A STOCHASTIC-MODEL FOR ELASTIC-PLASTIC FRACTURE-ANALYSIS OF CIRCUMFERENTIAL THROUGH-WALL-CRACKED PIPES SUBJECT TO BENDING

A probabilistic model is developed for nonlinear fracture-mechanics analysis of through-walled-cracked pipes subject to bending loads. It involves elastic-plastic finite element analysis for estimating energy release rates, J-tearing theory for characterizing ductile fracture and standard structural reliability methods for conducting probabilistic analysis. Evaluation of the J-integral is based on the deformation theory of plasticity and power-law idealizations of stress-strain and fracture toughness curves. This allows the J-integral to be expressed in terms of non-dimensional influence functions (F- and h(1)-functions) that depend on crack size, pipe geometry and material hardening constant. The equations for these functions (and hence, J) for a cracked pipe are developed in closed-form based on recent results of elastic-plastic finite element analysis. This makes the subsequent stochastic analysis computationally feasible to conduct probabilistic pipe fracture evaluations. Both analytical and simulation methods are formulated to determine probabilistic characteristics of J for a circumferential through-wall-cracked pipe as a function of applied bending moment. The same methods are used later to compute failure probability of the cracked pipes. Several failure criteria associated with crack initiation, unstable crack growth and Net-Section-Collapse are used to determine such probabilities. Numerical applications are provided to illustrate the proposed methodology. First, the validity of the J-integral based on the proposed equations for predicting the crack driving force in a through-wall-cracked pipe is evaluated by comparing with available results in the current literature. Second, probability densities of the J-integral are predicted as a function of applied loads. Third, failure probabilities corresponding to various performance criteria are evaluated for a stainless steel nuclear piping in the Boiling Water Reactor plant. The effects of correlation and distribution properties of random input on failure probability are also evaluated.