## 5 Conclusions  
This paper presents real-time high-temperature (25, 200, 400, and 600 \({}^{\circ}\)C) cyclic loading and unloading tests on granite under various stress paths. The effects of temperature and cyclic loading-unloading paths on the mechanical properties of granite were analyzed using scanning electron microscopy. The key conclusions are as follows:  
1. As the number of cycles increases, the hysteresis loop of the constant lower limit cyclic loading shifts positively along the strain axis, with its area gradually expanding. Additionally, rising temperatures cause the hysteresis loop to become more sparse. In contrast, throughout the variable lower limit cyclic loading process, the hysteresis loop remains nearly closed, with relatively low energy dissipation, indicating predominantly elastic deformation.
2. Compared to real-time high-temperature uniaxial tests, at temperatures between 25 \({}^{\circ}\)C and 400 \({}^{\circ}\)C, the specimen experiences minimal thermal damage. Under cyclic loading, the strength of the specimens decreased by approximately 15.33 MPa in the uniaxial test. In contrast, under cyclic loading with constant and variable lower limits, the strength increased by 4.99 MPa and 3.42 MPa, respectively, the granite exhibits a \"hardening\" effect. When the temperature reaches 600 \({}^{\circ}\)C, thermal degradation intensifies significantly, weakening the strengthening effect of cyclic loading. Consequently, the specimen's strength decreases rapidly. As temperature increases, the elastic modulus in the constant lower limit cycling mode decreases. In contrast, in the variable lower limit cycling mode, the elastic modulus first increases and then decreases, showing a moderate enhancement at 200 \({}^{\circ}\)C. The peak strain in the variable lower limit cycling mode increases linearly with temperature, whereas, in the constant lower limit cycling mode, it follows a \"U-shaped\" trend.
3. The energy densities of both the constant lower limit and variable lower limit cycles increase continuously with the number of cycles. The energy dissipation ratio in the constant lower limit cycle first decreases and then increases. In contrast, in the variable lower limit cycle, it initially increases, then stabilizes, and finally exhibits a significant rise near failure.
4. At 25 \({}^{\circ}\)C, internal cracks in granite primarily appear as intracrystalline cracks. At 200 \({}^{\circ}\)C, the internal cracks in granite are primarily transgranular and intergranular cracks. At 400 \({}^{\circ}\)C, the internal cracks in granite are primarily intergranular cracks, accompanied by some transgranular cracks. At 600 \({}^{\circ}\)C, under coupled temperature-stress conditions, many granite crystals subjected to cyclic loading and unloading exhibited a pronounced increase in fracture surface damage, accompanied by a significant rise in both the number and width of cracks. Different cyclic loading and unloading modes also influenced the microdamage patterns of the specimens. Crack penetration and crystal fragmentation were more severe and complex in specimens subjected to the variable lower limit cycle than in those under the constant lower limit cycle.  
Conceptualization, F.Z. and C.L.; data curation, C.L.; methodology, F.Z., C.L. and K.L.; software, Y.Z. and S.L.; supervision, M.L.; writing--original draft, F.Z.; writing--review and editing, M.L. All authors have read and agreed to the published version of the manuscript.  
This work was jointly supported by the National Natural Science Foundation of China (Grant No. 51979100).  
Not applicable.  
The raw data supporting the conclusions of this article will be made available by the authors upon request.  
The authors declare no conflicts of interest.