Application of Modern Approaches to the Numerical Modeling of the Stress-Strain State for the Strength Assessment of Complex Units of the NPP Primary Circuit Equipment. Part 3. Application of Submodeling Technique and Extended Finite Element Method for Calculation of the Reactor Pressure Vessel Nozzle Zone

Recent studies have shown that nozzle zones are one of the most dangerous elements of the reactor vessel. High stresses in such nodes can lead to the appearance of angular cracks. At the same time, the issue of choosing the critical dimensions and direction of crack location from the point of view of calculations for resistance to brittle fracture remains open. The paper presents the results of numerical modeling of the stress-strain state of the nozzle zone of the reactor vessel by the classical finite element method (FEM) and the extended finite element method (XFEM) using the submodeling technique. The results of numerical modeling by the classical FEM for the mode of hydraulic testing of the reactor vessel pressure vessel nozzle zone with three types of cracks are presented: surface, subweld, and a crack with 1 mm penetration into the weld. For twelve types of cracks with variations in their size and direction of location in the reactor vessel pressure vessel nozzle zone, the results of calculations of resistance to brittle fracture by the XFEM method for one of the characteristic modes of thermal shock are presented. The calculation results proved that axial cracks are more dangerous than circular cracks of the same dimensions. Cracks with a semi-axis ratios a/c = 0.3 and a/c = 0.7 are more dangerous for the axial and circumferential directions, respectively. At the same time, cracks with a/c = 0.3 are more sensitive to the direction of location than cracks with a/c = 0.7. It was shown that the use of the XFEM method makes it possible to conduct a rapid assessment of the resistance to brittle fracture with the possibility of varying the shape, size, and location of the crack, which allows one to effectively determine its critical size and the most dangerous location in the structural element.