Time-dependent reliability assessment of fatigue crack growth modeling based on perturbation series expansions and interval mathematics

A novel method of the time-dependent reliability, which combines the perturbation series expansions with the interval mathematics, is presented in this study for life prediction of fatigue crack growth problems. Distinct from the treatment in statistical analysis, characteristic parameters that exist in structural crack propagation model are described as unknown-but-bounded (UBB) variables with perturbation terms owing to the fact of variability of geometric sizes, material properties, and loading conditions. Then, based on the perturbation principle and the Taylor extension approach, a new interval perturbation series expansion method (PSEM) to predict boundary rules of the fatigue crack length a(t) is derived. Meanwhile, the auto-correlation features between a(t_k) and a(t_k+1) are also confirmed by employing the interval process theory. Additionally, inspired by the classical out-crossing approach in random process issues, a non-probabilistic time-dependent reliability (NTR) index R_s(T), as a safety measure for in-service engineering structures with crack, is defined, and its solution algorithm is expounded in details. Numerical examples are eventually proposed to demonstrate the validity of the developed methodology of uncertainty quantification and reliability evaluation.