Estimation of failure probability of cracked pipes of high energy piping system using first order reliability model

Deterministic fracture analysis of structures has been conventionally used to estimate the safety of structures under observed or postulated flaws. The chief ingredients in a deterministic fracture mechanics analysis are the initial crack size, crack driving force, applied stress and the material properties. However, crack size, postulated loading, mechanical and fracture parameters are often subjected to considerable scatter or uncertainty. Consequently, the result of deterministic fracture mechanics analysis must be viewed with some skepticism. Quite often, conservative bounds on inputs are employed on these results by providing a conservative estimate to results, however this may lead to prediction of overly conservative and unrealistic results. These uncertainties encourage us to adopt a statistical or probabilistic approach to the structural integrity. This paper presents a FORM based stochastic model to estimate failure probabilities of a straight pipe with a through-wall crack in the circumferential direction, using R6 method. R6 is a well-known engineering assessment procedure for the evaluation of the structural integrity of flawed structure. First Order Reliability methods (FORM) are efficient techniques to estimate low failure probabilities. The pipe is subjected to an in-plane bending moment. The scatter in the crack size, mechanical and fracture properties is considered. The probability of failure is studied for variation in applied loads. The study is performed by constructing failure assessment diagram (FAD) using Option 1 and 2 of R6. The input variables to the stochastic model are non-Gaussian and correlated. Nataf's transformation is applied to estimate the failure probabilities. (orig.)