Study on the Effect of High Temperature and Cyclic Loading and Unloading Methods on the Mechanical Properties of Granite

Abstract

During the formation of deep rock bodies, such as hot dry rock, they are frequently exposed to high temperatures and repeated stress perturbations. The prolonged interaction of these two factors is a potential cause of deep underground rock instability. To investigate the effects of high temperature and cyclic loading–unloading modes on rock mechanical properties, cyclic tests were conducted on granite under real-time high-temperature conditions using a multifunctional high-temperature testing machine. By comparing uniaxial compression test results with scanning electron microscopy (SEM) observations, the following was found: (1) The uniaxial compressive strength and elastic modulus of granite under real-time high-temperature conditions initially increase and then decrease as the temperature rises, while the peak strain consistently increases with temperature. (2) Under both cyclic loading–unloading modes, the mechanical properties of granite first improve and then deteriorate as the temperature increases. (3) As the temperature rises, microcracks in granite under both cyclic loading–unloading methods evolve from intracrystalline to intergranular cracks. The fracture surfaces of granite exhibit a significant increase in fracture severity, along with a noticeable rise in both the number and width of cracks. Crack propagation and crystal integrity degradation are more severe and complex in specimens subjected to variable lower limit cyclic loading–unloading than in those under constant-limit cyclic loading–unloading. These findings are of significant theoretical value for studying rock stability under simultaneous high-temperature and cyclic stress conditions.

1. Introduction

While hot dry rock (HDR) resources are essential for global energy supply, conventional hydraulic fracturing technology has certain limitations. Firstly, extracting rock with high fracturing pressure is challenging. For instance, in the Pohang project in South Korea, the fracturing pressure of a 4100 m deep HDR reservoir reached 100 MPa [1]. Secondly, conventional hydraulic fracturing struggles to create a complex fracture network, leading to poor connectivity. Under cyclic loading, rocks are susceptible to fatigue damage, leading to strength reduction and the formation of intergranular cracks. To address this issue, researchers have proposed a novel technique: cyclic hydraulic fracturing, also called cyclic soft fracturing (CSS) or fatigue hydraulic fracturing (FHF) [2,3,4,5]. Cyclic hydraulic fracturing employs the “injection-stop” or “high-low-displacement cyclic pumping” method, inducing fatigue damage in reservoir rocks under cyclic loading. This accelerates crack propagation and promotes the formation of fracture networks, thereby enhancing the heat recovery efficiency of the Enhanced Geothermal System (EGS). Cyclic hydraulic fracturing promotes internal crack development in HDR by gradually softening the rock material, thereby enhancing crack propagation and significantly reducing the fracture initiation pressure [6,7]. In summary, conventional hydraulic fracturing typically requires high fracture initiation stresses but achieves high extraction efficiency, whereas cyclic hydraulic fracturing lowers the fracture initiation stress and enhances extraction efficiency in HDR. However, elevated temperatures and repeated loading cycles can accelerate crack propagation in rocks, thereby reducing thermal extraction efficiency and compromising overall project safety. Therefore, studying the mechanical properties of rocks under real-time high-temperature and cyclic loading conditions is crucial for ensuring the safety of deep-earth engineering.

The mechanical behavior of granite at real-time temperatures remains underexplored in the existing research and literature. Current research primarily focuses on two aspects. First, there are studies on the mechanical properties of rocks after exposure to high temperatures or under real-time high-temperature conditions, analyzing the effects of temperature on the physico-mechanical properties of granite, including strength, peak strain, elastic modulus, porosity, and wave velocity. While the mechanical properties of granite after heat treatment have been extensively studied [8,9,10], research on its real-time high-temperature behavior remains limited. In recent years, an increasing number of researchers have investigated the mechanical properties of granite under real-time high-temperature conditions. Ma et al. [11] performed real-time high-temperature triaxial compression tests on granite specimens using a self-developed true triaxial testing system. They found that the mechanical properties of granite initially increased and then decreased with rising temperature, revealing the existence of a critical temperature threshold. Yang et al. [12] developed a fully coupled thermo-mechanical model within the framework of conventional state dynamics. They found that high temperatures induce thermal cracking, causing the rock to transition from a mixed tensile–shear damage mode to a predominantly tensile damage mode and eventually to a purely tensile damage mode as temperature increases. Through triaxial compression tests at both real-time high temperatures and post-heat treatment conditions, Yang et al. [13] found that the elastic modulus of the rock was inversely proportional to temperature. Additionally, the number of cracks in rocks tested at real-time high temperatures was significantly greater than in those tested after heat treatment. Second, there are studies on different loading paths [14,15] and cyclic loading limits [16,17,18,19] for rocks. Yuan et al. [20] conducted graded cyclic loading–unloading tests and observed that, as loading amplitude increased, the hysteresis loop area of the stress–strain curve expanded, and the elastic modulus during loading was greater than during unloading. Jiang et al. [21] performed fatigue tests at varying loading–unloading rates and found that strain was inversely proportional to these rates. The strain exhibited a “U-shaped” trend throughout the cyclic loading–unloading process.

Previous studies have primarily examined the effects of temperature or cyclic loading on the mechanical properties of rocks, while the combined influence of temperature and cyclic stress remains underexplored. However, deep rocks exist in highly complex geological environments and are frequently influenced by temperature and stress variations. This study conducts uniaxial compression tests on granite at different real-time temperatures (25 °C, 200 °C, 400 °C, and 600 °C) and cyclic loading–unloading tests at varying temperatures under both constant and variable lower limits. Additionally, scanning electron microscopy (SEM) is employed to investigate the coupled effects of temperature and stress on the mechanical properties and microcrack evolution of granite. These findings provide valuable insights for related engineering applications.

2. Materials and Methods

2.1. Sample Preparation

The granite rock samples used in this study were sourced from Huangbai Town, Miluo City, Yueyang City, Hunan Province. At room temperature, the rock samples appeared grayish-white, with smooth, flat surfaces, uniform grains, and a natural density of 2.68 g/cm³. The specimens were machined into cylinders of φ38 mm × 76 mm (Figure 1) based on the rock test dimensions recommended by ISRM [22], with their end faces polished to maintain surface flatness within ±0.2 mm. XRD analysis reveals that the granite is primarily composed of quartz (23.16%), plagioclase feldspar (30.37%), potassium feldspar (28.02%), and mica (18.45%). Figure 2 displays an orthogonally polarized microscopic image of the granite, where mica was predominantly located around the feldspar, with a few black holes present in the interior. Quartz and feldspar were distributed in a flaky pattern.

2.2. Experimental Equipment

The test was conducted using a real-time high-temperature electronic universal testing machine, which consists of a loading system, a temperature control system, and a data acquisition system (Figure 2). The reaction frame of the testing apparatus has a maximum load capacity of 300 kN. The relative error in the specimen deformation and moving beam displacement is within ±0.5%, and the test force control rate can be adjusted between 0.5% and 5% FS/s. The high-temperature fixture was made from materials with high rigidity and good linear motion characteristics, ensuring that the overall stiffness requirements were met during the test. The high-temperature furnace can reach a maximum heating temperature of 1200 °C, with temperature control accuracy within ±1 °C. Axial strain was measured using two high-precision differential displacement transducers (LVDTs) with an accuracy of 0.01 mm. During the test, both transducers were installed, and data were collected simultaneously.

The results were then averaged to ensure accuracy and reliability. The tester can perform variable angle shear tests, Brazilian split tests, three-point bending tests, and uniaxial tests under various real-time temperatures, making it a multifunctional device.

2.3. Experimental Procedure

Uniaxial compression tests were conducted at real-time temperatures of 25 °C, 200 °C, 400 °C, and 600 °C. The specimens were placed on the test platform, and the high–low temperature chamber was closed and sealed with high-temperature cotton to prevent heat loss during warming [23]. The wiring was then connected, and circuit safety was verified. The specimen was heated at a rate of 5 °C/min. Upon reaching the target temperature, it was maintained for 2 h to ensure uniform internal heating [24]. After reaching thermal equilibrium, the specimen was loaded at the target temperature using displacement control at a rate of 0.1 mm/min until failure. The basic mechanical parameters of the specimen are presented in

Table 1. Uniaxial compression test results at real-time temperature.

T (°C)	σs (MPa)	εs (10−3)	E (GPa)
25 °C	149.42 ± 12.25	6.53 ± 0.12	31.87 ± 1.40
200 °C	171.64 ± 13.73	6.67 ± 0.11	33.39 ± 1.79
400 °C	134.09 ± 13.34	7.91 ± 0.44	23.20 ± 1.02
600 °C	78.81 ± 2.74	11.63 ± 0.31	8.98 ± 0.33

.

Based on this, cyclic loading and unloading tests with constant and variable lower limits were conducted under high-temperature conditions. The heating method was identical to that of the first set of tests. Once the target temperature was reached, according to the recommendations for rock tests issued by the International Society for Rock Mechanics (ISRM) [22], cyclic loading and unloading tests were performed at a rate of 0.1 mm/min. The two cyclic loading and unloading paths are illustrated in Figure 3. Constant lower limit cyclic loading and unloading: Loading begins at 0 MPa and increases to 10 MPa, followed by unloading to 0 MPa at the same rate, completing one cycle. The target stress for each subsequent loading increased by 10 MPa, while the unloading stress remained at 0 MPa. This process was repeated until specimen failure. Variable lower limit cyclic loading and unloading: The target stress for each loading was identical to that of the constant lower limit test. However, only the first unloading reached 0 MPa. In subsequent cycles, the unloading target was set to the maximum stress achieved in the previous loading, continuing until specimen failure. To minimize errors and ensure test accuracy, three specimens were tested under each condition [25,26].

3. Experimental Result Analysis

3.1. Stress–Strain Curve

Figure 4 and Figure 5 present the stress–strain curves for cyclic loading and unloading under real-time high-temperature conditions, with constant and variable lower limits, respectively. Compared to the uniaxial compression curves, the specimens exhibit greater overall deformation under cyclic loading and unloading conditions. However, the stress path did not alter the overall trend of the stress–strain curve, and the granite specimens still exhibited brittle failure characteristics.

Figure 4 and Figure 5 show that the outer envelope curve of each loading stage in both cyclic methods follows a similar trend to the conventional uniaxial compression curve. Each loading–unloading process intersects the upper stress point of the previous loading curve, indicating that granite specimens exhibit a deformation “memory” effect [27]. At 200–400 °C, the deviation between the outer envelope curves and the uniaxial compression curves in both cyclic methods increases (Figure 4b,c and Figure 5b,c) but gradually converges at 600 °C (Figure 4d and Figure 5d). Additionally, the loading curves in both cyclic methods do not follow the previous unloading path but instead lie above the unloading curve, forming a plastic hysteresis loop [28]. This phenomenon occurs because rock is a natural material that contains defects such as microcracks and pores, resulting in non-ideal elastic behavior. When the rock is loaded to a certain stress level and then unloaded, the unloading curve does not coincide with the original loading curve but lies below it. This mismatch, together with the adjacent reloading curves, forms a closed hysteresis loop [29]. As the number of cycles increases, the hysteresis loops in both cyclic modes gradually shift toward the strain axis, exhibiting a “migration” phenomenon. Simultaneously, the loop area expands, and significant strain accumulation occurs as failure approaches. Notably, the “migration” effect is more pronounced in the constant lower limit cycle, leading to a more distinct hysteresis loop. As the number of cycles in the constant lower limit test increases, internal damage in the rock samples intensifies, leading to a reduction in stiffness. The hysteresis area expands. However, the specimens retain sufficient elastic recovery time, and the deformation is mainly elastic. In the variable lower limit test, the loading and final unloading curves are nearly linear and overlap, forming a nearly closed hysteresis loop. As the number of cycles increases, microcrack propagation and damage occur in the rock samples, causing a slight increase in the hysteresis area. However, the loop remains nearly closed. Due to the relatively high lower limit of stress, the deformation that occurs is difficult to recover, leading to accelerated crack propagation and predominantly plastic deformation. The constant lower limit cycle is primarily associated with elastic deformation and exhibits minimal energy dissipation. In contrast, the variable lower limit cycle is characterized by plastic deformation and results in significant energy dissipation. This observation is consistent with the findings of subsequent studies on energy dissipation [30,31]. With increasing temperature, the initially dense hysteresis loops gradually become more sparse. At 600 °C, individual loop curves become clearly distinguishable (Figure 4d and Figure 5d). High-temperature exposure degrades the mechanical properties of granite, increasing plastic deformation under axial stress. Although the outer envelope curves of both cyclic loading methods follow similar trends, their offset from the uniaxial compression curve differs due to variations in stress paths. The variable lower limit cycle remains closer to the uniaxial compression curve at 200–600 °C.

3.2. Peak Strength

Figure 6 presents the relationship between peak strength and temperature under three different loading methods. The figure shows that, at 25 °C, the strengths under cyclic loading and unloading exceed those under uniaxial compression. This suggests that cyclic loading enhances the rock’s mechanical properties by raising its crack damage threshold, making it harder for pre-existing closed cracks to reopen [32]. Furthermore, the strength in the variable lower limit cycling mode exceeds that in the constant lower limit mode, indicating that a higher stress lower limit enhances the cyclic strengthening effect. At 200 °C, the thermal strengthening effect on granite becomes evident. Compared to room temperature, the specimen strength increased to 171.64 MPa under uniaxial compression (14.87% increase), 167.87 MPa under the constant lower limit (8.58% increase), and 177.63 MPa under the variable lower limit (13.23% increase). The constant lower limit method yielded the lowest strength. This phenomenon can be attributed to the differential thermal expansion of granite minerals, particularly quartz and feldspar, which partially fill pre-existing microcracks. Additionally, the adsorbed water within the rock evaporates or contracts, leading to tighter intergranular contact and, consequently, an increase in peak strength. Thermal hardening effects have begun to emerge [28]. As temperature increases, thermal damage begins to outweigh the thermohardening effect [33]. At 400 °C, the strength under uniaxial compression dropped significantly to 134.09 MPa, falling below its room-temperature value. High-temperature-induced thermal cracks increased specimen fragility; this is consistent with Huang et al. [34]. Although the strength under cyclic loading also declined (to 158.18 and 160.30 MPa), it remained above the room-temperature level. At this stage, cyclic loading mitigated thermal degradation, suppressing microcrack propagation and helping maintain granite’s strength. At 600 °C, thermal damage dominates, causing the strengths under all three loading conditions to drop sharply to similar levels: 78.81, 84.57, and 75.87 MPa, and the reductions were 41.23%, 46.54%, and 52.67%, respectively. This indicates that thermal deterioration intensifies significantly between 400 °C and 600 °C, and fatigue effects begin to manifest at this stage [35]. At this stage, the strength in the variable lower limit cycling mode falls slightly below that of the uniaxial compression test. This indicates that, under the effect of high temperature, the effect of the variable lower limit cycle on the specimen may change from strengthening to fatigue damage [36]; this is consistent with Zhu et al. [37]. When combined with the findings of this study, it suggests that elevated temperatures initiate thermal cracking, while cyclic loading further promotes the formation of pores and microcracks due to fatigue. Ultimately, under temperature–stress coupling, this leads to cumulative fatigue damage and a notable reduction in mechanical strength. At 600 °C, the specimens subjected to the variable lower limit cycle exhibited lower strength than those under the constant lower limit cycle. Because the higher lower stress limit in the variable lower limit cycle continuously subjects the specimens to greater stress, accelerating crack propagation and causing increased damage and weakening of the rock. In contrast, the constant lower limit cycle has a lower stress limit of 0, allowing for sufficient elastic recovery time, which results in more stable crack growth and slower strength degradation.

3.3. Deformation Characteristics

3.3.1. Elastic Modulus

Figure 7 presents the relationship between the elastic modulus of granite and the number of cycles at different temperatures. The dashed segments represent the real-time elastic modulus obtained from uniaxial compression tests at high temperatures. The cyclic loading and unloading modulus of elasticity was calculated using the same method as the uniaxial compression test. Specifically, the slope of the linear segment corresponding to 40–60% of peak stress in each loading cycle was taken as the modulus of elasticity [38]. Under both constant and variable lower limit cyclic loading conditions, the elastic modulus exhibited a three-stage trend as the number of cycles increased. In the first stage (approximately before 4–6 cycles), the specimens experienced low stress levels, causing the native pores and cracks within the rock to compress continuously, resulting in a rapid increase in the elastic modulus. Under the constant lower limit condition, the elastic modulus increased by 14.67, 15.20, 12.02, and 8.87 GPa from 0 to 6 cycles at different temperatures. Under the variable lower limit condition, the increases were 16.96, 20.71, 16.29, and 10.13 GPa, respectively. In the second stage, increasing axial stress caused the initial cracks in the specimens to densify. However, new cracks also formed during unloading, reducing the effect of pore closure and slowing the increase in elastic modulus. In the third stage, during the later phase of cyclic loading and unloading, damage progressively accumulates, gradually reducing the specimen’s bearing capacity and stiffness, ultimately leading to failure.

Comparing Figure 7a,b, each specimen underwent no more than 20 loading cycles before failure, and the elastic modulus under the variable lower limit condition exhibits noticeable fluctuations during loading, unlike the smooth and gradual changes observed under the constant lower limit condition. This fluctuation is attributed to the small-amplitude stress loading amplitude in variable lower limit loading, which prevents sufficient elastic recovery before the next cycle, leading to short-term oscillations in the elastic modulus. The influence of loading stage and temperature varied between the two cycling methods. During the initial loading stage, the elastic modulus increases more rapidly under the variable lower limit cycle than under the constant lower limit cycle at all temperatures. At this stage, the elastic modulus under uniaxial compression test can be reached faster by the variable lower limit cycle than by the constant lower limit cycle. This suggests that small-amplitude stress loading accelerates primary pore closure, resulting in a rapid increase in elastic modulus. In the later stage of cyclic loading, the elastic modulus remains similar under both cycling methods at room temperature. Under the same number of cycles, the elastic modulus under variable lower limit cycling is generally higher than that under constant lower limit cycling. This indicates that, at high temperatures, specimens subjected to variable lower limit cycling exhibit greater resistance to deformation and damage. In the uniaxial constant lower limit cycling test, the elastic modulus decreases with increasing real-time temperature. This occurs because damage accumulation and microcrack expansion progress more slowly under constant lower limit cycling due to the fixed lower limit stress. However, at high temperatures, thermal expansion and crack propagation gradually reduce the elastic modulus. In the variable lower limit cycling test, the elastic modulus first increases from 25 °C to 200 °C and then decreases beyond 200 °C. This trend occurs because the increasing lower limit stress in variable lower limit cycling allows rock specimens to experience higher stress values. Between 25 °C and 200 °C, mineral particles experience volume expansion and intergranular compaction due to thermal and mechanical influences, leading to an initial rise in elastic modulus. However, further temperature increases promote crack propagation and damage, gradually reducing the elastic modulus. The elastic modulus of granite specimens decreases significantly at 600 °C compared to 25–400 °C under both cycling methods. This may be due to the phase transition of quartz from α-phase to β-phase near 573 °C [39], which induces additional thermal microcracks. Additionally, a comparison of the number of cycles in the fatigue degradation stage between the two cycling methods reveals that the degradation of elastic modulus is significantly slower in the variable lower limit cycle. Once the crack of the sample develops to a certain level under constant lower limit cycle loading and unloading, it rapidly experiences damage. In contrast, the specimen subjected to variable lower limit cycle loading enters a damage accumulation stage, where fatigue damage occurs once irreversible deformation reaches a certain level. The number of cycles of the specimen will be gradually shortened with increasing temperature, highlighting the significant impact of temperature on the fatigue properties of rock materials. These variations suggest that both temperature and cycling methods influence the elastic modulus and the physical and mechanical properties of the specimen.

3.3.2. Peak Strain

The peak strain versus temperature curves of the specimens under different loading and unloading methods were derived from the strain data of the cyclic loading and unloading curves at the peak stress point (Figure 8). As shown in the figure, with increasing temperature, the peak strains of the uniaxial compression test, constant lower limit, and variable lower limit cyclic loading and unloading tests all exhibit an increasing trend. Notably, after reaching 400 °C, the magnitude of this upward trend increases substantially: from 7.55‰ to 11.52‰ under uniaxial compression (a 52.58% increase), from 9.33‰ to 14.14‰ under constant lower limit (a 51.55% increase), and from 10.74‰ to 13.16‰ under variable lower limit (a 22.53% increase). At 573 °C, the quartz crystals within the granite undergo a phase change from α-phase to β-phase, resulting in the formation of numerous crystal-penetrating cracks and a sharp increase in the rate of thermal crack generation [40]. Additionally, the peak strains under both constant lower limit and variable lower limit cycles were significantly higher than those observed in uniaxial compression tests at all temperatures, indicating that cyclic loading led to increased internal deformation of the granite specimens.

Observing the peak strain curves under the two loading cycles, it is evident that, as temperature increases, the peak strain of specimens in the variable lower limit cycle follows a steady, linear upward trend. In contrast, the peak strain of specimens under the constant lower limit cycle decreases slightly (by 10.37%) at 200 °C, forming a “U-shaped” trend. This occurs due to thermal expansion at low temperatures, which causes internal cracks in the specimen to close, allowing sufficient time for deformation recovery under the constant lower limit cycle. Under the variable lower limit cycle loading and unloading method, once high temperature and fatigue damage reach a critical level, the specimen at each temperature rapidly exhibits damage responses. The peak strain continues to increase with temperature because the variable lower limit cycle does not allow sufficient elastic recovery time before the next cycle, leading to greater residual deformation.

3.4. Energy Density

Figure 9 presents a schematic diagram illustrating the calculation of the cyclic energy density of the specimen. In the diagram, the area enclosed by the loading curve (OA) and the strain represents the input energy density, while the area enclosed by the unloading curve (BA) and the strain corresponds to the elastic energy density. The dissipated energy density is represented by the area enclosed by the loading curve (OA), the unloading curve (BA), and the strain. The corresponding formula is given as follows:

$$U_I=U_E+U_D$$

(1)

$$U_I={\displaystyle \int {\sigma }_L}\mathrm{d}\epsilon$$

(2)

$$U_E={\displaystyle \int {\sigma }_U}\mathrm{d}\epsilon$$

(3)

where $U_I$ represents the input energy density (MJ·m⁻³), $U_E$ denotes the elastic energy density (MJ·m⁻³), $U_D$ refers to the dissipated energy density (MJ·m⁻³), ${\sigma }_L$ corresponds to the loading section curve (OA), ${\sigma }_U$ represents the unloading section curve (BC), and $\epsilon$ denotes the axial strain.

As cyclic loading and unloading progress, the ratio of dissipated energy to input energy density provides insight into the damage evolution of rock samples. Therefore, the energy dissipation ratio is introduced, defined as the ratio of the dissipated energy of the specimen to the total input energy during each loading cycle [41]. Figure 10 illustrates the variation in constant lower limit cyclic energy density and dissipation ratio with the number of cycles under real-time temperature conditions. As shown in Figure 11, the input energy density (Figure 10a) and elastic energy density (Figure 10b) at each temperature exhibit a nearly linear increase with the number of cycles. In contrast, the dissipated energy density (Figure 10c) rises sharply near failure. This indicates that, during the early to middle stages of cyclic loading, the internal structure of the rock samples primarily undergoes reversible elastic deformation. Microcrack propagation is limited, and both energy input and storage increase steadily, allowing the samples to remain in a relatively stable load-bearing state. As loading cycles progress, microscopic defects accumulate within the rock samples. The number of microcracks increases and eventually coalesces, resulting in enhanced irreversible deformation. Once crack growth reaches a certain level, the rock samples enter a stage of accelerated damage, marked by a sudden increase in dissipated energy density per cycle. Additionally, temperature significantly influences the mechanical behavior of rocks. At elevated temperatures, the bonding forces between mineral grains weaken, and heat-induced cracks form and grow more readily. This accelerates the accumulation of dissipated energy and hastens the destabilization and failure of the rock samples. However, the variations in input, elastic, and dissipation energies at 25 °C under constant lower limit-graded cyclic loading and unloading are relatively minor compared to those at 200 °C, due to three main factors. First, at 25 °C, energy release from crack propagation in rock samples primarily results from brittle failure, leading to instantaneous energy accumulation and release without significant delay. At 200 °C, although crack propagation may be slightly accelerated, the overall brittle failure mechanism remains unchanged, leading to a rapid and instantaneous energy release. Consequently, variations in input, elastic, and dissipation energies remain minimal. Second, as rock samples gradually accumulate damage and develop microcracks during constant lower limit cycling, they retain sufficient elastic recovery time due to the fixed lower limit stress. As the temperature rises from 25 °C to 200 °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 °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 °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 °C and 400 °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. Figure 11d illustrates the variation in the energy dissipation ratio in the variable lower limit cycle as a function of the number of cycles. It can be observed that, as the number of cycles increases, the energy dissipation ratio of the variable lower limit cycle rises rapidly during the first two cycles before stabilizing. As the specimen approaches failure, the energy dissipation ratio rises again. At this stage, microcracks within the specimen begin to coalesce, forming a macroscopic fracture surface. Consequently, the dissipated energy density surges, leading to a substantial increase in the dissipation ratio. Throughout the loading process, the energy dissipation ratio of the constant lower limit cycle remains below 50% and generally decreases as the number of cycles increases. In contrast, after the second cycle, the energy dissipation ratios of the variable lower limit cycles exceed 50%, indicating that an increase in the lower stress limit promotes crack propagation within the specimen, thereby increasing the dissipation ratio. This effect is particularly evident in the 600 °C variable lower limit cycle, where the final energy dissipation ratio reaches 74.08%, indicating that nearly three-quarters of the input energy is dissipated (Figure 11d).

3.5. Microscopic Damage Characteristics

To study the effect of high temperature and cycling mode on the internal microstructure of granite specimens, scanning electron microscopy (SEM) was used to observe the micro-morphology of the granite specimen sections after real-time high-temperature cyclic loading and unloading tests at 500× magnification. Figure 12 presents SEM images of granite specimens under varying temperature and cycling mode conditions. At 25 °C, the microstructures of the specimens in both loading modes were relatively intact, with minimal spalling of rock debris (Figure 12a,e). At this temperature, the grains in the specimens are closely packed, with a more complete microstructure. Cracks are primarily intracrystalline, existing within the mineral grains. These primary cracks cause localized damage, with limited crack propagation. Under variable lower limit loading, the specimens exhibited more intracrystalline cracks and a lower degree of crystal integrity compared to constant lower limit loading. At 200 °C, the specimens primarily exhibited transgranular and intergranular cracks, with a striated slip band appearing under variable lower limit loading (Figure 12f). This behavior is due to the increased strength of granite under this loading mode. High temperatures cause the internal mineral particles to slip more easily under stress. Simultaneously, high temperatures cause some initial microcracks to close, resulting in polygonal cracks around the mineral particles that have not fully formed closed polygons. As the temperature increases to 400 °C, cracks in the specimens are dominated by intergranular cracks, accompanied by transgranular cracks. Locally closed polygonal cracks appear under variable lower limit loading, with more transgranular and intergranular cracks than under constant lower limit loading (Figure 12g). At 600 °C, both cyclic loading and unloading lead to widespread transgranular and intergranular cracks, with many crystals splitting into smaller fragments. The fracture surfaces of granite exhibit a significant increase in fracture severity, along with a noticeable rise in both the number and width of cracks. Crystals under variable lower limit loading and unloading also exhibit localized holes from large cracks (Figure 12d,h).

As shown in Figure 12, most intergranular cracks occur between quartz and feldspar grains at temperatures between 200 °C and 400 °C [42]. This occurs because quartz has a high thermal expansion coefficient, significantly different from other minerals. Under high temperatures, mismatched deformation at quartz boundaries generates local thermal stresses, leading to cracking at crystal junctions [43]. Transgranular cracks primarily develop within feldspar grains due to their lower strength. During testing, feldspar experiences both mechanical stress and thermal expansion, increasing the likelihood of crack initiation and propagation. At 600 °C, mica decomposition and the quartz α-β phase transition cause a sudden volume increase in certain mineral components [39], leading to extensive microcrack formation. The results indicate that temperature significantly influences crack development in granite, while different unloading methods also affect crack formation. As temperature increases, the number, length, openness, and connectivity of granite cracks also increase. Additionally, micro-damage intensifies, with specimens in the variable-lower limit cyclic test exhibiting greater rupture than those in the constant-lower limit cyclic test.

4. Discussion and Analysis

4.1. Mechanical Analysis

Based on previous research and the experiments conducted in this study, the formation mechanism of a complex fracture network in HDR during cyclic hydraulic fracturing can be summarized below (Figure 13).

Thermal stress-induced fracture formation is shown in Figure 13a. HDR is subjected to thermal stress, leading to the volume expansion of internal mineral particles. This expansion generates additional stress, damages the internal structure, and induces the formation of thermal stress cracks. With the “injection-stop” or “high-low-displacement cyclic pumping” of water, there will be cyclic stress on the rock. Coupled thermal and cyclic stress induces crack network formation (Figure 13b). The stress generated under thermal–mechanical coupling exceeds that from thermal or mechanical stress alone, making the rock more susceptible to fatigue damage. As a result, cracks near the wellbore gradually turn, branch, and eventually evolve into a fracture network.

Cyclic hydraulic fracturing primarily relies on thermal–stress coupling to induce fatigue damage in reservoir rock. This process initiates, redirects, and bifurcates fractures, ultimately forming a connected fracture network around the wellbore that enables efficient heat extraction. Overall, damage from cyclic loading and unloading tests is more complex than that from uniaxial compression tests, suggesting that cyclic hydraulic fracturing is more effective in fracture generation than conventional methods and offers broader application potential.

4.2. Limitations of the Present Study

This study provides preliminary insights into the mechanical behavior of granite under real-time high-temperature cyclic loading and unloading conditions. In the future, it can be further supplemented from the following aspects: the absence of confining pressure, rock sample dimensions do not match the engineering scale on site, and the absence of real pore-fluid conditions.

5. Conclusions

This paper presents real-time high-temperature (25, 200, 400, and 600 °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:

• 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.
• Compared to real-time high-temperature uniaxial tests, at temperatures between 25 °C and 400 °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 °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 °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.
• 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.
• At 25 °C, internal cracks in granite primarily appear as intracrystalline cracks. At 200 °C, the internal cracks in granite are primarily transgranular and intergranular cracks. At 400 °C, the internal cracks in granite are primarily intergranular cracks, accompanied by some transgranular cracks. At 600 °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.