Damage-Based Modeling and Analysis of Reactor Vessels With Numerous Base Metal Ultrasonic Indications

Abstract

The numerous indications recently found by UT-inspection in the reactor pressure vessel shell forgings at two Belgian nuclear power plants have raised some concerns about the effects of such indications on the vessel integrity and fitness for continued service. The UT indications have been attributed to hydrogen flaking, and preliminary estimates give a density of ∼40 indications per liter, with diameter of about 10–14 mm, oriented at a shallow ∼10° angle to the vessel inner surface. This type of high-density indications would not be characterized as geometric flaws with well defined crack-tip geometry that permits high-fidelity application of traditional fracture mechanics methods. An alternative analysis approach, with higher fidelity simulation of this type of “distributed discontinuities”, is proposed, as described in this paper. From a behavioral standpoint, the UT indications at Doel 3 and Tihange 2 represent material discontinuities whose mechanical effect can be evaluated using a damage-mechanics-based constitutive model. Previously, a special multiphase damage model was developed for cladding with zirconium hydrides, of similar morphology to the Doel 3 indications, in which the metal matrix and the hydride platelets are treated as separate material phases interacting at their interfaces with appropriate constraint conditions between them to ensure strain and stress compatibility. The hydride precipitates are represented as a brittle material and the metal matrix is modeled as a ductile elastic-plastic material. This damage model was implemented in a finite element computer program, and was validated using ring-tension and ring-compression tests of cladding specimens with various hydride morphologies. The model was able to predict specimens complete stress-strain curves and failure states with very high accuracy. The above described damage model is adapted to the high-density UT indications, morphology and distribution similar to the conditions of the Doel 3 vessel. The “hydrogen flakes” are characterized in the model as distributed damage of known orientation and volume fraction. A vessel of typical geometry and radiation-dependent mechanical properties is analyzed for various values of volume fraction of hydrogen flakes, and considering a transient loading scenario that conservatively simulates pressurized thermal shock. Interlinking of the “hydrogen flakes” and propagation of damage through the wall under the specified loading condition are part of the model’s capability of directly predicting whether or not vessel failure will occur. Thus, vessel susceptibility to failure and failure margin are judged by the degree of damage propagation through the wall.