Investigation of fracture process zone properties of mode I fracture in heat-treated granite through digital image correlation
Introduction
Rock fractures exhibit a strong nonlinear region around the crack tip [1], [2] commonly known as the fracture process zone (FPZ). The FPZ is made of microcracks, and it disobeys the basic assumptions of linear elastic fracture mechanics. Generally, a rock fracture can be characterized by the cohesive crack model [3], [4], which includes a real and a cohesive crack. The FPZ can be regarded as a cohesive crack on which a distributed cohesive stress that tends to close the zone.
Crack opening displacement (COD) and FPZ length are important material properties in the cohesive crack model. The crack tip opening displacement (CTOD) is defined as the separation between the top and bottom surfaces of a physical crack tip [5], and each type of material exist a critical CTOD [6]. Only when the CTOD reaches this critical value does the crack expand unstably. The CTOD is measured by a linear variable displacement transformer, a clip gauge, an extensometer and Fiber Bragg Grating [7], [8], [9]. The FPZ and crack growth can be estimated by optical and acoustical methods. Wei et al. [10] carried out acoustic emission (AE) tests and finite element simulations on FPZ. The research indicated the presence of a large FPZ at the crack tip of the rock specimen. Labuz et al. [1] used an AE technology to calculate the FPZ length for charcoal granite (approximately 40 mm) and Rockville granite (90 mm). Nasseri et al. [11] also used an AE system and direct optical method to analyze the width of the FPZ of granite. They also studied the microcrack density at the FPZ. Chen et al. [12] constructed a shear test method for examining the shear fracture triggering position and fracture propagation in charcoal granite.
Recent studies have used digital image correlation (DIC) technology to identify the fracture parameters of rock materials with high accuracy [13], [14]. In those studies, a series of digital images of a specimen surface were acquired continuously during experimentation. Images before and after deformation were matched through a correlation algorithm, and the displacement field of the specimen surface was computed [15]. Shah et al. [9] used DIC techniques to compute the surface displacements, COD, crack length and crack tip location of concrete beams. The research found a good correlation between the DIC-computed fracture parameters and their experimental values.
According to Alam et al. [16], the evolution of fracture length exhibited similar trends for both AE and DIC techniques. However, DIC is more helpful in measuring fracture length than AE, because it measures the crack length based on crack openings. Wu et al. [17] found that the FPZ length in concrete increased during crack propagation but decreased after the FPZ had fully developed. Additionally, the FPZ length at the peak load increased with an increase in specimen height. Qing Lin et al. [15], [18] used DIC techniques to compute the CTOD and the FPZ length in sandstone under a three-point bending (TPB) test. At the onset of unstable propagation (peak load), the critical crack tip opening displacement (CTODc) was 45 μm under mixed mode loading and 30 μm under mode I, and the FPZ length was 10–12 mm for the mixed mode and 5–7 mm for mode I. Dong et al. [19] used DIC to investigate the fracture process at rock–concrete interfaces under TPB and the four-point shearing (FPS) of rock–concrete composite beams. They observed that the FPZ length at peak load was far longer for a specimen under FPS than under TPB. Lu et al. [20] proposed a new microscale visualization experimental system for measurement of the microdeformation behavior of specimens during real-time loading. In their research, the calculated localized strain zones from the micrograph-based DIC were narrower than those calculated from the macrograph-based DIC. The average CTODc calculated using the micrograph-based DIC was approximately 1.3 times larger than that calculated using the macrograph-based DIC. Aliabadian et al. [21] used DIC to investigate crack initiation and propagation in Hawkesbury sandstone under the Brazilian test. The results revealed the development of an FPZ on the location of crack initiation prior to the development of a macro-crack. After full development of the FPZ, a large crack was observed.
With the development of hot dry rock (HDR) geothermal energy extraction and high-level radioactive waste disposal, high-temperature rock mechanics has drawn research interest. High temperature triggers thermal cracking of the rock and changes to the internal structure. The physical and mechanical properties of rocks vary with temperature. For example, decreases in elastic modulus and mechanical strength, as well as the increases of permeability are noted with temperature changes [22], [23], [24]. At first, the fracture toughness of a rock in high-temperature environment increased slightly at approximately 100–200 ℃, and then decreased steadily with further increase in the temperature [25], [26], [27]. The influence of thermal treatment on the mode I fracture toughness of rocks was also studied. The toughness increased at approximately 100–150 ℃ when compared with the room temperature, and thereafter decreased with the gradual increase of temperature [28], [29], [30]. Scanning electron microscopy (SEM) images of rocks showed that the microcrack density and structural disintegration of mineral grains increased with temperature. The increasing thermal crack density and pulverization of minerals are the main two mechanisms by which stiffness and toughness of the rocks reduced [28], [29]. Therefore, the FPZ properties of heat-treated rocks change with temperature.
Increased attention has been paid to the study of the FPZ for the following reasons. First, linear elastic fracture mechanics is invalid for rock due to the existence of the FPZ [1], [2]. Second, the relationship between the cohesive stress and COD in the FPZ is usually used to describe the softening behavior of rock and to simulate the crack propagation path in rock using the finite element method [31]. The FPZ properties of rock at room temperature have been systematically studied [1], [7], [8], [10], [11], [12], [15], [18], [19], [20], [21]. Additionally, the effects of temperature on rock fracture toughness and crack growth have been studied [25], [26], [27], [28], [29], [30]. However, the investigations on the FPZ properties of heat-treated granite have been limited. Understanding FPZ properties of heat-treated granite makes it easier to further develop rock fissures and form better channels through pores and cracks in HDR. This improves the heat energy exchange efficiency and facilitates geothermal extraction from HDR.
In this study, a new method based on the displacement field measured by DIC is proposed for the calculation of the FPZ tip location. The FPZ length and COD of heat-treated specimens were measured by TPB. The influence of thermal treatment on the FPZ properties of mode I fracture was analyzed.
Section snippets
Specimen preparation
The granite specimens were collected from Pingyi in the Shandong Province in China. The specimens were in natural water state with a density of 2.71 g/cm3. The uniaxial compressive strength of granite is 160 MPa, and its single axial tensile strength is 17.9 MPa. All specimens were cut from the same block of rock. The specimen was notched at the mid-span with a thin cutting blade of thickness 1.0 mm. The dimensions of the specimen are height H = 40 mm, length L = 180 mm, span S = 160 mm,
Fracture process zone size
Fig. 4 shows the cohesive crack model, including a real crack and an FPZ. Point A is the tip of the FPZ, and point B is its end. From micro-mechanism of fracture propagation, FPZ development was considered as the nucleation and coalescence of microcracks in the vicinity of the crack tip [1], [7]. The location of A changes with loading. Before the peak load, B is located at the notch tip, as shown in Fig. 4a. After the peak load, the location of B changes with loading, as shown in Fig. 4b.
Variation of FPZ length
Ten samples failed to capture the process of crack initiation and propagation by DIC in the experiment. After completion of the experiment, the results from forty specimens were obtained. The FPZ properties of heat-treated granite obtained using the proposed method is shown in Table 1. The FPZ length increased during crack propagation but decreased after the FPZ was fully developed, as shown in Fig. 9. Before the peak load, real crack did not extend, and the FPZ was propagated during the
Conclusions
We proposed a new method for calculating the location of a fracture process zone tip based on a displacement field measured by digital image correlation. The length of the fracture process zone and the crack opening displacement of the thermal treatment granite specimens were measured through three-point bending. Properties of the fracture process zone were significant to understanding of the characteristics of nonlinear fracture mechanics of heat-treated rocks. The influence of thermal
Declaration of Competing Interest
We have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (grant numbers 51504220, U1810104 and 51404161).
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