Modelling of random fatigue by cumulative jump processes

Abstract The paper is concerned with stochastic modelling of fatigue crack growth under random loading and other uncertainties. A new model based on cumulative random jump processes is proposed. The fatigue crack length (at arbitrary time t ) is represented as a random sum of random (non-negative) increments. A number of crack's increments in interval [0, t ] is characterized by a counting stochastic process N(t) . First, the cumulative model with underlying Poisson process is presented; to account for the dependence of the growth intensity upon the state of the process the model with underlying birth process is then developed. In both cases the probability distribution of the crack size and the life-time distribution are determined analytically. The model parameters are related to fatigue data contained in existing empirical crack growth equations. The results are illustrated graphically for real data.