ABSTRACT
Three sizes are important for the characterization of the propagation of fatigue cracks—initial size, detectable size and acceptable size. The theoretical model of a fatigue crack progression can be based on a linear elastic fracture mechanics. Depending on location of an initial crack, the crack may propagate in structural element that could be described by calibration functions. Single edge-cracked steel element with rectangular cross-section under relative short edge fatigue damage under pure tension, pure bending, three and four point bending load have been chosen for applications of the theoretical solution suggested in the studies. When determining the required level of reliability, it is possible to specify the time of the first inspection of the construction which will focus on the fatigue damage. Using a conditional probability and Bayesian approach, times for subsequent inspections can be determined based on the results of the previous inspection. For probabilistic calculation of fatigue crack progression, the original and new probabilistic method—the Direct Optimized Probabilistic Calculation (DOProC), which uses a purely numerical approach based on optimized numerical integration without any simulation techniques or approximationapproach. This provides more accurate solutions to probabilistic tasks, and, in some cases, allows to considerably fasten completion of computations with the taking into account the statistical dependence of random input variables.
