RANDOM FATIGUE CRACK-GROWTH - A 1ST PASSAGE PROBLEM

The random residual in the logarithmic form of the Paris-Erdogan equation is for a single stress cycle modeled as a weighted average of a white noise material property process over the crack increment. This leads to a stochastic Paris-Erdogan equation that determines the crack increment implicitly in terms of a probability distribution of the smallest solution to the equation. This is a first passage problem in Brownian motion. For all weighting functions consistent with this model the solutions of the first passage problem has the form as a randomized Paris-Erdogan equation simply with a multiplicative random variable on the right side of the equation. It is independently and identically distributed from stress cycle to stress cycle. For each of two specific weighting functions the probability distribution of this random factor is obtained.