## 1 Introduction  
During the production and processing of materials, the presence of machining defects is inevitable. These initial defects often fall into the category of microscopic imperfections that are difficult to observe with the naked eye. The mechanical distribution characteristics near these defects are crucial areas of study, especially in the context of large-scale structures such as mechanical and civil engineering projects. In recent years, there has been a growing body of research dedicated to the study of microdefects in alloys [1; 2; 3; 4]. The research methods for studying microdefects have evolved from classical elastoplastic mechanics theories [5] to numerical approaches such as finite element analysis [6] and extended finite element methods [7]. This evolution has also seen a shift from idealized models to more complex ones [8; 9]. In recent years, with the development of computational materials science, cellular automata [10] and molecular dynamics [11] have gradually been introduced into the study of microdefects. Due to the inherent differences between the microscale and macroscale properties of materials [12; 13; 14], there is currently a lack of comprehensive research that unifies the microscale properties of materials with their macroscopic performance. Molecular dynamics methods, as a numerical method for detailed microscopic modeling at the molecular scale, have recently been widely applied to the research of mechanical properties of different types of crystalline materials [15; 16; 17]. [PERSON] and [PERSON] et al. studied the fatigue mechanical behavior of single magnesium crystals with different orientations using the MD method [18], and then, reviewed atomic simulation studies of microscopic crack extension in nickel and cooper [19]. It was shown that vacancies [20] in the microstructure as well as elemental composition [21] affect the calculation results, and there were potential influence rules among the factors, so the response surface method was used for the analysis. However, due to the huge number of molecular dynamics calculations and high hardware requirements, the orthogonal test method was used for the experimental design in order to reduce the number of simulation tests. Metal structures often operate in complex environments and are subjected to varying temperatures, making it crucial to study their material properties under different temperature conditions. The high-temperature mechanical performance of steel requires extensive consideration [22; 23; 24; 25]. However, previous research has mainly relied on practical macroscopic experiments, and there have been limitations in terms of economic feasibility and the macro-micro coupling perspective. Therefore, there is an urgent need to explore the material properties of carbon steel using molecular dynamics methods. To facilitate broader engineering applications, this paper aims to establish a mathematical model related to temperature, vacancy rate, and carbon content based on molecular dynamics simulation results. Representative volume element, as a commonly used method for the research of the mechanics of inhomogeneous media [26], has been used to study the mechanical properties of multidirectional amorphous polymers using the RVE method by borrowing the continuum mechanics assumption [27], to construct representative volume elements considering inertial forces and body forces at the microscopic scale [28], and to conduct fatigue crack growth research on carbon steel by assessing representative volume elements. Temperature is one of the main factors affecting the mechanical properties of mild steel [29; 30], yet there are few studies on microscopic cracking with coupled temperature-stress fields.