# Experimental Study on Nanomechanical Properties of Yunnan Red-Bed Mudstone

Authors: Xian Ye; Yongcai Liu; Haibin Xue; Guo Li; Jin Xing
Journal: Geofluids
 (2022)

---

## Abstract

As a natural building material and building environment, red-bed mudstone has special engineering properties due to its special formation conditions. The engineering disaster caused by these special properties is becoming increasingly prominent. Therefore, it is of great theoretical significance and practical engineering value to study the macro- and micromechanical properties of red-bed mudstone. Nanoindentation mechanical tests are carried out on the red-bed mudstone from Chuxiong, Jingdong, and Nanhua in Yunnan. The microstructure, residual indentation morphology, and nanomechanical parameters of red-bed mudstone in different areas are compared and analyzed. The results show that the load-displacement curves can be divided into four stages, which are the compaction stage, linear elastic stage, holding stage, and unloading stage. Under the same loading and holding time conditions, sample 3 (Nanhua) has the deepest residual indentation, and SEM tests show that the damage to indentation is obvious. Sample 2 (Jingdong) has the shallowest residual indentation. The indentation morphology is complete and the size is small by SEM tests. The residual indentation depth of sample 1 (Chuxiong) is between sample 2 and sample 3. The average elastic modulus of sample 1 (Chuxiong) is38.0±2.29 GPa. The average hardness is 1.36±0.42 GPa, and the fracture toughness is 0.966±0.048 MPa·m0.5. The average elastic modulus of sample 2 (Jingdong) is 40.1±2.03 GPa. The average hardness is 1.71±0.35 GPa, and the fracture toughness is 1.142±0.053 MPa·m0.5. However, the average elastic modulus of sample 3 (Nanhua) is 25.1±2.53 GPa. The average hardness is 0.61±0.21 GPa, and the fracture toughness is 0.507±0.043 MPa·m0.5. Overall, the elastic modulus and the hardness of sample 2 (Jingdong) are the greatest because of its high quartz crystal content. It shows that the nanomechanical properties of red-bed mudstone in Jingdong are better than those in Chuxiong and Nanhua. The results can provide a basis for revealing the regional differences in macroscopic mechanical properties of Yunnan red-bed mudstone.


---

## Body

## 1. Introduction

Yunnan red-bed mudstone is widely used in engineering constructions as natural building material and building environment. Because of the particular formation conditions, it has special engineering properties. With the planning and construction of the Yunnan expressway and railway network, more and more red-bed mudstone engineering disasters are prominent. It is of great significance to understand and master the macro- and micromechanical properties of red-bed mudstone for engineering constructions. At present, the macroscopic mechanical properties of red-bed mudstone are mainly studied by laboratory tests and in situ tests. The microproperty study mainly focuses on the semiquantitative analysis of mineral composition by XRD and the surface morphology by SEM. These studies mainly describe the microphysical properties of red-bed mudstone, but there are relatively few studies on micromechanical indexes.Nanoindentation is one of the important methods for nondestructive testing of material mechanical properties. This technology was first proposed by Kalei in 1968 [1], and the range of mechanical tests is at micro- and nanoscale, providing a possibility for the mineral mechanical test. Through the development of Oliver and Pharr [2], the load-displacement curve of the indentation point can be obtained at micro- and nanoscale, and elastic modulus, hardness, fracture toughness, and other parameters can be obtained to provide convenience for the study of material micro- and nanoproperties. At first, the technology is widely used in metal, film, coating, ceramics, glass, and polymer fields. With the development of microscopic rock mechanics, nanoindentation technology has been applied to study rock mechanical properties. Compared with the macromechanical property test of rock, the advantage of the nanoindentation test is that mechanical parameters can be obtained only with a small sample.The loading rate affects the mechanical behavior of shale in nanoindentation by Shi et al. [3]. The influence of retention time on the hardness, Young’s modulus, and creep characteristics of shale was discussed by Shi et al. [4]. Using nanoindentation technology, shale nanomechanical indexes such as elastic modulus, hardness, and fracture toughness were obtained by Liu et al. [5]. Elastoplastic mechanical properties of mudstone clay minerals and detrital minerals in coal rock mass were analyzed, and the influence of quartz and kaolinite on mechanical properties of coal rock mass was discussed by Sun et al. [6, 7]. Elastic modulus of quartz, feldspar, and mica in granite was obtained, and the macromechanical index of granite was obtained by the scaling upgrade method by Zhang et al. [8]. Based on nanoindentation technology, an estimation model of coal fracture strength was proposed, and fracture energy and fracture zone were estimated by using brittle failure theory and inrush phenomenon on the loading curve by Manjunath and Jha [9]. Mechanical properties of coal samples under the conditions of drying and saturated salt solution were studied through nanoindentation tests. The results were compared with those obtained by the acoustic wave test method, and the limitation of the acoustic wave test method was pointed out by Zhang et al. [10]. Hardness and elastic modulus of shale were analyzed and discussed by using indentation technology, and the relationship between the macroscopic and microscopic mechanical properties was evaluated, and a calculation model for rock mechanical parameters at the nanometer scale was proposed by Chen et al. [11]. Through nanoindentation technology, elastic modulus, hardness, fracture toughness, and other mechanical parameters of bedded shale of Lower Silurian Longmaxi Formation of Youyang area in southeast Chongqing were obtained by Shi et al. [12]. Through nanoindentation technology, the influence of water-rock interaction on shear mechanical properties of granite fractures was studied, and it was found that granite fractures were more likely to be damaged after long-term immersing by Dou et al. [13]. The microscopic mechanical properties of shale taken from Longmaxi Formation in the southern Sichuan area were studied by introducing nanoindentation technology by Liu et al. [14]. A set of nano- and micromechanical data for shale samples was provided to constrain the macroscopic mechanical properties determined by the shale microstructure by Graham et al. [15]. The influence of organic matter on shale mechanical properties was studied by Zhao et al. [16]. At present, there are few studies on the nanomechanical properties of red mudstone.Yunnan red mudstone has the characteristics of low strength, weak permeability, and strong hydrophilicity, and it is easy to disintegrate, weather, and be softened after absorbing water. However, the success rate of macrotest sampling is very low and very difficult. Hence, it is very difficult to prepare samples and control test conditions for laboratory macrotests. The above problems can be avoided to a certain extent by nanoindentation technology from the microscopic point of view. In this paper, nanoindentation technology is used to carry out experimental research on red-bed mudstone from three different areas in Yunnan province. Nanomechanical property indexes of samples from different areas are obtained. Residual indentation morphology of samples from different areas is observed by SEM. Combined with a thin section examination of rock, the relationship between nanomechanical properties and mineral composition of red-bed mudstone in different areas of Yunnan is analyzed. The results provide a theoretical basis for revealing the regional differences in macroscopic mechanical properties of Yunnan red-bed mudstone.


## 2. Basic Principles and Test Procedures of Nanoindentation Technology

### 2.1. Basic Principles of Nanoindentation

The nanoindentation test is a microscopic measurement technique for continuous control and measurement of load and displacement. The mechanical properties such as elastic modulus, hardness, and fracture toughness are measured at the nanoscale by contact mechanics analysis. In the nanoindentation test, the indenter is pressed into the sample gradually, the elastic deformation of the sample near the indenter first occurs, and the plastic deformation of the sample begins to produce with the increase of load. Finally, an indentation matching the indenter shape appears in the sample. The load-displacement curves can be obtained by nanoindentation tests. Mechanical indexes such as elastic modulus and hardness of rock at the microscopic scale can be calculated by the load-displacement curve, as shown in Figure1. The specific calculation method is as follows:
(1)S=dPdhh=hm,H=PmaxAc,Er=π2β⋅SA,1Er=1−ν2E+1−νi2Ei,where P is load (mN), h is indenter displacement (nm), hm is maximum indenter displacement (nm), S is material stiffness (N/m), H is material hardness (GPa), A is contact area (nm2), v is material Poisson’s ratio, Er is reduced modulus (GPa), E is material elastic modulus (GPa), β is a constant related to indenter geometry, Ei is indenter elastic modulus (GPa) and is 1141 GPa, and vi is indenter Poisson’s ratio and is 0.07.Figure 1
Typical load-displacement curve of single nanoindentation.For theBerkovich indenter, the relationship between indenter contact depth and projected area of the contact area is as follows:
(2)Ac=33tan2θ⋅hc2,where θ is the angle between the indenter central axis and the indenter side and is 65.27°. Therefore, Ac=24.56hc2. hc is contact depth, as shown in Figure 2. The specific expression is as follows:
(3)hc=h−εPS,Figure 2
Schematic diagram of loading and unloading process [17].whereε is constant related to indenter shape. For the Berkovich indenter, ε=0.75.


### 2.2. Fracture Toughness Calculation

Fracture toughness (Kc) is the material inherent property and represents the ability to resist crack propagation under external load [18]. It can be calculated with the energy analysis method by using the nanoindentation test. Although the indentation test is a nondestructive test and is used to evaluate elastic properties of materials in most cases, the stress intensity factor at the crack tip reaches the critical value with the increase of load [19]. In other words, there are two situations in the indentation process. One is that there is no microcrack and the whole indentation process is an elastic-plastic deformation process; the other is that cracks continue to initiate and propagate as the load increases.The principle of determining rock fracture toughness with the energy analysis method is as follows.According to Cheng’s theory [18], the total input energy (Ut) is the sum of fracture energy (Uc), plastic energy (Up), and elastic energy (Ue), as shown in Figure 3. Fracture energy can be expressed as follows:
(4)Ut=Uc+Ue+Up,where the relationship between total energy (Ut) and plastic energy (Up) is as follows:
(5)UpUt=1−1−3hp/hm2+2hp/hm31−hp/hm2.Figure 3
Schematic diagram of total energy and unloading energy.The calculation formula of total energy (Ut) is as follows:
(6)Ut=∫0hmPdh.According to linear elastic fracture mechanics, the critical energy release rate (Gc) is the energy released per unit area during the crack propagation process and can be calculated as follows:
(7)Gc=∂Uc∂Ac=UcAmax,where for Berkovich indenter, Amax=24.56hm2.Therefore, the fracture toughness can be expressed as follows:(8)Kc=Gc×Er≈Gc×E1−v2.


### 2.3. Nanoindentation Experimental Equipment

The nanoindentation tests are carried out on the Agilent nanoindenter G200, as shown in Figure4. The maximum load is 500 mN, and the load resolution is 50 nN. The Berkovich indenter is selected for this test. The maximum indenter displacement is 1.5 mm. The maximum indentation depth is 500 μm, and the displacement resolution is 0.01 nm.Figure 4
Agilent nanoindenter G200.


### 2.4. Experimental Procedure

Representative mudstone samples from three regions of Chuxiong, Jingdong, and Nanhua in Yunnan are successively named sample 1, sample 2, and sample 3, as shown in Figure5.Figure 5
Diagram of representative mudstone samples.
(a)
Chuxiong(b)
Jingdong(c)
NanhuaThe indentation area is set as the dot matrix. The dot matrix of Chuxiong (sample 1), Jingdong (sample 2), and Nanhua (sample 3) is10×10, 8×8, and 10×10, respectively. The horizontal and vertical distance of the indentation points is 50 μm. The specific experimental procedure is as follows.


#### 2.4.1. Cutting the Sample

A large red-bed mudstone sample was precisely cut. The irregular red-bed mudstone blocks were cut into thin slices with a thickness of about 5 mm and cross-section of about10mm×10mm.


#### 2.4.2. Polishing the Sample

The samples were polished by using 600-, 800-, 1000-, 2000-, 3000-, 5000-, and 7000-grit paper in sequence. The polishing time for 7000-grit paper was no less than 0.5 hours to ensure that the sample surface was flat and smooth.


#### 2.4.3. Cleaning the Sample

The sample was cleaned ultrasonically with anhydrous ethanol to make the sample surface have no impurities.


#### 2.4.4. Drying the Sample

Finally, the samples were placed in an oven at 50°C for no less than 24 hours to ensure that the sample was completely dry. After that, the sample was stored in an airtight container for later use. The prepared sample of red-bed mudstone is shown in Figure6.Figure 6
Nanoindentation sample.
(a)
Sample 1 (Chuxiong)(b)
Sample 2 (Jingdong)(c)
Sample 3 (Nanhua)


#### 2.4.5. Observing the Sample Surface Microstructure

The sample surface microstructure was observed to find a relatively smooth and flat area. This area should be able to lay a certain number of points evenly to avoid the dense effect.


#### 2.4.6. Loading Stage

The loading-holding-unloading mode was adopted in nanoindentation tests. The maximum load is 100 mN. The loading time and the unloading time are both 15 s. The holding time is 10 s. The load-time curve is shown in Figure7. After setting the parameters, the program was started to do the dots by a nanoindenter. The specific schematic diagram is shown in Figure 8.Figure 7
Load-time curve of nanoindentation.Figure 8
Indentation bitmap.


#### 2.4.7. Processing Data

The experimental data was processed by usingNanosuite software.


## 2.1. Basic Principles of Nanoindentation

The nanoindentation test is a microscopic measurement technique for continuous control and measurement of load and displacement. The mechanical properties such as elastic modulus, hardness, and fracture toughness are measured at the nanoscale by contact mechanics analysis. In the nanoindentation test, the indenter is pressed into the sample gradually, the elastic deformation of the sample near the indenter first occurs, and the plastic deformation of the sample begins to produce with the increase of load. Finally, an indentation matching the indenter shape appears in the sample. The load-displacement curves can be obtained by nanoindentation tests. Mechanical indexes such as elastic modulus and hardness of rock at the microscopic scale can be calculated by the load-displacement curve, as shown in Figure1. The specific calculation method is as follows:
(1)S=dPdhh=hm,H=PmaxAc,Er=π2β⋅SA,1Er=1−ν2E+1−νi2Ei,where P is load (mN), h is indenter displacement (nm), hm is maximum indenter displacement (nm), S is material stiffness (N/m), H is material hardness (GPa), A is contact area (nm2), v is material Poisson’s ratio, Er is reduced modulus (GPa), E is material elastic modulus (GPa), β is a constant related to indenter geometry, Ei is indenter elastic modulus (GPa) and is 1141 GPa, and vi is indenter Poisson’s ratio and is 0.07.Figure 1
Typical load-displacement curve of single nanoindentation.For theBerkovich indenter, the relationship between indenter contact depth and projected area of the contact area is as follows:
(2)Ac=33tan2θ⋅hc2,where θ is the angle between the indenter central axis and the indenter side and is 65.27°. Therefore, Ac=24.56hc2. hc is contact depth, as shown in Figure 2. The specific expression is as follows:
(3)hc=h−εPS,Figure 2
Schematic diagram of loading and unloading process [17].whereε is constant related to indenter shape. For the Berkovich indenter, ε=0.75.


## 2.2. Fracture Toughness Calculation

Fracture toughness (Kc) is the material inherent property and represents the ability to resist crack propagation under external load [18]. It can be calculated with the energy analysis method by using the nanoindentation test. Although the indentation test is a nondestructive test and is used to evaluate elastic properties of materials in most cases, the stress intensity factor at the crack tip reaches the critical value with the increase of load [19]. In other words, there are two situations in the indentation process. One is that there is no microcrack and the whole indentation process is an elastic-plastic deformation process; the other is that cracks continue to initiate and propagate as the load increases.The principle of determining rock fracture toughness with the energy analysis method is as follows.According to Cheng’s theory [18], the total input energy (Ut) is the sum of fracture energy (Uc), plastic energy (Up), and elastic energy (Ue), as shown in Figure 3. Fracture energy can be expressed as follows:
(4)Ut=Uc+Ue+Up,where the relationship between total energy (Ut) and plastic energy (Up) is as follows:
(5)UpUt=1−1−3hp/hm2+2hp/hm31−hp/hm2.Figure 3
Schematic diagram of total energy and unloading energy.The calculation formula of total energy (Ut) is as follows:
(6)Ut=∫0hmPdh.According to linear elastic fracture mechanics, the critical energy release rate (Gc) is the energy released per unit area during the crack propagation process and can be calculated as follows:
(7)Gc=∂Uc∂Ac=UcAmax,where for Berkovich indenter, Amax=24.56hm2.Therefore, the fracture toughness can be expressed as follows:(8)Kc=Gc×Er≈Gc×E1−v2.


## 2.3. Nanoindentation Experimental Equipment

The nanoindentation tests are carried out on the Agilent nanoindenter G200, as shown in Figure4. The maximum load is 500 mN, and the load resolution is 50 nN. The Berkovich indenter is selected for this test. The maximum indenter displacement is 1.5 mm. The maximum indentation depth is 500 μm, and the displacement resolution is 0.01 nm.Figure 4
Agilent nanoindenter G200.


## 2.4. Experimental Procedure

Representative mudstone samples from three regions of Chuxiong, Jingdong, and Nanhua in Yunnan are successively named sample 1, sample 2, and sample 3, as shown in Figure5.Figure 5
Diagram of representative mudstone samples.
(a)
Chuxiong(b)
Jingdong(c)
NanhuaThe indentation area is set as the dot matrix. The dot matrix of Chuxiong (sample 1), Jingdong (sample 2), and Nanhua (sample 3) is10×10, 8×8, and 10×10, respectively. The horizontal and vertical distance of the indentation points is 50 μm. The specific experimental procedure is as follows.


### 2.4.1. Cutting the Sample

A large red-bed mudstone sample was precisely cut. The irregular red-bed mudstone blocks were cut into thin slices with a thickness of about 5 mm and cross-section of about10mm×10mm.


### 2.4.2. Polishing the Sample

The samples were polished by using 600-, 800-, 1000-, 2000-, 3000-, 5000-, and 7000-grit paper in sequence. The polishing time for 7000-grit paper was no less than 0.5 hours to ensure that the sample surface was flat and smooth.


### 2.4.3. Cleaning the Sample

The sample was cleaned ultrasonically with anhydrous ethanol to make the sample surface have no impurities.


### 2.4.4. Drying the Sample

Finally, the samples were placed in an oven at 50°C for no less than 24 hours to ensure that the sample was completely dry. After that, the sample was stored in an airtight container for later use. The prepared sample of red-bed mudstone is shown in Figure6.Figure 6
Nanoindentation sample.
(a)
Sample 1 (Chuxiong)(b)
Sample 2 (Jingdong)(c)
Sample 3 (Nanhua)


### 2.4.5. Observing the Sample Surface Microstructure

The sample surface microstructure was observed to find a relatively smooth and flat area. This area should be able to lay a certain number of points evenly to avoid the dense effect.


### 2.4.6. Loading Stage

The loading-holding-unloading mode was adopted in nanoindentation tests. The maximum load is 100 mN. The loading time and the unloading time are both 15 s. The holding time is 10 s. The load-time curve is shown in Figure7. After setting the parameters, the program was started to do the dots by a nanoindenter. The specific schematic diagram is shown in Figure 8.Figure 7
Load-time curve of nanoindentation.Figure 8
Indentation bitmap.


### 2.4.7. Processing Data

The experimental data was processed by usingNanosuite software.


## 2.4.1. Cutting the Sample

A large red-bed mudstone sample was precisely cut. The irregular red-bed mudstone blocks were cut into thin slices with a thickness of about 5 mm and cross-section of about10mm×10mm.


## 2.4.2. Polishing the Sample

The samples were polished by using 600-, 800-, 1000-, 2000-, 3000-, 5000-, and 7000-grit paper in sequence. The polishing time for 7000-grit paper was no less than 0.5 hours to ensure that the sample surface was flat and smooth.


## 2.4.3. Cleaning the Sample

The sample was cleaned ultrasonically with anhydrous ethanol to make the sample surface have no impurities.


## 2.4.4. Drying the Sample

Finally, the samples were placed in an oven at 50°C for no less than 24 hours to ensure that the sample was completely dry. After that, the sample was stored in an airtight container for later use. The prepared sample of red-bed mudstone is shown in Figure6.Figure 6
Nanoindentation sample.
(a)
Sample 1 (Chuxiong)(b)
Sample 2 (Jingdong)(c)
Sample 3 (Nanhua)


## 2.4.5. Observing the Sample Surface Microstructure

The sample surface microstructure was observed to find a relatively smooth and flat area. This area should be able to lay a certain number of points evenly to avoid the dense effect.


## 2.4.6. Loading Stage

The loading-holding-unloading mode was adopted in nanoindentation tests. The maximum load is 100 mN. The loading time and the unloading time are both 15 s. The holding time is 10 s. The load-time curve is shown in Figure7. After setting the parameters, the program was started to do the dots by a nanoindenter. The specific schematic diagram is shown in Figure 8.Figure 7
Load-time curve of nanoindentation.Figure 8
Indentation bitmap.


## 2.4.7. Processing Data

The experimental data was processed by usingNanosuite software.


## 3. Comparative Analysis of Nanomechanical Properties of Yunnan Red-Bed Mudstone

### 3.1. Result Analysis of Thin Section Examination Test of Red-Bed Mudstone in Different Regions

The thin-section mesostructure of Yunnan red-bed mudstone in three regions is shown in Figure9. It can be found that the clastic rock content of sample 1 (Chuxiong) is 52%, calcite content is 27%, chlorite content is 6%, and clastic crystal quartz content is 15%; quartz crystal content of sample 2 (Jingdong) is 36%, calcite crystal content is 14%, chlorite content is 12%, limonite content is 25%, and chalcedony content is 13%; calcite content of sample 3 (Nanhua) is 34%, clastic rock content is 41%, chlorite content is 6%, clastic crystal calcite content is 6%, and clastic crystal quartz content is 13%.Figure 9
Thin-section mesostructure of Yunnan red-bed mudstone in three regions.


### 3.2. Residual Indentation Morphology Analysis of Red-Bed Mudstone in Different Regions

Comparative analysis of residual indentation morphology of Yunnan red-bed mudstone in the three regions is shown in Figure10. Under the same loading and holding time conditions, sample 3 (Nanhua) has the deepest residual indentation, and SEM tests show that the damage to indentation is obvious. Sample 2 (Jingdong) has the shallowest residual indentation. The indentation morphology is complete and the size is small by SEM tests. The residual indentation depth of sample 1 (Chuxiong) is between sample 2 and sample 3.Figure 10
Comparative analysis of residual indentation morphology of Yunnan red-bed mudstone in the three regions.
(a)
Sample 1 (Chuxiong)(b)
Sample 2 (Jingdong)(c)
Sample 3 (Nanhua)


### 3.3. Analysis of nanomechanical indexes of Red-Bed Mudstone in Different Regions

The nanoindentation load-displacement curves of Yunnan red-bed mudstone samples in three regions are shown in Figure11. It can be seen that the indentation displacement of sample 3 (Nanhua) is the largest and the indentation displacement of sample 2 (Jingdong) is the smallest under the same loading and holding conditions. The nanoindentation displacement-time curves of Yunnan red-bed mudstone samples in three regions are shown in Figure 12. It can be seen that the residual indentation depth of sample 1 (Chuxiong) is 2073.00 nm, the residual indentation depth of sample 2 (Jingdong) is 1540.45 nm, and the residual indentation depth of sample 3 (Nanhua) is 2508.66 nm. It shows that sample 2 (Jingdong) has the best mechanical properties, then sample 1 (Chuxiong), and sample 3 (Nanhua) has the worst.Figure 11
Nanoindentation load-displacement curves of Yunnan red-bed mudstone samples in three regions.
(a)
Sample 1 (Chuxiong)(b)
Sample 2 (Jingdong)(c)
Sample 3 (Nanhua)Figure 12
Nanoindentation displacement-time curves of Yunnan red-bed mudstone samples in three regions.
(a)
Sample 1 (Chuxiong)(b)
Sample 2 (Jingdong)(c)
Sample 3 (Nanhua)The statistical analysis diagrams of elastic modulus and hardness of Yunnan red-bed mudstone in three regions are shown in Figures13 and 14, respectively. It can be seen that elastic modulus and hardness distribution of Yunnan red-bed mudstone in the three regions conform to the normal distribution. Among them, sample 2 (Jingdong) has the smallest elastic modulus distribution span, while sample 1 (Chuxiong) and sample 3 (Nanhua) have larger distribution spans. It is found that the elastic modulus of sample 1 (Chuxiong) is 38.0±2.29 GPa and hardness is 1.36±0.42 GPa, elastic modulus of sample 2 (Jingdong) is 40.1±2.03 GPa and hardness is 1.71±0.35 GPa, and elastic modulus of sample 3 (Nanhua) is 25.1±2.53 GPa and hardness is 0.61±0.21 GPa. Due to the high content of quartz crystal in sample 2 (Jingdong), its mechanical properties are the best.Figure 13
Normal distribution diagrams of elastic modulus of Yunnan red-bed mudstone in three regions.
(a)
Sample 1 (Chuxiong)(b)
Sample 2 (Jingdong)(c)
Sample 3 (Nanhua)Figure 14
Normal distribution diagrams of hardness of Yunnan red-bed mudstone in three regions.
(a)
Sample 1 (Chuxiong)(b)
Sample 2 (Jingdong)(c)
Sample 3 (Nanhua)Through nanoindentation load-displacement curves, fracture toughness of sample 1 (Chuxiong), sample 2 (Jingdong), and sample 3 (Nanhua) is calculated based on the energy analysis method, as shown in Figure15. The average fracture toughness of sample 1 (Chuxiong), sample 2 (Jingdong), and sample 3 (Nanhua) is 0.966±0.048 MPa·m0.5, 1.142±0.053 MPa·m0.5, and 0.507±0.043 MPa·m0.5, respectively. It can be seen that the fracture toughness of minerals with large elastic modulus is relatively large.Figure 15
Fracture toughness distribution of Yunnan red-bed mudstone in three regions.


## 3.1. Result Analysis of Thin Section Examination Test of Red-Bed Mudstone in Different Regions

The thin-section mesostructure of Yunnan red-bed mudstone in three regions is shown in Figure9. It can be found that the clastic rock content of sample 1 (Chuxiong) is 52%, calcite content is 27%, chlorite content is 6%, and clastic crystal quartz content is 15%; quartz crystal content of sample 2 (Jingdong) is 36%, calcite crystal content is 14%, chlorite content is 12%, limonite content is 25%, and chalcedony content is 13%; calcite content of sample 3 (Nanhua) is 34%, clastic rock content is 41%, chlorite content is 6%, clastic crystal calcite content is 6%, and clastic crystal quartz content is 13%.Figure 9
Thin-section mesostructure of Yunnan red-bed mudstone in three regions.


## 3.2. Residual Indentation Morphology Analysis of Red-Bed Mudstone in Different Regions

Comparative analysis of residual indentation morphology of Yunnan red-bed mudstone in the three regions is shown in Figure10. Under the same loading and holding time conditions, sample 3 (Nanhua) has the deepest residual indentation, and SEM tests show that the damage to indentation is obvious. Sample 2 (Jingdong) has the shallowest residual indentation. The indentation morphology is complete and the size is small by SEM tests. The residual indentation depth of sample 1 (Chuxiong) is between sample 2 and sample 3.Figure 10
Comparative analysis of residual indentation morphology of Yunnan red-bed mudstone in the three regions.
(a)
Sample 1 (Chuxiong)(b)
Sample 2 (Jingdong)(c)
Sample 3 (Nanhua)


## 3.3. Analysis of nanomechanical indexes of Red-Bed Mudstone in Different Regions

The nanoindentation load-displacement curves of Yunnan red-bed mudstone samples in three regions are shown in Figure11. It can be seen that the indentation displacement of sample 3 (Nanhua) is the largest and the indentation displacement of sample 2 (Jingdong) is the smallest under the same loading and holding conditions. The nanoindentation displacement-time curves of Yunnan red-bed mudstone samples in three regions are shown in Figure 12. It can be seen that the residual indentation depth of sample 1 (Chuxiong) is 2073.00 nm, the residual indentation depth of sample 2 (Jingdong) is 1540.45 nm, and the residual indentation depth of sample 3 (Nanhua) is 2508.66 nm. It shows that sample 2 (Jingdong) has the best mechanical properties, then sample 1 (Chuxiong), and sample 3 (Nanhua) has the worst.Figure 11
Nanoindentation load-displacement curves of Yunnan red-bed mudstone samples in three regions.
(a)
Sample 1 (Chuxiong)(b)
Sample 2 (Jingdong)(c)
Sample 3 (Nanhua)Figure 12
Nanoindentation displacement-time curves of Yunnan red-bed mudstone samples in three regions.
(a)
Sample 1 (Chuxiong)(b)
Sample 2 (Jingdong)(c)
Sample 3 (Nanhua)The statistical analysis diagrams of elastic modulus and hardness of Yunnan red-bed mudstone in three regions are shown in Figures13 and 14, respectively. It can be seen that elastic modulus and hardness distribution of Yunnan red-bed mudstone in the three regions conform to the normal distribution. Among them, sample 2 (Jingdong) has the smallest elastic modulus distribution span, while sample 1 (Chuxiong) and sample 3 (Nanhua) have larger distribution spans. It is found that the elastic modulus of sample 1 (Chuxiong) is 38.0±2.29 GPa and hardness is 1.36±0.42 GPa, elastic modulus of sample 2 (Jingdong) is 40.1±2.03 GPa and hardness is 1.71±0.35 GPa, and elastic modulus of sample 3 (Nanhua) is 25.1±2.53 GPa and hardness is 0.61±0.21 GPa. Due to the high content of quartz crystal in sample 2 (Jingdong), its mechanical properties are the best.Figure 13
Normal distribution diagrams of elastic modulus of Yunnan red-bed mudstone in three regions.
(a)
Sample 1 (Chuxiong)(b)
Sample 2 (Jingdong)(c)
Sample 3 (Nanhua)Figure 14
Normal distribution diagrams of hardness of Yunnan red-bed mudstone in three regions.
(a)
Sample 1 (Chuxiong)(b)
Sample 2 (Jingdong)(c)
Sample 3 (Nanhua)Through nanoindentation load-displacement curves, fracture toughness of sample 1 (Chuxiong), sample 2 (Jingdong), and sample 3 (Nanhua) is calculated based on the energy analysis method, as shown in Figure15. The average fracture toughness of sample 1 (Chuxiong), sample 2 (Jingdong), and sample 3 (Nanhua) is 0.966±0.048 MPa·m0.5, 1.142±0.053 MPa·m0.5, and 0.507±0.043 MPa·m0.5, respectively. It can be seen that the fracture toughness of minerals with large elastic modulus is relatively large.Figure 15
Fracture toughness distribution of Yunnan red-bed mudstone in three regions.


## 4. Discussion

The relationship between fracture toughness and elastic modulus of red-bed mudstone in three regions is shown in Figure16, respectively. It can be seen that the relationship between fracture toughness and elastic modulus is linear. This is because the increase in elastic modulus can increase ultimate fracture strength, thereby improving fracture resistance [20].Figure 16
Fitting curve of mudstone fracture toughness and elastic modulus.
(a)
Sample 1 (Chuxiong)(b)
Sample 2 (Jingdong)(c)
Sample 3 (Nanhua)Compared with macromechanical indexes, elastic modulus, hardness, and fracture toughness of red-bed mudstone are larger. This is because the size of the indentation head is very small in the nanoindentation test, and the mineral crystals around the indentation act on the indentation head, which is equivalent to the confining pressure effect on the sample in the macrotest. The corresponding mechanical properties under confining pressure will be further studied in subsequent tests.


## 5. Conclusion

With the planning and construction of the Yunnan expressway and railway networks, more and more red-bed mudstone engineering disasters have emerged. Understanding and mastering the macro- and micromechanical properties of red-bed mudstone are of great significance to engineering construction. Taking Yunnan red-bed mudstones in three regions as the research objects, micromechanical parameters of red-bed mudstones were obtained by nanoindentation tests. A comparative analysis of micromechanical properties of red-bed mudstones in different areas in Yunnan was carried out. The main conclusions are as follows:(1)
The average elastic modulus of sample 1 (Chuxiong) is38.0±2.29 GPa. The average hardness is 1.36±0.42 GPa, and the fracture toughness is 0.966±0.048 MPa·m0.5. The average elastic modulus of sample 2 (Jingdong) is 40.1±2.03 GPa. The average hardness is 1.71±0.35 GPa, and the fracture toughness is 1.142±0.053 MPa·m0.5. However, the average elastic modulus of sample 3 (Nanhua) is 25.1±2.53 GPa. The average hardness is 0.61±0.21 GPa, and the fracture toughness is 0.507±0.043 MPa·m0.5(2)
The residual indentation depth of sample 1 (Chuxiong) is about 2000 nm, the residual indentation depth of sample 2 (Jingdong) is about 1500 nm, and the residual indentation depth of sample 3 (Nanhua) is about 2500 nm. It shows that sample 2 (Jingdong) has the best mechanical properties, then sample 1 (Chuxiong), and sample 3 (Nanhua) has the worst(3)
It can be seen from nanomechanical indexes of Yunnan red-bed mudstones in the three regions that three samples are from the center of Yunnan and belong to red-bed mudstones, but the micromechanical properties of them are quite different. Therefore, it can be inferred that there are great differences in macroscopic mechanical properties and reveals the regional differences in the distribution of red-bed mudstone



---

*Source: 6208096-2022-07-07.xml*