The integrity assessment to evaluate the safety margin of reactor pressure vessels (RPV) often considers only the crack initiation and excludes the crack propagation analysis. This contribution focuses on crack propagation analysis in RPV steels. The eXtended Finite Element (XFEM) method implemented in ABAQUS is applied to a thick-walled cylindrical specimen with a circumferential crack at the inner surface in order to simulate crack propagation in embrittled RPV subjected to Pressurized Thermal Shock (PTS). The thick-walled cylinder considered in this study was tested in the FALSIRE project, which results reported the crack opening displacement (COD) and the crack-arrest cycles occurring during the cooling down process. In order to simulate the cylinder with the XFEM, a reduced three-dimensional finite element (FE) model of a small sector (a slice of the cylinder) is used by applying cyclic symmetry boundary conditions. The COD evolution during the PTS transient is calculated and compared against the experimental COD. In the experiment, the COD shows several initiation-arrest-re-initiation cycles and final arrest. However, the results from the simulation show a smooth continuous increase of the COD indicating a progressive crack growth.
Abstract In this paper, an integrity assessment of a reference Reactor Pressure Vessel (RPV) under Pressurized Thermal Shock (PTS) is performed. The assessment is based on a multi-step simulation scheme, which includes the thermo-hydraulic, thermo-mechanical and fracture mechanics analyses. The proposed strategy uses a three dimensional (3D) finite element model (FEM) of the RPV with the Abaqus code to solve the thermo-mechanical problem for the scenario of a Large-Break Loss-of-Coolant Accident (LBLOCA). In order to obtain the boundary conditions for the thermal analysis, the thermo-hydraulic results from a 3D RPV model developed in the system code TRACE are used. The fracture mechanics analysis is carried out on submodels defined on the areas of interest. Submodels containing cracks or flaws are also located in regions of the RPV where there might be a concentration of stresses during the PTS. The calculation of stress intensity factor (SIF) makes use of the eXtended FEM (XFEM) approach. The computed SIF of the postulated cracks at the inner surface of the RPV wall are compared with the ASME fracture toughness curve of the embrittled RPV material. For different transient scenarios, the boundary conditions were previously calculated with a computational fluid dynamics (CFD) model. However, cross-verification of the results has shown consistency of both CFD and TRACE models. Moreover, the use of the later is very convenient for the integrity analyses as it is clearly less computationally expensive than CFD. Therefore, it can be used to calculate different PTS scenarios including different break sizes and break locations. The main findings from fracture mechanics analyses of the RPV subjected to LBLOCA are summarized and compared. The presented results also allow us to study the influence of the dynamic cooling plume on the stress intensity factor in more detail than with the conventional one-dimensional method. However, the plumes calculated with both approaches are different. How much this difference affects the integrity assessment of the RPV is discussed in the paper.
The core region of the reactor pressure vessel (RPV) can be considered as a hollow cylinder disregarding the geometrical details such as the nozzles. Under this consideration, a cylindrical mock-up with an axial crack can be used to investigate the behavior of initial defects under thermal shock (TS). In order to assess the crack initiation, propagation and arrest of an initial defect and to design mock-ups for TS experiments, a combined simulation approach of the Initiation-Growth-Arrest (IGA) algorithm and XFEM is proposed. The mock-up is designed taking into account the propagation of the initial defect and its arrest as well as several experimental criteria such as weight, size of the specimen, experimental feasibility, etc. The simulation strategy uses the stress intensity factors at every time increment of the TS event to estimate the possible crack propagation and brittle failure of the cylinder. The criterion for initiation of the crack propagation uses the temperature-dependent fracture toughness (KIc) of the material described by ASME fracture toughness model. For the crack arrest, the simulation approach uses the crack arrest fracture toughness of the material. After introducing the IGA algorithm and its implementation for XFEM, a 3D finite element model of a cylinder and material properties corresponding to an embrittled steel are introduced. Then, the IGA algorithm is combined with a closed-weight function formula (WFF) for axial crack in hollow cylinders, which is used as reference solution. The XFEM-initiation-growth-arrest (XFEM-IGA) and closed-weight function-initiation-growth-arrest (WFF-IGA) methods are applied on cylinders with different geometries to select the geometry of the mock-up designed for a thermal shock experiment. The results show that the crack stops for thick cylinders after several initiation-arrest cycles and that a reduction of the thickness provokes propagation of the crack until through-wall-crack happens. Beside the performance and application to an axial edged crack in a hollow cylinder, some limitations of the presented model are also discussed.
Abstract The finite element simulation of fracture propagation of BCC metals is challenging, as it needs to incorporate the brittle, ductile-brittle transition and ductile behavior presented by the fracture toughness. In this contribution, we restrict ourselves to the use of XFEM method to simulate the cleavage fracture due to initial flaws in the reactor pressure vessel of a reference design of the two-loop PWR nuclear power plant. A hypothetical large break loss of coolant accident is selected as accident scenario to obtain the loading conditions under which the crack is subjected. The thermal-mechanical calculation is performed using a finite element model of the whole RPV and the initial and boundary conditions are determined from the thermal-hydraulic simulation of the transient in TRACE. The method proposed in this contribution is based on the cohesive segment approach implemented in ABAQUS, which requires the definition of the damage properties of the material. The segment approach does not use the fracture toughness as failure criterion. Instead, it uses a traction separation law that is able to capture the brittle fracture behavior of ferritic steel. The crack propagation in XFEM uses a propagation criterion based on a cohesive damage initiation criterion and a damage evolution model. In order to implement the damage evolution model, the fracture energy release rate is directly related to the fracture toughness. The postulated crack is inserted in a submodel to reduce the computational cost of the calculation. The location of such submodel corresponds to the region of the core that suffers maximum irradiation and is subjected to high tensile stresses due to the cooling plume generated during the transient PTS cooling. The crack propagation analysis of postulated axial crack showed that its propagation happens in axial direction in those finite elements close to the inner surface because the energy release rate GI is larger than the critical energy release rate GIC. At the deepest point of the crack, the stresses in the finite element fulfil the damage initiation criterion but the crack does not propagate in radial direction (GI < GIC).