# The Application of Numerical Ductile Fracture Simulation in the LBB Evaluation of Nuclear Pipes
## 5 Conclusions  
In this study, the LBB evaluation of nuclear pipes (SA312 TP304L stainless steel) is performed based on the results of fracture resistance tests and numerical ductile fracture simulations. The conclusions are as follows:  
1. The extended SMCS model is employed to accurately simulate the crack propagation behavior in full-scale nuclear pipes with circumferential cracks. By introducing a mesh-dependent critical damage parameter (\(\omega_{\rm c}\)), the dependence of crack-tip stress-strain fields on mesh size was effectively reduced, enabling the use of larger element sizes in simulations. The \(\omega_{\rm c}\) values for specific mesh sizes were calibrated by comparing the simulation results with experimental data from CT specimens.
2. Through CDFD analysis, the critical load levels were calibrated for pipes with different initial crack lengths and compared. For a pipe with a large initial crack length (\(20=180^{\circ}\)), the critical load levels in the LBB concept predicted based on the J-R curve of a CT specimen are close to those predicted based on the J-R curve of a full-scale pipe, while for a pipe with a short initial crack length (\(20=60^{\circ}\)), using a CT specimen to predict the critical load level of the pipe may result in significant conservatism.
3. Crack growth behaviors of full-scale nuclear pipes with circumferential cracks are simulated accurately by the extended SMCS model, and the maximum supported load levels predicted based on the simulation results are in good agreement with those predicted based on the full-scale pipe test results. This approach for the design of nuclear pipes by simulating full-scale pipe fractures with an extended SCMS model not only reduces conservatism but also saves significant time and costs.  
However, it should be noted that the mesh-dependent critical damage parameter (\(\omega_{\rm c}\)) is an empirical parameter lacking strong theoretical justification. Moreover, currently, this approach has only been tested on SA312 and TP304L pipes, so its general applicability requires further verification.  
Conceptualization, Y.F. and T.S.; methodology, Y.F. and T.S.; software, B.L.; validation, Y.F. and T.S.; formal analysis, Y.F.; investigation, Y.F.; resources, T.S.; data curation, B.L.; writing--original draft preparation, Y.F.; writing--review and editing, T.S.; visualization, B.L.; supervision, T.S.; project administration, C.-S.S.; funding acquisition, C.-S.S. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (No. 2018R1A2A1A05077886) and the China Postdoctoral Science Foundation (No. 2024M753829).  
Figure 15: Comparison of CDFD analysis results: (**a**) comparison of \(M_{max}\); (**b**) comparison of \(f_{inst}\).  
Data Availability Statement: Data will be made available on request.  
We acknowledge the financial support provided by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (No. 2018R1A2A1A05077886) and the China Postdoctoral Science Foundation (No. 2024M753829).  
The authors declare no conflicts of interest.