Probabilistic elastic-plastic fracture analysis of cracked pipes with circumferential through-wall flaws

A probabilistic fracture model was developed to analyze circumferential through-walled-cracked pipes subjected to bending loads. It involved elastic-plastic finite element analysis for estimating energy releases rates, J-tearing theory for characterizing ductile fracture, and standard methods of structural reliability theory for conduction probabilistic analysis. The evaluation of J-integral was based on the deformation theory of plasticity and power-law idealizations of the stress-strain and fracture toughness curves. This allows J to be expressed in terms of non-dimensional influence functions (F- and h1-functions) that depend on the crack size, pipe geometry, and material hardening constant. New equations were proposed to represent these functions and were applied to conduct stochastic pipe fracture evaluations. Both analytical and simulation methods were formulated to determine the probabilistic characteristics of J. The same methods were used later to predict the failure probability of pipes as a function of the applied load. Numerical examples are provided to illustrate the proposed methodology. The validity of J-integral based on the proposed equations for predicting crack driving force in a through-wall-cracked pipe was evaluated by comparing with available results in the current literature. Probability densities of J-integral were predicted as a function of applied loads. Failure probabilities corresponding to three different performance criteria were evaluated for a stainless steel nuclear piping in the Boiling Water Reactor plant. The results suggest that large differences may exist in the failure probability estimates produced by these performance criteria