A Simple Reliability Model for the Fatigue Failure of Repairable Offshore Structures

Abstract

A simple reliability model for fatigue failure of tubular welded joints used in the construction of offshore oil and gas platforms is proposed. The stress-life data obtained from large-scale fatigue tests conducted o n tubular joints is used as the starting point in the analysis and is combined with a fracture mechanics model to estimate the distribution of initial defect sizes. This initial defect distribution is hypothetical but it agrees well with other initial defect distributions quoted in the literature and when used with the fracture mechanics model results in failure probabilities identical to those obtained from the stress-life data. This calculated distribution of initial defect sizes is modified as a result of crack growth under cyclic loading and the probability of failure as a function of fatigue cycles is calculated. The failure probability is modified by inspection, and repair and the results illustrate the trade-off between inspection sensitivity and inspection interval for any desired reliability. NOMENCLATURE A S = hot spot stress range a, = initial defect depth AK = stress intensity factor range da/dN = crack growth rate a,= final crack depth N = no. of fatigue cycles (T = standard deviation of fatigue lives p = mean of fatigue lives Lnl,(a,) = probability density function for initial defect depth C, m =constants in crack growth law f(a,) = probability density function for crack depth at N cycles PODfa) = probability of detecting crack of depth a a(90) = crack depth corresponding to 90% POD a, = crack depth at N cycles j = no. of inspections i = current inspection a,k = depth of crack at kth inspection which was introduced by repair at the ith inspection f;,(a,) = distribution for repaired portion of the total crack density function that was repaired at inspection i f(a,= -,) = probability density function for crack sizes just before the ith inspection a n = , = crack depth at ith inspection