A probabilistic model for fatigue crack initiation and propagation

Simulations of fatigue in piping and reactor pressure vessels have been performed using an approach which combines models for initiation and propagation of surface cracks. The statistical distribution of the number of cycles to crack initiation (i.e., 3-mm crack) is considered to be lognormal. The medium number of cycles to crack initiation is a function of the material type, water/air environment, temperature, dissolved oxygen content, sulfur content and strain rate. The fatigue damage due to various stress amplitudes is calculated by Miner's rule, which is used to predict the statistical distribution of cycles to initiation. The probability of crack initiation equals the probability that the damage ≥1. Initiated fatigue cracks grow based on fracture mechanics rules. The parameters governing the fatigue crack growth rates are considered stochastic variables. A Latin Hypercube simulation approach has been developed to predict the probability that an initiated flaw will extend by fatigue crack growth mechanisms and become a through-wall flaw.