Modeling of random fatigue crack growth lifetime

A statistical model is proposed for the analysis of fatigue crack growth, based on the theory of fracture mechanics and stochastic process. The fatigue growth process is approximated as a diffusive Markov process. The associated backward Fokker-Plank equation and boundary conditions are written, and the distribution of crack growth time under a given crack size is obtained by using an Eigenfunction method. The sought distribution is expressed in the form of a convergent infinite series. Two examples are presented to illustrate the application of the method. The predicted results seem to agree with the experimental data.