Stochastic modeling of fatigue crack growth

A new lognormal fatigue crack propagation model has been presented in which a two-dimensional state vector has been employed to introduce experimentally observed history dependence of fatigue crack growth. Markov process theory has been used to formulate a well-posed boundary-value problem for the statistics of the random time to reach a critical crack size conditional on the initial flaw size. A robust Petrov-Galerkin finite element method was then utilized for the solution of the boundary value problem. In the examples, the commonly used power-law crack propagation model is employed for simplicity, however, more complex models could have been employed with little additional effort. Finally, excellent correlation with the experimental results was found.