## 3 Experimental Result Analysis
### Energy Density
As the temperature rises from 25 \({}^{\circ}\)C to 200 \({}^{\circ}\)C, microcracks within the rock samples may become more active; however, this increased activity does not typically lead to significant changes in energy accumulation or release. Finally, while temperature variations may induce certain microstructural changes (e.g., accelerated microcrack expansion), the overall damage pattern of crack propagation and accumulation remains largely unchanged in brittle rocks, particularly within the 25-200 \({}^{\circ}\)C range. Unlike plastic materials, brittle materials typically experience sudden failure, with energy dissipation primarily occurring during crack propagation and rock rupture rather than accumulating over time due to temperature variations. Figure 10d depicts the variation in the energy dissipation ratio with the number of cycles during constant lower limit cycling, exhibiting a \"U-shaped\" trend. This trend can be divided into three distinct phases: an accelerated descending phase, a stabilized phase, and a destructive ascending phase. The first two stages correspond to the accelerated descending phase and the stable transition phase, representing the compaction and elastic deformation processes of the specimen. During these stages, the input energy is converted into elastic energy stored within the specimen. The third stage corresponds to the destructive ascending phase. As the loading stress approaches the peak stress, the specimen enters the yielding phase, experiencing fatigue damage under cyclic loading. This leads to accelerated deformation, with a significant portion of the initially stored elastic energy converting into dissipated energy. Consequently, the dissipation ratio increases  
until the granite specimen undergoes catastrophic failure. Additionally, as the temperature increases, the stable transition phase of the specimen gradually shortens. At 600 \({}^{\circ}\)C, the energy dissipation ratio curve exhibits almost no stable transition phase, directly shifting from the first to the third stage, with the dissipation ratio decreasing from 50.00% in the first cycle to 27.12% in the ninth cycle. In contrast, between 25 \({}^{\circ}\)C and 400 \({}^{\circ}\)C, the energy dissipation ratio decreases only slightly, from approximately 23% to 13%. Figure 11 presents the variation curves of variable lower limit cyclic energy density and dissipation energy ratio as a function of the number of cycles under real-time temperature conditions. Overall, the input energy density (Figure 11a), elastic energy density (Figure 11b), and dissipated energy density (Figure 11c) exhibit an increasing trend. From the early to mid-cycle stages, the growth rates of all three energy densities decelerate. However, near failure, the growth rates of input and dissipated energy densities accelerate, whereas that of elastic energy density continues to decline. Although input energy continues to increase, a larger portion is dissipated through irreversible damage. As a result, elastic energy growth becomes limited, leading to a relative slowdown in the increase in elastic energy density. Later in the cycle, the overall structural integrity of the rock sample deteriorated significantly. Cracks begin to interconnect, and extensive shear slip occurs, leading to a sharp rise in dissipated energy density. To sustain further deformation, the loading system must input additional energy, which accelerates the growth of input energy density. As the rock sample approaches its load-bearing limit, its capacity to store elastic energy diminishes, causing the growth of elastic energy density to slow or even plateau. This suggests that, under variable lower limit cyclic loading and unloading, the specimen's capacity to store elastic energy approaches its limit before failure. The rapidly increasing input energy density primarily contributes to crack propagation, ultimately leading to specimen failure.