Probability of Fracture for HFIR Pressure Vessel Caused by Random Crack Size or by Random Toughness

The probability of fracture (or the fracture fragility) for a range of internal pressure-pulses for the HFIR pressure vessel is obtained. The fracture is assumed to be caused by randomly distributed cracks and by fracture toughness of variable magnitudes. The probability curve is applied to estimate the vessel fracture strength against the pressure-pulses of hypothetical accident. Both the crack population and the fracture toughness are assumed to be random variables of given distribution functions. Possible hoop stress is based on the numerical solution of the vessel response after a point pressure-pulse is applied at the center of the reactor vessel. The fluid-structure interaction and radiation embrittlement are both considered in the analysis. Only elastic fracture mechanics is used. The probability of vessel fracture for a single crack caused by either a variable crack depth or a variable toughness is first derived. Then the probability of fracture with multiple number of cracks is obtained. The probability of fracture is further extended to include different levels of confidence and variability.