# Fracture Threshold Analysis and Parameter Matching of Cut-Out Induced Bolts for Subway Couplers
## 5 Conclusions  
This paper investigates the phenomenon of premature breakage of tensile break bolt-type overload protection in the rigid wall impact test of a train coupler. Based on the cut-out zone of the bolts, the effects of the depth and width of the cut-out zone on the fracture time, fracture force, and fracture area were studied and analyzed. The following conclusions were drawn:  
1. The strength of the cut-out induced bolts need to match the collision dynamics behavior of the coupler. The bolts with excessive strength will prevent the timely disconnection of the coupler from the vehicle, leading to excessive impact acceleration and even climbing phenomena. The bolts with insufficient strength will cause the bolts to fail during the coupler's operation, resulting in too low energy absorption by the coupler and preventing it from effectively absorbing kinetic energy.
2. The simulation results indicate that during the coupler collision process, the peak force generated by the impact causes the cut-out induced bolts to neck, leading to a reduction in bolt strength. In the design of cut-out induced bolts, the influence of the peak impact force on the bolts should be considered, and a certain margin should be left in terms of strength.
3. The experimental design for the cut-out zone structural parameters of the cut-out induced bolts was conducted using the Latin Hypercube method. The Moving Least Squares method was used to fit the fracture force from the simulation results. Additionally, the simulation results were categorized based on the working condition of the expansion tube at the time of bolt fracture, and the decision boundary for the cut-out zone structural parameters was determined using the Random Forest algorithm. Finally, a surrogate model was constructed based on the fitting and classification models, and combined with a genetic algorithm. The following optimal parameters for the cut-out zone of the overload protection bolts were obtained: a width of 17.74 mm and a depth of 1.37 mm. Through structural optimization of the cut-out zone, the cut-out induced bolts' fracture force increased from 1147.5 kN to 1828.44 kN (a 59.34% improvement), with a fracture time extending from 20.9 ms to 69 ms. The structurally optimized cut-out induced bolts enable the coupler to meet the energy absorption requirements for C-II class vehicles specified in EN 15227.  
Methodology, L.Y., S.Y., M.X. and J.X.; Software, S.Y. and M.X.; Validation, F.Z. and J.X.; Formal analysis, L.Y.; Investigation, P.X.; Data curation, L.Y.; Writing--original draft, L.Y.; Writing--review & editing, S.Y., F.Z. and J.X.; Supervision, P.X.; Funding acquisition, P.X. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Natural Science Foundation of China (U24B20121), and the Leading Talents in Science and Technology of Hunan Province (2019 RS3018).  
Not applicable.  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{c c c c c c} \hline  & **Width (mm)** & **Depth (mm)** & & **Width (mm)** & **Depth (mm)** \\ \hline
38 & 13.53 & 2.69 & 77 & 0.99 & 2.53 \\ \hline
39 & 14.53 & 1.39 & 78 & 17.74 & 1.42 \\ \hline \end{tabular}
\end{table}
Table 1: _Cont._