# The Application of Numerical Ductile Fracture Simulation in the LBB Evaluation of Nuclear Pipes
## 1 Introduction
[15] adopted [PERSON]'s damage model based on CDM to predict the stress-state-dependent plastic behavior and fracture of 304L stainless steel. [PERSON] et al. [16] employed a combined framework of CDM and Beremin models to characterize the two competing failure mechanisms in the ductile-to-brittle transition (DTB) region of ferritic steels and predict the fracture toughness scatter band in relation to temperature. However, it should be noted that CDM does not explicitly account for the microscopic mechanisms governing material fracture. The micromechanics of damage postulates that material damage evolution originates from the nucleation and propagation of microdefects, including dislocations, slip bands, microvoids, and microcracks, with microvoids and microcracks being the predominant damage forms. As a typical micromechanical damage model, the Gurson-Tvergaard-Needleman (GTN) model [17] effectively simulates ductile fracture through micromechanical processes including void nucleation, growth, and coalescence. [PERSON] et al. [18] primarily investigated the ductile fracture prediction of titanium foil considering size effects based on the shear-modified GTN damage model. Comparisons with experimental results verified the accuracy and feasibility of the model. [PERSON] et al. [19] improved the GTN model by introducing an independent shear damage variable along with strain rate hardening, thermal softening, and viscous resistance terms to predict the Taylor impact fracture behavior of 7 XXX aluminum alloys under high strain rates. However, the complex parameter system of the improved model increased calibration difficulty. In contrast, the stress-modified critical strain (SMCS) model offers a simplified approach by focusing on void growth and assuming constant stress triaxiality, thereby reducing the number of required parametersand facilitating more efficient material calibration. [PERSON] et al. [20] introduced a finite element damage method based on the SMCS model. By incorporating this model into FE analysis, the initiation and propagation of cracks can be effectively simulated. [PERSON] et al. [21] extended the SMCS model by introducing a constant to characterize the effect of thermal aging on the multiaxial fracture strain of CF8M stainless steel and further utilized the J-R curve to evaluate the fracture toughness of CF8M. [PERSON] et al. [22] predicted the degradation of the fracture toughness in thermally aged CF8A materials under cyclic loading conditions by applying the SMCS model, i.e., the thermal embrittlement constant. However, FE ductile fracture simulation is more often used to predict the crack growth behaviors of small specimens rather than large components like full-scale pipes [23; 24; 25; 26]. As the FE ductile fracture simulation shows a high dependence on the element size near the crack tip, an element size of less than 0.2 mm is usually required to simulate the crack growth behaviors validly [26; 27; 28]. The use of such small elements to predict the crack growth behaviors of full-scale pipes may cause numerical problems. [PERSON] et al. [28] effectively reduce the element size dependence by introducing an element-size-dependent critical damage parameter into the SMCS model. In this study, the extended SMCS model is applied to predict the J-R curves of three full-scale pipes with a circumferential through-wall crack under a four-point-bending load. To demonstrate the validity of FE ductile fracture simulation in the LBB evaluation of nuclear pipes, the critical load levels at which cracked pipes suddenly break down predicted based on the FE simulation results are compared to those predicted based on the fracture resistance test results of CT specimens and full-scale pipes.