as a compound Poisson process to describe the random property associated with loading times as well as stress of overloads. The proposed probabilistic model takes a form of a system of random differential equations of Ito type driven by the compound Poisson process. Finally, numerical demonstration is carried out for generating crack growth samples based upon the proposed model.