Reliability estimation of fatigue crack growth prediction via limited measured data

In view of limited uncertainty information, a time-dependent reliability estimation procedure that combines the determined crack growth model with interval mathematics is presented as a theoretical basis for structural damage tolerance design. Firstly, by virtue of the theory of non-probabilistic interval process, an interval process model of fatigue crack propagation is investigated, in which we describe uncertain crack length a(N) at any load cycle N as interval variable and define the corresponding auto-covariance function and the correlation coefficient function to further characterize the correlation of a(N) at different cycles. By comparison of the critical crack length acritical, the uncertainty properties of the time-varying limit-state function can be given as well. Furthermore, inspired by the first-passage approach in random process theory, a new measure index of non-probabilistic time-dependent reliability is proposed as a feasible way for precisely evaluating the safe life of in-service engineering structures with crack. The corresponding solution algorithm is further discussed. Some application examples demonstrate the usage, efficiency and accuracy of the developed methodology eventually.