# Microscopic Investigation of Rate Dependence on Three-Point Notched-Tip Bending Sandstone

Authors: Wenshuai Li; Faiz U. A. Shaikh; Lianguo Wang; Yinlong Lu; Kai Wang; Zhaolin Li
Journal: Shock and Vibration
 (2019)

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## Abstract

The cracking process in rock or concrete is usually characterized by the formation of microcracks that eventually form a propagating macrocrack. A series of three-point bending experiments were performed on sandstone containing Mode I crack under different loading rates. The microscopic monitoring system was established to capture the cracking process at notch tip. The loading rate dependence of microcracking behaviour was analysed based on load-time curves, acoustic emission (AE), microscopic images, and micrograph-based digital image correlation (DIC) technology. Results showed that the specimens underwent a short period of compression and elastic deformation stage under high loading rate, and the peak loads increased with the increase in loading rate. The AE results revealed that the fracturing process can be divided into elastic stage, damage stage, and postpeak stage, and more extensive damage occurred before the peak under low loading rate. It can be observed from microscopic images that the crack was initiated during the elastic stage, which was earlier than that determined from the AE monitoring. In addition, the microcracks were initiated at multiple locations and were mainly located at the interfaces between dense grains under low loading rate, while microcracks were observed inside the grains under high loading rate. Furthermore, the DIC results showed that the crack opening displacement (COD) of 0.6 mm/min at the peak was almost twice than that of 3.0 mm/min. The COD under the same loading rate at the peak can be considered as the material property of sandstone.


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## Body

## 1. Introduction

With increase in demand for resources and energy, the relevant rock engineering activities, such as deep mining and development of geothermal resources, have increased [1–7]. The cracking process in quasibrittle materials such as rocks and concretes in geotechnical engineering is usually characterized by the formation of microcracks that eventually merge and form a propagating macrocrack. Previous studies have shown that, during the cracking process of rock, the local deformation and damage (microcracking) behaviour occurring in the microregion near the crack tip play a decisive role in controlling the macroscopic fracture behaviour [8]. Moreover, in deep mining, crack initiation and propagation due to the mining rate effect cause rib spalling, rock burst, and other disasters [9–11]. Therefore, the research focusing on the cracking process of rock under different loading rates on a microscale is of great significance to better understand rock fracture behaviour and establish fracture mechanical model.Previous studies have focused on the fracture behaviour of rock materials [12]. For example, Muralidhara et al. [13] and Ohno et al. [14] studied the fracture characteristics of concrete and determined the length of fracture process zone and initiation stress using acoustic emission (AE) location or energy. Based on AE locations and electronic speckle pattern interferometry images, Lin et al. [15] quantified the fracture characteristics in sandstone damage zones. For different loading rates, Backers et al. [16, 17] discussed the influence of loading rates on fracture toughness and surface roughness. Wang et al. [18] studied the anisotropic shale tensile failure by performing the Brazilian splitting tests under different strain rates. Mahanta et al. [19] studied the strain rate sensitivity to rock fracture toughness, and the results indicated that, with increasing strain rates, the fracture toughness and tensile strength gradually increased. Previous studies have shown that the parameters of fracture velocity, rock strength, and fracture initiation toughness exhibited significant loading rate dependence [20–24]. However, the conventional monitoring methods, including AE and strain gauge, cannot supply adequate information about crack propagation, which restrict its application.In recent years, digital image correlation (DIC) technology has been widely used to examine the fracture behaviour of quasibrittle materials [25–31]. Based on DIC technology, Lin and Labuz [32] defined the merged position of horizontal displacement contours as the fracture tip. Zhang et al. [33] described the fracture process of specimens using DIC, which was consistent with the AE results. Chen et al. [34] performed the three-point bending (TPB) tests to investigate the fracture parameters, such as crack opening displacement (COD). Due to low requirements for the measuring environment, simple realization, and complete deformation measurements, DIC technology provided a better way to examine crack propagation and rock fracture behaviour.However, experimental investigations of mechanical properties and fracture behaviour of rocks were commonly performed at a macroscopic level [23]. In order to obtain the microcracking and microdeformation characteristics around the crack tip more accurately, combining a microscopic imaging platform with high spatial resolution with the DIC technique is an important trend to further develop rock fracture mechanical experiments [35–37]. Currently, the scanning electron microscope platforms have been used to conduct dynamic in situ detection under external loading [38]. Moreover, the DIC technology has been successfully applied across multiple length scales by generating a suitable speckle pattern at each scale [37, 39]. Nevertheless, due to harsh experimental conditions, there are many problems with the loading, testing, and specimen preparation for such experiments.In this study, a series of TPB fracture experiments under different loading rates were conducted on sandstone containing a Mode I crack using a rigid electrohydraulic servocontrolled loading system. Moreover, a microscopic visualization monitoring system was established to observe the real-time in situ fracture characteristic of large-scale specimen at microscale. After that, quantitative measurements of microcracking and microdeformation behaviours in the microregion were achieved by micrograph-based DIC. Furthermore, the AE system was adopted to analyse the AE behaviour during the experiment. The loading rate dependence of microcracking and microdeformation behaviours was analysed and discussed.


## 2. Specimen Preparation and Experimental Setup

### 2.1. Specimen Preparation

The red sandstone was collected from Junan County, Linyi City, Shandong Province of China. The sandstone belongs to the Wangshi and Qingshan groups of Mesozoic Cretaceous. Table1 presents the detailed information about the tested sandstone. The sandstone was processed into a series of beam specimens with dimensions of 200 mm × 40 mm × 55 mm, as shown in Figure 1. All the specimens were fabricated from a large block of red sandstone. Meanwhile, the surfaces of specimens were polished using fine sand, and the nonparallelism and nonperpendicularity were both less than 0.02 mm. A thin saw blade was used to prefabricate a straight notch at the center of the bottom of the specimen (Mode I in Figure 1). The notch tip was smooth with the height and width of 15 mm and 1 mm, respectively (Figure 1(a)). A two-dimensional Cartesian coordinate system o-xy was established for subsequent analysis and discussion. The origin of the coordinate system was located at the center of the prefabricated notch tip on the specimen surface, whereas the x-axis and y-axis represented the width and height directions of the notch, respectively (Figure 1(a)). The tested sandstone specimens are shown in Figure 1(b). Three tests were repeated for each loading rate to minimize the dispersion of test results caused by the heterogeneity of the sandstone specimen.Table 1
Detailed information of the tested sandstone.
Properties
Parameters
Main mineral components
41.0% feldspar
34.8% debris
12.6% quartz
11.6% agglutinate
Initial porosity
7.3 (±1.1)%
Grain size (mm)
0.1∼0.35, medium-grained
Average density (kg/m3)
2380Figure 1
Preparation of the sandstone specimens for the TPB experiments: (a) schematic of the specimen and (b) the tested sandstone specimens.
(a)
(b)


### 2.2. Experimental Method and Device

The TPB tests were performed under five constant loading rates ofv = 0.6 mm/min (TPB-0.6), 1.0 mm/min (TPB-1.0), 1.4 mm/min (TPB-1.4), 1.8 mm/min (TPB-1.8), and 3.0 mm/min (TPB-3.0) using a rigid electrohydraulic servocontrolled loading system to investigate the effect of loading rate on fracture characteristics of the sandstone specimen. During the tests, the microscopic visualization monitoring system was arranged in front of the specimen (Figure 2(a)). Additionally, a DS2-8B AE monitoring system (Softland Times Scientific & Technology Co., Ltd, China; Figure 2(b)) was used to capture the AE activity inside the specimen during the loading process. The system consisted of AE host, AE sensors, and preamplifiers. The AE sensor had a diameter of 8 mm, and its monitoring frequency range was 100–900 kHz. The AE signals were amplified with the gain of 40 dB in a preamplifier, and the AE preamplifier had the advantages of low noise, wide bandwidth, impact resistance, and small volume. The time parameters for AE waveforms included peak definition time, hit definition time, and hit locking time and were set to be 50, 100, and 100 μs, respectively. In addition, the threshold was set to be 10 mV to avoid the possibility of electronic or environmental noise [40]. A total of two AE sensors arranged around the specimen were directly in contact with the surface of the specimen (Figure 2(a)).Figure 2
Real-time in situ cracking microscopic visualization monitoring system: (a) schematic of the test system, (b) AE monitoring system, and (c) microscopic visualization monitoring system. Note: (1) long working distance microscope, (2) C-mount interface, (3) high-speed video camera, (4) precision electric mobile platform, (5) image acquisition and control system, (6) stepping motor controller, and (7) shock absorbing ground support.The microscopic visualization monitoring system was composed of a long working distance microscope, a high-speed camera, an image acquisition and control system, a precision electric mobile control platform, a shock absorbing ground support, and a lighting source, as shown in Figure2(c). All of the experimental equipment were placed on a shock absorbing ground support to minimize the influence of environmental vibrations on the image acquisition process. The detailed information of the microscopic visualization monitoring system can be found by Lu et al. [40].


### 2.3. DIC Analysis

DIC has the advantages of noncontact measurements and high precision and has been widely used to detect the fracture behaviour of rock and concrete. In this study, a series of micrographs were acquired using the microscopic visualization monitoring system. Then, the DIC technique was applied to accurately analyse the microscopic deformation behaviour in local microregions at notch tip during the loading process. In the DIC calculations, the deformation field in local microregions can be obtained by matching the measurement points of the images before (reference image) and after the deformation (target image) [35, 41], as illustrated in Figure 3.Figure 3
Schematic of the DIC calculation.A square reference subset of (2N + 1) × (2N + 1) pixels, centered at point Px,y, is selected from the reference image. Then, a searching subset (M > N) with the size of (2M + 1) × (2M + 1) pixels is chosen from the target image (Figure 3). Assume that the point P in the reference image with an x- and y-coordinate system is mapped into point P′ in the deformed image, the point P′x,y can be defined using the following equation:(1)x′=x+u+∂u∂xΔx+∂u∂yΔy,y′=y+v+∂v∂xΔx+∂v∂yΔy,where u and v are the displacement components of the subset center point in x and y directions, respectively. Furthermore, Δx and Δy are the distances from point P to subset center point, while ∂u/∂x, ∂u/∂y, ∂v/∂x, and ∂v/∂y are the gradients of displacement components for the subset.The correlation calculation is conducted between the reference subset and each searching subset based on a predefined correlation function. The subset with the maximum correlation coefficient is identified as the location of the target subset. The central pointP′x,y of the target subset (after deformation) can be regarded as the same point as the point P to be measured (before deformation). The zero-mean normalized sum of squared differences correlation criterion is used to evaluate the degree of similarity between the reference subset and the searching subset [41]:(2)CZNSSD=∑x=12N+1∑y=12N+1fx,y−fm∑x=12N+1∑y=12N+1fx,y−fm2−gx′,y′−gm∑x=12N+1∑y=12N+1gx′,y′−gm22,where fx,y is the pixel gray value at coordinates x,y in the reference subset of the reference image and gx′,y′ is the pixel gray value at coordinates x′,y′ in the searching subset of the target image. Furthermore, fm and gm are the mean intensity values of the reference and target subsets, respectively.


## 2.1. Specimen Preparation

The red sandstone was collected from Junan County, Linyi City, Shandong Province of China. The sandstone belongs to the Wangshi and Qingshan groups of Mesozoic Cretaceous. Table1 presents the detailed information about the tested sandstone. The sandstone was processed into a series of beam specimens with dimensions of 200 mm × 40 mm × 55 mm, as shown in Figure 1. All the specimens were fabricated from a large block of red sandstone. Meanwhile, the surfaces of specimens were polished using fine sand, and the nonparallelism and nonperpendicularity were both less than 0.02 mm. A thin saw blade was used to prefabricate a straight notch at the center of the bottom of the specimen (Mode I in Figure 1). The notch tip was smooth with the height and width of 15 mm and 1 mm, respectively (Figure 1(a)). A two-dimensional Cartesian coordinate system o-xy was established for subsequent analysis and discussion. The origin of the coordinate system was located at the center of the prefabricated notch tip on the specimen surface, whereas the x-axis and y-axis represented the width and height directions of the notch, respectively (Figure 1(a)). The tested sandstone specimens are shown in Figure 1(b). Three tests were repeated for each loading rate to minimize the dispersion of test results caused by the heterogeneity of the sandstone specimen.Table 1
Detailed information of the tested sandstone.
Properties
Parameters
Main mineral components
41.0% feldspar
34.8% debris
12.6% quartz
11.6% agglutinate
Initial porosity
7.3 (±1.1)%
Grain size (mm)
0.1∼0.35, medium-grained
Average density (kg/m3)
2380Figure 1
Preparation of the sandstone specimens for the TPB experiments: (a) schematic of the specimen and (b) the tested sandstone specimens.
(a)
(b)


## 2.2. Experimental Method and Device

The TPB tests were performed under five constant loading rates ofv = 0.6 mm/min (TPB-0.6), 1.0 mm/min (TPB-1.0), 1.4 mm/min (TPB-1.4), 1.8 mm/min (TPB-1.8), and 3.0 mm/min (TPB-3.0) using a rigid electrohydraulic servocontrolled loading system to investigate the effect of loading rate on fracture characteristics of the sandstone specimen. During the tests, the microscopic visualization monitoring system was arranged in front of the specimen (Figure 2(a)). Additionally, a DS2-8B AE monitoring system (Softland Times Scientific & Technology Co., Ltd, China; Figure 2(b)) was used to capture the AE activity inside the specimen during the loading process. The system consisted of AE host, AE sensors, and preamplifiers. The AE sensor had a diameter of 8 mm, and its monitoring frequency range was 100–900 kHz. The AE signals were amplified with the gain of 40 dB in a preamplifier, and the AE preamplifier had the advantages of low noise, wide bandwidth, impact resistance, and small volume. The time parameters for AE waveforms included peak definition time, hit definition time, and hit locking time and were set to be 50, 100, and 100 μs, respectively. In addition, the threshold was set to be 10 mV to avoid the possibility of electronic or environmental noise [40]. A total of two AE sensors arranged around the specimen were directly in contact with the surface of the specimen (Figure 2(a)).Figure 2
Real-time in situ cracking microscopic visualization monitoring system: (a) schematic of the test system, (b) AE monitoring system, and (c) microscopic visualization monitoring system. Note: (1) long working distance microscope, (2) C-mount interface, (3) high-speed video camera, (4) precision electric mobile platform, (5) image acquisition and control system, (6) stepping motor controller, and (7) shock absorbing ground support.The microscopic visualization monitoring system was composed of a long working distance microscope, a high-speed camera, an image acquisition and control system, a precision electric mobile control platform, a shock absorbing ground support, and a lighting source, as shown in Figure2(c). All of the experimental equipment were placed on a shock absorbing ground support to minimize the influence of environmental vibrations on the image acquisition process. The detailed information of the microscopic visualization monitoring system can be found by Lu et al. [40].


## 2.3. DIC Analysis

DIC has the advantages of noncontact measurements and high precision and has been widely used to detect the fracture behaviour of rock and concrete. In this study, a series of micrographs were acquired using the microscopic visualization monitoring system. Then, the DIC technique was applied to accurately analyse the microscopic deformation behaviour in local microregions at notch tip during the loading process. In the DIC calculations, the deformation field in local microregions can be obtained by matching the measurement points of the images before (reference image) and after the deformation (target image) [35, 41], as illustrated in Figure 3.Figure 3
Schematic of the DIC calculation.A square reference subset of (2N + 1) × (2N + 1) pixels, centered at point Px,y, is selected from the reference image. Then, a searching subset (M > N) with the size of (2M + 1) × (2M + 1) pixels is chosen from the target image (Figure 3). Assume that the point P in the reference image with an x- and y-coordinate system is mapped into point P′ in the deformed image, the point P′x,y can be defined using the following equation:(1)x′=x+u+∂u∂xΔx+∂u∂yΔy,y′=y+v+∂v∂xΔx+∂v∂yΔy,where u and v are the displacement components of the subset center point in x and y directions, respectively. Furthermore, Δx and Δy are the distances from point P to subset center point, while ∂u/∂x, ∂u/∂y, ∂v/∂x, and ∂v/∂y are the gradients of displacement components for the subset.The correlation calculation is conducted between the reference subset and each searching subset based on a predefined correlation function. The subset with the maximum correlation coefficient is identified as the location of the target subset. The central pointP′x,y of the target subset (after deformation) can be regarded as the same point as the point P to be measured (before deformation). The zero-mean normalized sum of squared differences correlation criterion is used to evaluate the degree of similarity between the reference subset and the searching subset [41]:(2)CZNSSD=∑x=12N+1∑y=12N+1fx,y−fm∑x=12N+1∑y=12N+1fx,y−fm2−gx′,y′−gm∑x=12N+1∑y=12N+1gx′,y′−gm22,where fx,y is the pixel gray value at coordinates x,y in the reference subset of the reference image and gx′,y′ is the pixel gray value at coordinates x′,y′ in the searching subset of the target image. Furthermore, fm and gm are the mean intensity values of the reference and target subsets, respectively.


## 3. Results and Discussion

### 3.1. Load-Time Curve

Figure4 shows the typical load-time (P-t) curves for TPB tests on specimens under different loading rates (0.6, 1.0, 1.4, 1.8, and 3.0 mm/min). The results showed that the P-t curve under different loading rates increased with time, and after reaching the peak value, it decreased with time, leading to strain softening. For TPB-0.6-1, the specimen underwent a long period of compression and elastic deformation. At a high loading rate, the specimen reached the peak load in a relatively short time. The average peak loads under different loading rates are shown in Figure 5. As the loading rate increased, the peak load increased as well.Figure 4
Typical load-time curves for the TPB tests on sandstone specimens under different loading rates.Figure 5
Average peak loads for the TPB tests on sandstone specimens under different loading rates.


### 3.2. AE Behaviour

AE can be used to monitor crack initiation and propagation in rock specimens [42]. Figure 6 shows the typical load-time (P-t) curves together with AE count rate for the loading rates of 0.6, 1.0, 1.4, 1.8, and 3.0 mm/min. During the loading process, AE characteristics for specimens under different loading rates exhibited similar behaviour, which can be divided into three stages, including elastic stage (Stage I), damage stage (Stage II), and postpeak stage (Stage III) (Figure 6). Amongst these, Stage II began at the load, at which the AE signal increased significantly for the first time [43, 44].Figure 6
Typical variation in load and AE count rate with time for TPB tests under different loading rates: (a) 0.6 mm/min, (b) 1.0 mm/min, (c) 1.4 mm/min, (d) 1.8 mm/min, and (e) 3.0 mm/min. I, II, and III represent elastic stage, damage stage, and postpeak stage, respectively.
(a)
(b)
(c)
(d)
(e)For specimen TPB-0.6-1 (Figure6(a)), during Stage I, there were almost no AE events, which indicated that no fracturing occurred (Figure 6(a)). When the specimen was loaded to 79.4% of the Ppeak (Stage II), the AE count rate increased significantly and the microcrack began to appear. During Stage III, the AE events continued to increase rapidly, and the AE activity became significantly intense. The macrocracks appeared during this stage and led to failure of specimens. However, under high loading rate, few AE events occurred before the peak (Figures 6(b)–6(e)), whereas during Stage II, the number of AE events decreased significantly (Figure 6(e)). The results clearly showed that the loading rate significantly affected the damage process.


### 3.3. Crack Initiation and Propagation

In order to visually identify the microscopic fracture characteristics during the loading process under different loading rates, the images of the cracking process captured using the microscopic visualization monitoring system were analysed. Figure7 shows the typical microscopic cracking process under the loading rates of 0.6 mm/min (Figure 7(a)) and 3.0 mm/min (Figure 7(b)). In the figure, the field of view of 0.8 mm × 1.0 mm around the notch tip was selected.Figure 7
Microscopic cracking process with the field of view of 0.8 mm × 1.0 mm around notch tip under the typical loading rates of (a) 0.6 mm/min (TPB-0.6-1) and (b) 3.0 mm/min (TPB-3.0-1) observed using the microscopic visualization monitoring system. “Pre70” denotes the 70% ofPpeak prior to the peak, while “Post90” denotes the 90% of Ppeak after the peak.
(a)
(b)For specimen TPB-0.6-1, it can be observed that, when the specimen was loaded to 70% ofPpeak (Point A in Figure 7(a)), a new crack initiated above the notch tip. This observation implied that the crack initiation load, as determined by the captured microscopic image, was smaller than that determined from the AE results, which was 79.4% of the Ppeak (Point B in Figure 6(a)). Further analysis of the captured microscopic images showed that the microcracks were initiated at multiple locations at the notch tip (Point C in Figure 7(a)). At the peak, a total of three cracks (Crack 1, Crack 2, and Crack 3) appeared in the field of view (Point D in Figure 7(a)). When the load increased to the postpeak stage, Crack 3 opened further, whereas Crack 2 was closed (Point E in Figure 7(a)). These new cracks gradually propagated and coalesced into one main crack (Point F in Figure 7(a)). The main crack propagated further upwards in a zigzag and irregular way, approximately along the loading direction until the specimen failed. It was clear that the propagation of microcracks was not instantaneous, but rather gradual along the regions of weak strength. As revealed by microscopic images in Figure 7(a), specimen failure results of gradual localized deformation took place in the grain boundary of the microstructure (Crack 1 in Point B, Crack 2 in Point C, and Crack 3 in Point D). It can be considered that the stress did not reach the grain strength.For comparison, Figure7(b) shows the microscopic cracking process under the loading rate of 3.0 mm/min. Clearly, the crack was observed at 84% of Ppeak, which was earlier than that determined from the AE results 92.5% of Ppeak (Point D in Figure 6(e)). At the peak, three cracks appeared in the field of view (Crack 1, Crack 2, and Crack 3; Point E in Figure 7(b)). The three cracks at the peak were narrower than those under the loading rate of 0.6 mm/min (Point D in Figure 7(a)). After the peak, the three cracks gradually propagated and connected with each other (Point G in Figure 7(b)). Compared with the specimen TPB-0.6-1, a microcrack was observed inside the grain in the specimen TPB-3.0-1 (Crack 3; Point E in Figure 7(b)). This was due to the reason that microcracks did not have sufficient time to propagate and were forced to propagate along a shorter path with higher resistance under a high loading rate [45, 46].Furthermore, Figure8 shows the typical surface microscopic images at the peak under different loading rates, as observed using the microscopic visualization monitoring system. In this case, the microscopic crack morphologies at the peak under five different loading rates were both irregular. For specimen TPB-0.6-1, the microcracks were formed at multiple locations at the notch tip with a certain width. When the loading rates increased, narrower cracks at the peak were observed. This was because the microcracks did not have sufficient time to fully propagate under a high loading rate, which was accompanied by few AE events before peak (Figure 6). The crack opening width under different loading rates will be quantitatively discussed in Section 3.4. Moreover, it can be observed that these localized microcracks were mainly located at the interfaces between dense grains, especially for low loading rate, whose tortuous propagation was conditioned by the arrangement of grains or weak zones.Figure 8
Typical microscopic failure modes at the peak for five loading rates, as observed using the microscopic visualization monitoring system.Table2 summarizes the crack initiation load ratios of the tested specimens with different loading rates, as obtained from the AE monitoring and the microscopic images. The results showed that the crack initiation loads, determined from the captured microscopic images using the microscopic visualization monitoring system, were smaller than those determined from the AE results. This observation indicated that the microscopic visualization monitoring system can capture more crack initiation information than the AE. Furthermore, the crack initiation load ratio at the peak observed using the microscopic images increased dramatically from the loading rate of 0.6 mm/min to 3.0 mm/min. Compared with the specimen of TPB-0.6, the average value of the crack initiation load ratio with the loading rates of 1.0, 1.4, 1.8, and 3.0 mm/min was increased by ∼2.0, 4.1, 8.8, and 10.1%, respectively. This result can be explained based upon the microscopic damage mechanism. Under the low loading rate, the microcracks were fully propagated, leading to a low initiation load and more AE events before peak (Figure 6(a)). However, under a high loading rate, the microcracks did not have sufficient time to propagate, which brought about a high crack initiation load and few AE events.Table 2
Crack initiation loads of specimens with different loading rates obtained from AE results and microscopic visualization monitoring system.
Specimen no.
AE monitoring
Microscopic monitoring
Experiment (%)
Average (%)
Experiment (%)
Average (%)
TPB-0.6-1
79.4
79.3
64.2
71.3
TPB-0.6-2
76.3
70.5
TPB-0.6-3
82.3
79.1
TPB-1.0-1
91.1
88.0
69.3
72.7
TPB-1.0-2
87.5
75.1
TPB-1.0-3
85.4
73.6
TPB-1.4-1
90.6
90.4
74.8
74.2
TPB-1.4-2
88.8
71.6
TPB-1.4-3
91.8
76.2
TPB-1.8-1
85.2
90.0
81.2
77.6
TPB-1.8-2
89.9
76.4
TPB-1.8-3
91.8
75.3
TPB-3.0-1
92.5
92.1
79.8
78.5
TPB-3.0-2
93.2
80.6
TPB-3.0-3
90.5
75.2


### 3.4. Deformation Characteristics at Notch Tip

Based on the captured microscopic images of specimens, the DIC technique was applied to quantitatively calculate the displacement fields at the notch tip. Figure9 shows the distributions of horizontal incremental displacement at the notch tip for specimen TPB-0.6-1 under different loading levels. A range of 0.8 mm × 1.0 mm ahead of the notch was selected for DIC calculation, as shown in Figure 9. The incremental displacement was calculated based on the comparison of two selected images at different loading levels (i.e., the reference and the target images). For example, “Pre70-Pre79.4” in Figure 9 indicated that the images captured at 70% Ppeak and 79.4% Ppeak were selected as the reference image and the target image for DIC calculation, respectively. It should be noted that the DIC algorithm involved larger computational errors if the displacement increment was large. To avoid computational errors resulting from excessive microdeformation, the horizontal incremental displacement was evaluated under a short loading level, such as “Pre70-Pre79.4” or “Pre90-Pre95” in Figure 9, instead of “Pre70-Pre95.” In addition, Figure 10 presents the total horizontal incremental displacement for specimen TPB-0.6-1 at the notch tip under different loading levels (y = 0 mm above the notch tip). Of course, the total displacements can be obtained by summing all the incremental displacements, as shown in Figure 10.Figure 9
Distributions of horizontal incremental displacement at notch tip for specimen TPB-0.6-1 with the range of 0.8 mm × 1.0 mm based on the DIC calculation obtained from the microscopic images under different loading levels.Figure 10
Variation in total horizontal incremental displacement for specimen TPB-0.6-1 along the liney = 0 mm in Figure 9 under different loading levels.It can be seen from Figure9 that the discontinuous deformation zone at multiple locations at the notch tip was clearly observed during the late elastic stage (“Pre70-Pre79.4” in Figure 9). The contours merged on the side of the notch, at x = 0, y = 0–0.5 mm. During the initial stage of damage, the discontinuous deformation zone coalescence was detected in the DIC calculation region (“Pre85-Pre90” and “Pre90-Pre95” in Figure 9). When the specimen was loaded to 90% Ppeak, a horizontal displacement jump (Figure 10) appeared at the notch tip, which was due to the opening of induced cracking. The crack opening width was 13.85 μm (the horizontal displacement changes from approximately −9.31 μm to 4.54 μm in Figure 10). As the load increased to peak, the displacement discontinuous zone founded by “Pre95-Pre98” and “Pre98-Peak” did not follow the observation obtained from “Pre85-Pre90” and “Pre90-Pre95” (Figure 9). This can be explained that the DIC calculation results reflected the change between the two loading levels. At the peak, the displacement had a larger magnitude of jump and ranged from −23.15 μm to 17.51 μm (a jump magnitude of 40.66 μm). The discontinuous deformation zone obtained from the DIC results was consistent with the microscopic crack morphology (Figure 7(a)).By contrast, Figure11 plots the distributions of horizontal incremental displacement at the notch tip for specimen TPB-3.0-1 under different loading levels. For DIC calculations, a range of 0.6 mm × 0.9 mm ahead of the notch was selected, as shown in Figure 11. Figure 12 shows the variations in horizontal incremental displacement for specimen TPB-3.0-1 at the notch tip under different loading levels (y = 0 mm above the notch tip). In the elastic stage, the deformation discontinuous zone was observed (“Pre65-Pre75” and “Pre65-Pre84” in Figure 11). A horizontal displacement jump, from approximately −4.16 μm to 3.60 μm, as shown in Figure 12 (“Pre65-Pre84”), was detected at the notch tip. The displacement jump zone was 0.16 mm between x = −0.08 mm and x = 0.08 mm. As the test progressed to the peak, the horizontal displacement changed from −11.60 μm to 11.42 μm (crack opening width of 23.02 μm), while the displacement jump zone ranged from x = −0.07 mm to x = 0.08 mm (a jump zone of 0.15 mm). The discontinuous deformation zone and the displacement jump range were both narrow enough. This indicated that the macroscopic cracks had begun to form.Figure 11
Distributions of horizontal incremental displacement at notch tip for specimen TPB-3.0-1 with the range of 0.6 mm × 0.9 mm based on the DIC calculation obtained from the microscopic images under different loading levels.Figure 12
Variation in total horizontal incremental displacement for specimen TPB-3.0-1 along the liney = 0 mm in Figure 11 under different loading levels.Figure13 shows the total incremental CODs at the peak under five loading rates determined from the micrograph-based DIC. In the figure, the total CODs above the notch tip (y = 0 mm) were calculated by summing all the incremental opening displacements from crack initiation to peak. Clearly, the CODs under the same loading rate at the peak were nearly equal, which can be considered as the material property of sandstone. Moreover, the COD under the low loading rate was larger than that of the high loading rate. Compared with the specimen at the loading rate of 0.6 mm/min, the average value of COD at the peak with the loading rates of 1.0, 1.4, 1.8, and 3.0 mm/min was declined by ∼1.8, 2.9, 20.5, and 44.6%, respectively. This can be attributed to the fact that a high loading rate delayed both the microcracking localization and macrocrack propagation, leading to a decrease in the COD at the peak load.Figure 13
The total incremental CODs at the peak under five loading rates determined by DIC.


## 3.1. Load-Time Curve

Figure4 shows the typical load-time (P-t) curves for TPB tests on specimens under different loading rates (0.6, 1.0, 1.4, 1.8, and 3.0 mm/min). The results showed that the P-t curve under different loading rates increased with time, and after reaching the peak value, it decreased with time, leading to strain softening. For TPB-0.6-1, the specimen underwent a long period of compression and elastic deformation. At a high loading rate, the specimen reached the peak load in a relatively short time. The average peak loads under different loading rates are shown in Figure 5. As the loading rate increased, the peak load increased as well.Figure 4
Typical load-time curves for the TPB tests on sandstone specimens under different loading rates.Figure 5
Average peak loads for the TPB tests on sandstone specimens under different loading rates.


## 3.2. AE Behaviour

AE can be used to monitor crack initiation and propagation in rock specimens [42]. Figure 6 shows the typical load-time (P-t) curves together with AE count rate for the loading rates of 0.6, 1.0, 1.4, 1.8, and 3.0 mm/min. During the loading process, AE characteristics for specimens under different loading rates exhibited similar behaviour, which can be divided into three stages, including elastic stage (Stage I), damage stage (Stage II), and postpeak stage (Stage III) (Figure 6). Amongst these, Stage II began at the load, at which the AE signal increased significantly for the first time [43, 44].Figure 6
Typical variation in load and AE count rate with time for TPB tests under different loading rates: (a) 0.6 mm/min, (b) 1.0 mm/min, (c) 1.4 mm/min, (d) 1.8 mm/min, and (e) 3.0 mm/min. I, II, and III represent elastic stage, damage stage, and postpeak stage, respectively.
(a)
(b)
(c)
(d)
(e)For specimen TPB-0.6-1 (Figure6(a)), during Stage I, there were almost no AE events, which indicated that no fracturing occurred (Figure 6(a)). When the specimen was loaded to 79.4% of the Ppeak (Stage II), the AE count rate increased significantly and the microcrack began to appear. During Stage III, the AE events continued to increase rapidly, and the AE activity became significantly intense. The macrocracks appeared during this stage and led to failure of specimens. However, under high loading rate, few AE events occurred before the peak (Figures 6(b)–6(e)), whereas during Stage II, the number of AE events decreased significantly (Figure 6(e)). The results clearly showed that the loading rate significantly affected the damage process.


## 3.3. Crack Initiation and Propagation

In order to visually identify the microscopic fracture characteristics during the loading process under different loading rates, the images of the cracking process captured using the microscopic visualization monitoring system were analysed. Figure7 shows the typical microscopic cracking process under the loading rates of 0.6 mm/min (Figure 7(a)) and 3.0 mm/min (Figure 7(b)). In the figure, the field of view of 0.8 mm × 1.0 mm around the notch tip was selected.Figure 7
Microscopic cracking process with the field of view of 0.8 mm × 1.0 mm around notch tip under the typical loading rates of (a) 0.6 mm/min (TPB-0.6-1) and (b) 3.0 mm/min (TPB-3.0-1) observed using the microscopic visualization monitoring system. “Pre70” denotes the 70% ofPpeak prior to the peak, while “Post90” denotes the 90% of Ppeak after the peak.
(a)
(b)For specimen TPB-0.6-1, it can be observed that, when the specimen was loaded to 70% ofPpeak (Point A in Figure 7(a)), a new crack initiated above the notch tip. This observation implied that the crack initiation load, as determined by the captured microscopic image, was smaller than that determined from the AE results, which was 79.4% of the Ppeak (Point B in Figure 6(a)). Further analysis of the captured microscopic images showed that the microcracks were initiated at multiple locations at the notch tip (Point C in Figure 7(a)). At the peak, a total of three cracks (Crack 1, Crack 2, and Crack 3) appeared in the field of view (Point D in Figure 7(a)). When the load increased to the postpeak stage, Crack 3 opened further, whereas Crack 2 was closed (Point E in Figure 7(a)). These new cracks gradually propagated and coalesced into one main crack (Point F in Figure 7(a)). The main crack propagated further upwards in a zigzag and irregular way, approximately along the loading direction until the specimen failed. It was clear that the propagation of microcracks was not instantaneous, but rather gradual along the regions of weak strength. As revealed by microscopic images in Figure 7(a), specimen failure results of gradual localized deformation took place in the grain boundary of the microstructure (Crack 1 in Point B, Crack 2 in Point C, and Crack 3 in Point D). It can be considered that the stress did not reach the grain strength.For comparison, Figure7(b) shows the microscopic cracking process under the loading rate of 3.0 mm/min. Clearly, the crack was observed at 84% of Ppeak, which was earlier than that determined from the AE results 92.5% of Ppeak (Point D in Figure 6(e)). At the peak, three cracks appeared in the field of view (Crack 1, Crack 2, and Crack 3; Point E in Figure 7(b)). The three cracks at the peak were narrower than those under the loading rate of 0.6 mm/min (Point D in Figure 7(a)). After the peak, the three cracks gradually propagated and connected with each other (Point G in Figure 7(b)). Compared with the specimen TPB-0.6-1, a microcrack was observed inside the grain in the specimen TPB-3.0-1 (Crack 3; Point E in Figure 7(b)). This was due to the reason that microcracks did not have sufficient time to propagate and were forced to propagate along a shorter path with higher resistance under a high loading rate [45, 46].Furthermore, Figure8 shows the typical surface microscopic images at the peak under different loading rates, as observed using the microscopic visualization monitoring system. In this case, the microscopic crack morphologies at the peak under five different loading rates were both irregular. For specimen TPB-0.6-1, the microcracks were formed at multiple locations at the notch tip with a certain width. When the loading rates increased, narrower cracks at the peak were observed. This was because the microcracks did not have sufficient time to fully propagate under a high loading rate, which was accompanied by few AE events before peak (Figure 6). The crack opening width under different loading rates will be quantitatively discussed in Section 3.4. Moreover, it can be observed that these localized microcracks were mainly located at the interfaces between dense grains, especially for low loading rate, whose tortuous propagation was conditioned by the arrangement of grains or weak zones.Figure 8
Typical microscopic failure modes at the peak for five loading rates, as observed using the microscopic visualization monitoring system.Table2 summarizes the crack initiation load ratios of the tested specimens with different loading rates, as obtained from the AE monitoring and the microscopic images. The results showed that the crack initiation loads, determined from the captured microscopic images using the microscopic visualization monitoring system, were smaller than those determined from the AE results. This observation indicated that the microscopic visualization monitoring system can capture more crack initiation information than the AE. Furthermore, the crack initiation load ratio at the peak observed using the microscopic images increased dramatically from the loading rate of 0.6 mm/min to 3.0 mm/min. Compared with the specimen of TPB-0.6, the average value of the crack initiation load ratio with the loading rates of 1.0, 1.4, 1.8, and 3.0 mm/min was increased by ∼2.0, 4.1, 8.8, and 10.1%, respectively. This result can be explained based upon the microscopic damage mechanism. Under the low loading rate, the microcracks were fully propagated, leading to a low initiation load and more AE events before peak (Figure 6(a)). However, under a high loading rate, the microcracks did not have sufficient time to propagate, which brought about a high crack initiation load and few AE events.Table 2
Crack initiation loads of specimens with different loading rates obtained from AE results and microscopic visualization monitoring system.
Specimen no.
AE monitoring
Microscopic monitoring
Experiment (%)
Average (%)
Experiment (%)
Average (%)
TPB-0.6-1
79.4
79.3
64.2
71.3
TPB-0.6-2
76.3
70.5
TPB-0.6-3
82.3
79.1
TPB-1.0-1
91.1
88.0
69.3
72.7
TPB-1.0-2
87.5
75.1
TPB-1.0-3
85.4
73.6
TPB-1.4-1
90.6
90.4
74.8
74.2
TPB-1.4-2
88.8
71.6
TPB-1.4-3
91.8
76.2
TPB-1.8-1
85.2
90.0
81.2
77.6
TPB-1.8-2
89.9
76.4
TPB-1.8-3
91.8
75.3
TPB-3.0-1
92.5
92.1
79.8
78.5
TPB-3.0-2
93.2
80.6
TPB-3.0-3
90.5
75.2


## 3.4. Deformation Characteristics at Notch Tip

Based on the captured microscopic images of specimens, the DIC technique was applied to quantitatively calculate the displacement fields at the notch tip. Figure9 shows the distributions of horizontal incremental displacement at the notch tip for specimen TPB-0.6-1 under different loading levels. A range of 0.8 mm × 1.0 mm ahead of the notch was selected for DIC calculation, as shown in Figure 9. The incremental displacement was calculated based on the comparison of two selected images at different loading levels (i.e., the reference and the target images). For example, “Pre70-Pre79.4” in Figure 9 indicated that the images captured at 70% Ppeak and 79.4% Ppeak were selected as the reference image and the target image for DIC calculation, respectively. It should be noted that the DIC algorithm involved larger computational errors if the displacement increment was large. To avoid computational errors resulting from excessive microdeformation, the horizontal incremental displacement was evaluated under a short loading level, such as “Pre70-Pre79.4” or “Pre90-Pre95” in Figure 9, instead of “Pre70-Pre95.” In addition, Figure 10 presents the total horizontal incremental displacement for specimen TPB-0.6-1 at the notch tip under different loading levels (y = 0 mm above the notch tip). Of course, the total displacements can be obtained by summing all the incremental displacements, as shown in Figure 10.Figure 9
Distributions of horizontal incremental displacement at notch tip for specimen TPB-0.6-1 with the range of 0.8 mm × 1.0 mm based on the DIC calculation obtained from the microscopic images under different loading levels.Figure 10
Variation in total horizontal incremental displacement for specimen TPB-0.6-1 along the liney = 0 mm in Figure 9 under different loading levels.It can be seen from Figure9 that the discontinuous deformation zone at multiple locations at the notch tip was clearly observed during the late elastic stage (“Pre70-Pre79.4” in Figure 9). The contours merged on the side of the notch, at x = 0, y = 0–0.5 mm. During the initial stage of damage, the discontinuous deformation zone coalescence was detected in the DIC calculation region (“Pre85-Pre90” and “Pre90-Pre95” in Figure 9). When the specimen was loaded to 90% Ppeak, a horizontal displacement jump (Figure 10) appeared at the notch tip, which was due to the opening of induced cracking. The crack opening width was 13.85 μm (the horizontal displacement changes from approximately −9.31 μm to 4.54 μm in Figure 10). As the load increased to peak, the displacement discontinuous zone founded by “Pre95-Pre98” and “Pre98-Peak” did not follow the observation obtained from “Pre85-Pre90” and “Pre90-Pre95” (Figure 9). This can be explained that the DIC calculation results reflected the change between the two loading levels. At the peak, the displacement had a larger magnitude of jump and ranged from −23.15 μm to 17.51 μm (a jump magnitude of 40.66 μm). The discontinuous deformation zone obtained from the DIC results was consistent with the microscopic crack morphology (Figure 7(a)).By contrast, Figure11 plots the distributions of horizontal incremental displacement at the notch tip for specimen TPB-3.0-1 under different loading levels. For DIC calculations, a range of 0.6 mm × 0.9 mm ahead of the notch was selected, as shown in Figure 11. Figure 12 shows the variations in horizontal incremental displacement for specimen TPB-3.0-1 at the notch tip under different loading levels (y = 0 mm above the notch tip). In the elastic stage, the deformation discontinuous zone was observed (“Pre65-Pre75” and “Pre65-Pre84” in Figure 11). A horizontal displacement jump, from approximately −4.16 μm to 3.60 μm, as shown in Figure 12 (“Pre65-Pre84”), was detected at the notch tip. The displacement jump zone was 0.16 mm between x = −0.08 mm and x = 0.08 mm. As the test progressed to the peak, the horizontal displacement changed from −11.60 μm to 11.42 μm (crack opening width of 23.02 μm), while the displacement jump zone ranged from x = −0.07 mm to x = 0.08 mm (a jump zone of 0.15 mm). The discontinuous deformation zone and the displacement jump range were both narrow enough. This indicated that the macroscopic cracks had begun to form.Figure 11
Distributions of horizontal incremental displacement at notch tip for specimen TPB-3.0-1 with the range of 0.6 mm × 0.9 mm based on the DIC calculation obtained from the microscopic images under different loading levels.Figure 12
Variation in total horizontal incremental displacement for specimen TPB-3.0-1 along the liney = 0 mm in Figure 11 under different loading levels.Figure13 shows the total incremental CODs at the peak under five loading rates determined from the micrograph-based DIC. In the figure, the total CODs above the notch tip (y = 0 mm) were calculated by summing all the incremental opening displacements from crack initiation to peak. Clearly, the CODs under the same loading rate at the peak were nearly equal, which can be considered as the material property of sandstone. Moreover, the COD under the low loading rate was larger than that of the high loading rate. Compared with the specimen at the loading rate of 0.6 mm/min, the average value of COD at the peak with the loading rates of 1.0, 1.4, 1.8, and 3.0 mm/min was declined by ∼1.8, 2.9, 20.5, and 44.6%, respectively. This can be attributed to the fact that a high loading rate delayed both the microcracking localization and macrocrack propagation, leading to a decrease in the COD at the peak load.Figure 13
The total incremental CODs at the peak under five loading rates determined by DIC.


## 4. Conclusions

In this study, TPB fracture experiments on sandstone containing a Mode I crack were conducted using a rigid electrohydraulic servocontrolled loading system along with the microscopic visualization monitoring system and AE monitoring. The evolution of cracking process at notch tip and loading rate dependence of sandstone microcracking and microdeformation behaviour were analysed and discussed. The following conclusions can be drawn.The peak loads increased with the increase in the loading rate. The sandstone specimens underwent a short period of compression and elastic deformation stage under high loading rate. The microcracks did not have sufficient time to propagate and were forced to propagate along a short path with higher resistance under high loading rate.The AE monitoring results revealed that the fracturing process can be divided into three stages: elastic stage, damage stage, and postpeak stage. More extensive damage occurred before the peak load under low loading rate, indicating that microcracks could fully propagate, leading to a low crack initiation load.The evolution of the cracking process during the whole loading process of specimens was captured using the real-time microscopic visualization monitoring system under different loading rates. The microscopic images revealed that the crack initiated during Stage I, which was earlier than that determined from the AE monitoring. The microcracks initiated at multiple locations at the notch tip and gradually propagated and coalesced into one main crack. These localized microcracks were mainly located at the interfaces between dense grains, especially for low loading rate, whose tortuous propagation was conditioned by the arrangement of grains or weak zones. However, the microcrack was observed inside the grain under high loading rate.The displacement fields at the notch tip were quantitatively calculated using DIC technology at different loading rates. This procedure was based on the comparison of images acquired at different loading levels and provides quantitative descriptions of local responses. The results showed that the discontinuous deformation zone at multiple locations at the notch tip was clearly observed during the late elastic stage, which allowed the evaluation of the impact of material heterogeneity on the strain distribution and localization. As the load increased, the displacement jump range was narrow enough, which was consistent with the real microscopic crack morphology results. The CODs under the same loading rate at the peak can be considered as the material property of sandstone. The average COD at the peak under low loading rate (TPB-0.6) was almost twice than that of high loading rate (TPB-3.0).



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*Source: 4525162-2019-06-02.xml*