Probability function of fatigue crack growth in case of overloading

Studies of structural components under a fatigue environment including overloads are rather interesting in engineering practice today [1,2]. One main important task is to determine the probability distribution function in consideration of two failure modes on the certain fatigue load and overload level. The probability density function is making the effect of overloading under fatigue environment useful for estimating the residual life or to predict the failure of a component. The fatigue crack propagation in case of overloading can be modeled by a Markov's process. The obtained probability functions describe the probability of retarded crack growth propagation as a consequence of the overload cycle.