## 5 Conclusions  
Through molecular dynamics and response surface methodology, we successfully established a mathematical model for the microstructural properties of low-carbon steel. The reliability of the model was validated through variance analysis. We proposed a multi-scale representative volume element method that considers temperature-stress coupling to \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Temperature** & **Maximum Stress** & **Corrected Maximum** & \multirow{2}{*}{\(K_{h}\)} & \multirow{2}{*}{\(K_{w}\)} \\
**(K)** & **(MPa)** & **Stress (MPa)** & & \\ \hline
300 & 1593.2 & 1509.8 & 2.655333333 & 2.516333333 \\ \hline
573 & 2055.6 & 1661.9 & 3.578130168 & 2.892826681 \\ \hline
623 & 2515.7 & 1774.2 & 4.100704179 & 2.89202582 \\ \hline
673 & 2610.8 & 1716.1 & 4.600447569 & 3.023911473 \\ \hline
723 & 2807.4 & 1662.1 & 4.946611693 & 2.928604151 \\ \hline
773 & 2909.2 & 1547.4 & 5.13167875 & 2.729533788 \\ \hline
823 & 3022.5 & 1555.4 & 5.304492804 & 2.72972973 \\ \hline
873 & 2982.7 & 1453.1 & 5.110075554 & 2.489506416 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Boundary defect stress concentration coefficient. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Temperature** & **Maximum Stress** & **Corrected Maximum** & \multirow{2}{*}{\(K_{h}\)} & \multirow{2}{*}{\(K_{w}\)} \\
**(K)** & **(MPa)** & **Stress (MPa)** & & \\ \hline
300 & 1734.3 & 1453.6 & 2.8905 & 2.42266667 \\ \hline
573 & 2503.9 & 2091.5 & 4.092342895 & 3.418321484 \\ \hline
623 & 3389.5 & 2084.1 & 5.906389949 & 3.631658738 \\ \hline
673 & 3589.7 & 2110.1 & 5.832832329 & 3.428659636 \\ \hline
723 & 3821.6 & 2043 & 6.211761646 & 3.320763304 \\ \hline
773 & 3975.3 & 1972.7 & 6.4680041 & 3.209677682 \\ \hline
823 & 4047.2 & 1888.8 & 6.621402745 & 3.090162459 \\ \hline
873 & 4024.7 & 1778.7 & 6.698566982 & 2.960404773 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Center defect stress concentration coefficient. address stress redistribution caused by material size effects. In this study, we focused on two microcrack scenarios, namely, material boundary cracks and material center cracks, and investigated their stress distributions. This research also considered the coupling effects of temperature and stress, as well as the material size effect, and made corrections to the stress concentration factor of microcracks. It is worth noting that, when considering the size effect, the corrected stress concentration factor under high-temperature loads is significantly smaller than the uncorrected results. With increasing temperature loads, the correction effect becomes more pronounced. Under normal temperature conditions, traditional calculation methods are effective for micro-stress calculations in engineering applications. However, at high temperatures, it is necessary to consider the size effect for correction. The results of this study provide valuable insights into the high-temperature mechanical behavior of low-carbon steel materials. And useful references are also provided for future engineering applications. The proposed approach and models can be employed for material design optimization and crack analysis to ensure material performance stability under various temperatures and loads. Data curation, A.W. ; Funding acquisition, S.L., Y.G. and A.W. ; Methodology, S.L. and Y.G. ; Software, S.L. ; Writing--Original Draft, S.L. ; Writing--Review and Editing, A.W. and Y.H. All authors have read and agreed to the published version of the manuscript. This research was funded by the Shanxi Provincial Natural Science Foundation, China (grant number 20210302123217), the Innovation Project Fund for Graduate Students of Shanxi Province, China (grant number 2023 KY639), the Research Project Supported by the Shanxi Scholarship Council of China (grant number 2020-124), the Innovation Project Fund for Graduate Students of Taiyuan University of Science and Technology, China (grant number BY2022014), and the Scientific Research Project of the China Three Gorges Corporation (grant number Z212202019). Not applicable.