PSI - Issue 42

Diego F. Mora et al. / Procedia Structural Integrity 42 (2022) 224–235

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Diego F. Mora et. al./ Structural Integrity Procedia 00 (2019) 000 – 000

accident (LOCA) condition must be assessed. Experiments on real scale RPVs are expensive and almost unfeasible. One way to overcome this difficulty is to use thick-walled cylindrical mock-ups. The reason for using thick-walled cylinders is that higher hoop stresses are developed under pressurized thermal shock (PTS) or thermal shock (TS) than in thin-walled cylinders and consequently, similar stress states as in the RPV under LOCA can be simulated. Nevertheless, it must be taken into account that the real geometry of an RPV affects stresses, which is omitted in the thick-walled cylinder (Mora et al. 2020). In project FALSIRE (Sievers and Shulz 1994); Sievers and Shulz (1996), several experiments were carried out to examine different aspects of crack growth in cylinders made from RPV steel under PTS load. However, the numerical simulation of crack propagation in these materials remains challenging and needs to be addressed. At PSI, experiments on downscaled mock-ups are currently running on specimens with a smaller geometry than FALSIRE cylinders, which reduces the cost significantly and allows performing many experiments under the same condition to gain statistical relevant results. The aim of these experiments is the validation of the extended finite element method (XFEM) implemented in ABAQUS (ABAQUS 2012) applied to crack propagation of initial defects under PTS. In this contribution, the simulation of crack propagation in a mock-up subjected to a pressurized thermal shock transient similar to that occurring in a LOCA is presented. The experimental conditions (geometry, loads and materials) are taken from the well documented FALSIRE project. The results of the simulation are compared against the corresponding experimental data, with the future view on the applicability of XFEM on the planned downscaled mock-ups. In FALSIRE, the cylinders were made from two different ferritic steels. Cylinders made of a monolayer of 22NiMoCr 3 showed a ductile crack propagation whilst cylinders made of a bilayer of 17 MoV 8 4 mod and S3 NiMo 1 showed brittle crack propagation behavior in the layer made of 17 MoV 8 4 mod under PTS. Further work done by Merkert (Merkert 2002) confirmed that 17 MoV 8 4 mod behaves brittle under PTS loadings. Therefore, the material used in the finite element model corresponds to the specially heat-treated ferritic steel 17 MoV 8 4 mod. It exhibits a high ductile-to-brittle transition temperature (DBTT) as in a highly irradiated RPV steel and mimics the fracture mechanical behavior at the end-of-lifetime of the reactor. Correspondingly, this high DBTT is considered in the simulation approach. The temperature dependence of fracture toughness is described following the ASME models and is related to the maximum principal stress criteria for the initiation of crack propagation and crack arrest, where linear elastic fracture mechanics (LEFM) is applied. Thus, the modified temperature dependent stress criteria are included in the ABAQUS simulation by means of a subroutine UMDGINI. The mock-up under investigation contains a fully circumferential initial crack. Both, the loads and geometry of the cylinder are axisymmetric, however in the implementation of XFEM in ABAQUS, axisymmetric elements are not available. To avoid a full 3D finite element model and taking advantage of this symmetry, we proposed a model based on a cyclic symmetry of the cylinder allowing the use of 3D solid brick elements. The results show that the crack propagates through the cylinder but comparison against the experimental results shows an overestimation of the final crack depth. Furthermore, in contradiction to the experiment, in which the COD shows several initiation-arrest-re initiation cycles and final arrest, the simulation shows a smooth continuous increase of the COD indicating a progressive crack growth. The quality of the solution is demonstrated by a parameter analysis.

Nomenclature

i  o 

Inner diameter [m] Outer diameter [m]

Complementary subdomains in the node phantom method

0 0 , + −  

ˆ 

Crack direction of propagation Stress across the plane of the crack Maximum principal stress [MPa]

( ) r 

o  c 

max

Critical stress [MPa]

Stress components in cylindrical coordinates [MPa]

, zz     , rr