# Damage Characteristics of Thermally Deteriorated Carbonate Rocks: A Review
## 3 Crack Initiation and Propagation
#### 3.3.1 Brittle-Ductile Transition  
Rocks show brittle behavior at ambient conditions, whereas high pressure and temperature shift their behavior from brittle to ductile. During brittle flow, two phenomena are very common (1) slippage and (2) twining. When stress exceeds the critical limit, atoms in the crystal lattice slip on one another. In the case of twining, some portion of the crystal lattice takes up an orientation that is a mirror image of the untwined parent crystal [73; 74; 75]. The stress-strain trend shows that brittle failure of rock exhibits high peak strength at a lower value of axial strain and, after failure stress, immediately reduces to a minimum level. On the other hand, the ductile failure of a rock shows comparatively lower peak strength at a larger value of the axial strain, and, after failure, stress does not drop sharply [76]. In a loaded carbonate rock, the induced time-dependent strain initiates a microcracking event that governs the failure mechanism. The variations in the deformation behavior of limestone and dolostone under varying temperature conditions depend on the loading rate, strain amplitude, mineral composition, and internal defects [77]. Increasing axial stress induces tensile strain, which develops intergranular cracks. These cracks propagate in the direction or at an angle to the deviatoric stress. When crack propagation length becomes equal to the grain size, the coalescence of cracks enhances the stress effect; thus, the rock becomes deteriorated [78]. Therefore, researchers elucidate the rock damage mechanism in terms of micro-fissuring. [PERSON] and [PERSON] [79] explained the deformation behavior of limestone in five typical stages (see Figure 4). The stress-strain curves at ambient temperature and low confining pressures describe the deformation response as follows: stage 1 shows a concave upward gentle slope due to the nonlinear closure of the preexisting cracks. The fragmental length is based on the number of cracks in the rock. Stage 2 exhibits the elastic deformation after the compaction phase. It leads the integrated stress path to a yielding point by considering rock as a continuous medium. Stage 3 illustrates a concave downward slope leading to a threshold point. In this phase, stable microcracks develop and propagate in the direction or at an angle to the deviatoric stress. Preexisting cracks, weak planes, internal defects, and damaged grain boundaries contribute to this phase. Stage 4 depicts the concave downward curve leading to a peak strength point. It deals with the rock internal damage phase where  
Figure 3: Schematic diagram showing crack propagation and its offset around the fossil fragments adapted from [PERSON] et al. [71]. [PERSON] et al. (2007) performed a series of uniaxial compression tests on limestones heated at various temperature ranges (25-800 \({}^{\circ}\)C). As shown in Figure 5, at a temperature window of 25 to 600 \({}^{\circ}\)C, pre-failure stress-strain curves show a very similar kind of trend in their dilation phase, linear-elastic deformation phase, and brittle deformation phase. A nonlinear increment is found in their peak strength, with the rise in temperature up to 600 \({}^{\circ}\)C. Above a temperature of 600 \({}^{\circ}\)C, stress-strain curves give a lower value of peak strength at a comparatively larger value of axial strain, which is a clear indication of plastic deformation. In another study, [PERSON] et al. (2018) performed a triaxial compression test on thermally treated limestones (20-600 \({}^{\circ}\)C) at room temperature and low confining pressure of 15 MPa. The thermally treated samples showed almost the same peak stress before 450 \({}^{\circ}\)C, and, beyond this temperature, abnormal behavior was noted, as shown in the stress-strain curves (see Figure 6). With the increase in temperature, the percentage of strain accumulation also increases, and, at 600 \({}^{\circ}\)C, a limestone sample can endure maximum strain at the cost of minimum peak stress.