Palmgren–Miner’s rule and fracture mechanics-based inspection planning

A Palmgren–Miner’s rule and fracture mechanics (FM) based approach coupled with Bayesian updating in order to establish inspection plans for marine structures is proposed. A FM formulation based upon the British Standard (BS) 7910 is calibrated by S–N curves and Palmgren–Miner’s rule. A model is developed taking account of the uncertainties associated with S–N curves and Palmgren–Miner’s rule to quantify the random growth of a flaw predicted by the calibrated FM formulation. The long-term stress range acting on a structural component is fitted to a two-parameter Weibull distribution, according to the rules of the American Bureau of Shipping (ABS). The reliability after inspection is updated by the Bayesian approach accounting for the probability of detection (POD) and inspection results. An inspection plan is then set up on the basis of the comparison between the updated reliability and a target reliability index. Typical fatigue–prone structural details from a tanker are utilized for demonstration of the capabilities of the approach proposed.