Uncertainty quantification and calibration of a modified fracture mechanics model for reliability-based inspection planning

Efficient inspection and maintenance are important means to enhance fatigue reliability of engineering structures, but they can only be achieved efficiently with the aid of accurate pre-diction of fatigue crack initiation and growth until fracture. The influence of crack initiation on fatigue life has received a significant amount of attention in the literature, although its im-pact on the inspection plan is not generally addressed. Current practice in the prediction of fatigue life is the use of S-N models at the design stage and Fracture Mechanics (FM) models in service. On the one hand, S-N models are relatively easy to apply given that they directly relate fatigue stress amplitude to number of cycles of failure, however, they are difficult to extrapolate outside the test conditions employed to define the S-N curves. On the other hand, FM models like the Paris propagation law give measurable fatigue damage accumulation in terms of crack growth and have some ability to extrapolate results outside the test conditions, but they can only be a total fatigue life model if the initial crack size was known given that they do not address the crack initiation period. Furthermore, FM models generally introduce large uncertainties in parameters that are often difficult to measure such as initial crack size, crack growth rate, threshold value for stress intensity factor range, etc. This paper proposes a modified FM model that predicts the time to failure allowing for crack initiation period. The main novelty of the modified FM model is the calibration using S-N data (i.e., inclusive of crack initiation period) for an established criterion in fatigue life and reliability level. Sources of uncertainty associated to the model are quantified in probabilistic terms. The modified FM model can then be applied to reliability-based inspection planning. An illustrative example is performed on a typical detail of ship structure, where the optimum inspection plan derived from the proposed model is compared to recommendations by existing FM models. Results demonstrate to what extent is the optimum inspection plan influenced by the crack initiation period. The modified model is shown to be a reliable tool for both fatigue design and fatigue management of inspection and maintenance intervals.