Available via license: CC BY 4.0
Content may be subject to copyright.
Citation: Yang, L.; Mao, Y.; Yang, D.;
Han, Z.; Li, S.; Cai, J.; He, M. The
Characteristic and Distribution of
Shale Micro-Brittleness Based on
Nanoindentation. Materials 2022,15,
7143. https://doi.org/10.3390/
ma15207143
Academic Editor: Xiaoyan Li
Received: 19 August 2022
Accepted: 4 October 2022
Published: 13 October 2022
Publisher’s Note: MDPI stays neutral
with regard to jurisdictional claims in
published maps and institutional affil-
iations.
Copyright: © 2022 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
materials
Article
The Characteristic and Distribution of Shale Micro-Brittleness
Based on Nanoindentation
Liu Yang 1,2 , Yuting Mao 1,2 , Duo Yang 1,2 , Zhenchuan Han 1,2, Sheng Li 3, Jianchao Cai 4 ,*
and Manchao He 1,2
1State Key Laboratory for GeoMechanics and Deep Underground Engineering,
China University of Mining and Technology, Beijing 100083, China
2School of Mechanics and Civil Engineering, China University of Mining and Technology,
Beijing 100083, China
3Research Institute of Exploration and Development, Xinjiang Oilfield Company, PetroChina,
Karamay 834000, China
4State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum,
Beijing 102249, China
*Correspondence: caijc@cup.edu.cn
Abstract:
Shale is a special kind of rock mass and it is particularly important to evaluate its brit-
tleness for the extraction of gas and oil from nanoporous shale. The current brittleness studies are
mostly macro-evaluation methods, and there is a lack of a micro-brittleness index that is based on
nanoindentation tests. In this paper, nanoindentation tests are carried out on the surface of shale
to obtain mechanical property, and then a novel micro-brittleness index is proposed. Drawing a
heat map by meshing indentation, the distribution characteristics of the brittleness index for the
surface of shale and the variation laws between the mineral and brittleness index are explored. The
results showed that the dimensionless brittleness index involved parameters including indentation
irreversible deformation, elastic modulus, hardness and fracture toughness. The micro-brittleness
index of the shale ranged from 7.46 to 65.69, and the average brittleness index was 25.837. The
brittleness index exhibited an obvious bimodal distribution and there was great heterogeneity on the
surface of shale. The crack propagation channels were formed by connecting many indentation points
on the shale surface with high brittleness. The total brittleness index of quartz minerals was high, but
the cementation effect with different minerals was various. Although the general brittleness of clay
was low, the high brittleness index phenomenon was also exhibited. Studying the micro-brittleness
of shale provides a more detailed evaluation for the shale friability, which is used to determine the
optimal shale oil and gas recovery regime.
Keywords: shale; nanoindentation; brittleness index; friability
1. Introduction
With the development of advanced hydraulic fracturing and horizontal drilling tech-
nologies, the exploration and development of shale gas reservoirs has achieved great
success. Shale is a special rock material including multi-component minerals, widely
developed pores, fractures and bedding, which is liable to break and muddy [
1
,
2
]. In
previous studies, a complete shale core was required to obtain macroscopic mechanical
parameters to study the evaluation of shale brittleness. However, due to the fragility of
deep shale in the coring process, the existing brittleness evaluation methods for shale have
many shortcomings [
3
]. In recent years, many advances have been made in nanoscale
microscopic damage indentation experiments to measure micro-mechanical parameters.
Compared with conventional macroscopic experiments, the tested samples in nanoinden-
tation experiments are smaller and easier to obtain, which gives much convenience in
mechanical experiments [4–6].
Materials 2022,15, 7143. https://doi.org/10.3390/ma15207143 https://www.mdpi.com/journal/materials
Materials 2022,15, 7143 2 of 19
The brittleness of shale is a key factor that determines the failure characteristics of shale
under cyclic loading. By concluding all brittleness index evaluation methods in previous
research, four kinds of typical evaluation methods can be obtained. The first is related to the
mechanical strength parameter, i.e., the uniaxial compressive strength and tensile strength
are referred to give the ratio of both. The higher the ratio, the more brittle the rock [
7
–
10
].
The second is based on the stress–strain curve of the rock [
11
–
14
]. The third method uses
elastic parameters such as elastic modulus and Poisson’s ratio to evaluate rock brittleness.
The development of this method based on elastic constants generally assumes that a greater
elastic modulus and a smaller Poisson’s ratio favor fracturing, hence indicating a higher
brittleness of the rock [
15
–
17
]. In the fourth method, the mineral composition evaluation
method is introduced, and the ratio of the weight and volume fraction of the component
minerals that are beneficial to brittle failure to the component minerals is used as the
brittleness index in the hydraulic fracturing of shale gas reservoirs [
18
–
20
]. In addition to
the above, other evaluation methods such as abnormal logging data and changes in the
prominence of the internal friction angle are also used to evaluate shale brittleness [
21
,
22
].
Nanoindentation tests are popular in evaluating the local mechanical property of ma-
terial and are widely used in analyzing the local mechanical characteristics of geomaterial
or rock materials [
23
–
25
]. The influence of total organic carbon (TOC) and clay on the
mechanical properties of shale are explored by conducting nanoindentation tests, and it
can be found that with an increase in the TOC and clay, the elastic modulus decreases
gradually. The increasing thermal maturity of the TOC will induce the rising of the elas-
tic modulus [
26
]. The increasing TOC will result in the strength of the anisotropy of the
shale [
27
]. For the study of the variations among elastic modulus E, hardness Hand fracture
toughness K
c
, it can be found that an increasing tendency is exhibited between K
c
and E,
and the linear variation is obtained between Eand H[
28
]. In addition to the above studies,
the creep behaviors of shale and the effect of temperature and supercritical CO
2
on the
mechanical properties of shale are investigated [29,30].
However, most of the current research focuses on the brittleness evaluation for the
macro-parameters of shale, and the brittleness evaluation for the micro-parameters of shale
is rare by using nanoindentation method. This paper takes the shale of the second member
of the Paleogene Kongdian Formation in the Cangdong Sag, Bohai Bay Basin as the research
object. In this study, the micro-mechanical properties of shale are investigated by conduct-
ing nanoindentation tests, and a reasonable micro-brittleness index is proposed. Through a
series of scanning electron microscope (SEM) and quantitative mineral evaluation tests, the
changes in the brittleness index and mineral composition distribution were analyzed, and
the distribution changes in the shale surface brittleness index were further analyzed.
2. Methodology
2.1. Geological
The Bohai Bay Basin is a petroliferous basin in eastern China. In recent years, the
exploration of shale oil in the Cangdong Sag of the Bohai Bay Basin (Figure 1) has achieved
tremendous breakthrough [
31
]. The Cangdong Sag is located in the middle of the Bohai
Bay Basin, between the Cangdong and Xuxi faults in both the east and west direction,
with the Kongdian and Dongguang bulges retaining the Sag in the south–north direction.
Additionally, it is a secondary structure unit in the Huanghua depression of the Bohai Bay
Basin, with an area of about 1800 km
2
. During the sedimentation of the Second Member
of Kongdian Formation (EK
2
), the lake basin of the Cangdong Sag covered a large area.
Controlled by the EK
2
trough, an oil-bearing system with EK
2
as the source rock and
multiple sets of Kongdian Formation as reservoirs has formed.
Materials 2022,15, 7143 3 of 19
Figure 1. Geographical location and geological structure of Cangdong Sag.
2.2. Sample
The sample in this paper was taken from the shale in the middle ring zone in the
trough area. The shale in this area is mainly composed of quartz, carbonate minerals and
clay minerals. The tested shale sample was mixed, curing with an epoxy resin and a curing
agent whose size was set as a length of 5 mm, width of 5 mm and thickness of 3 mm. Then,
the cured samples were polished by using the polished section with 15
µ
m, 9
µ
m, 3
µ
m
and 0.5
µ
m to ensure the smoothness of the sample, as displayed in Figure 2. Finally, the
sample was placed on the sample table of the multifunctional ion thinning instrument for
argon ion polishing. To obtain the mineral component of the shale sample, the shale sample
in the same position was extracted to make experimental powder, which was performed by
X-ray diffraction (XRD).
Figure 2.
Schematic diagram of sample acquisition: (
a
) full diameter core, (
b
) shale rock sample for
nanoindentation, (c) schematic diagram of grid indentation.
2.3. Experimental Method
2.3.1. X-ray Diffraction (XRD)
The crushed samples were mixed with ethanol, hand ground and then smear mounted
on glass slides for XRD. The experiments were conducted on a LECO C-S diffractometer
(Leco Company, St. Joseph, MI, USA) using Co K
α
-radiation produced at 45 kV and 35 mA.
The diffracted beam was measured with a scintillation detector with a counting time of
20 s for each step of 0.02
◦
2
θ
. Diffract grams were recorded from 2
◦
to 76
◦
2
θ
. By further
analyzing the crystalline content of the shale, it had a specific X-ray diffraction pattern, and
the content of various minerals inside the sample could be obtained by analyzing the peak
intensity of the X-ray diffraction pattern.
Materials 2022,15, 7143 4 of 19
2.3.2. Mineral Petrological Detection
QEMSCAN is the abbreviation of a comprehensive automatic mineral petrological
detection method and the full name is quantitative evaluation of minerals by SCANning
electron microscopy. QEMSCAN became a registered trademark of the FEI in 2009. A
quantitative mineralogical analysis was provided by the QEMSCAN evaluation system (FEI
Company, Hillsboro, OR, USA). This scan evaluation was characterized by Quanta 650F and
energy-dispersive X-ray spectroscopy (EDS). This combination performs a mineralogical
analysis of the sample by scanning the surface of the sample. QEMSCAN determines the
mineralogical composition of the test sample by scanning the surface of the epoxy block in
raster mode (one pixel at a time) as it scans the minerals. The specific steps are: First, the
elemental characteristics of the pixels are determined using an EDS spectrometer (Nippon
PIGAKV Motor Co., Ltd., Tokyo, Japan) and are compared with a proprietary database of
known minerals to determine the mineral characteristics. The analysis of one pixel takes
about two to four milliseconds, and over a million pixels can be mapped per hour. The
resolution of the analysis can vary between 1
µ
m and 2 mm. After the mineralogy of each
pixel is determined, all pixel information is combined to generate an image for quantitative
mineralogy analysis.
2.3.3. SEM
The SEM test was performed with a Japanese JEOL JSM-7800F field emission scanning
electron microscope (Nippon PIGAKV Motor Co., Ltd., Tokyo, Japan), which consists
of a vacuum system, an electron optical system and an imaging system. The electron
optical system captures the scanning electron beam and serves as the excitation source
for physical signal generation. The minimum resolution is 3 nm, and the magnification is
4~100,000 times
. In addition, the energetic incident electrons bombarding the surface of the
material are emitted from the electron optical system, and the back-reflected electrons and
diffraction of the X-rays generated by this process are received and imaged by the probe.
2.4. Nanoindentation Technique
2.4.1. Principle
During the nanoindentation test, the variations between load and displacement can be
obtained by controlling the loading head load sample with the high-precision sensor. As
shown in Figure 3a, nanoindentation includes three stages, i.e., the loading, keep loading
and unloading stage. Elastoplastic deformation appears in the loading stage, and the
loading increases with an increase in pressed depth. The influence of the sudden change
in loading on mechanical parameters can be removed in the keep loading stage. In the
unloading stage, with the decreasing loading, the pressed depth will have part recovery,
which is assumed as elastic deformation and is used to calculate the mechanical property
of the pressed point.
2.4.2. Experimental Program
To ensure the most valuable indentation size, the initial indentation test was performed
before conducting a nanoindentation test of shale. As shown in Figure 3b, in order to
analyze the mechanical properties of a single mineral, the maximum indentation loading,
loading/unloading rate and holding time in this text were set as 500
µ
N, 100
µ
N/s and
5 s
, respectively. Due to the strong heterogeneity of the sample surface, a large number of
indentation points were applied with the grid indentation method, which makes it easy to
conduct a statistical analysis on the micro-mechanical properties of the samples. As shown
in Figure 2c, four indentation grids were set for comparative analysis. In each indentation
grid, the distance between the indentation points was 100
µ
m, and each indentation grid
contained 10 ×10 indentation points.
Materials 2022,15, 7143 5 of 19
Figure 3.
Nanoindentation experiment process: (
a
) schematic diagram of loading and unloading,
(b) schematic
illustration of indentation load-displacement curve. Pis the loading stress; S is the
contact stiffness; W
p
is plastic energy; Ws is elastic energy; W
c
is D-value between plastic energy and
pure plastic energy.
2.4.3. Calculation Method of Brittleness Index
The displacement–loading curve corresponds to each indentation point. As shown
in Figure 3b, h
max
represents the maximum indentation depth, h
f
is the indentation depth
after absolute unloading, h
s
and h
c
are the unrecoverable deformation depths at the edge of
the indentation and at the center of the indentation, respectively.
The Oliver and Pharr method was introduced to calculate the Hand Eof shale [32].
The Hcan be obtained by:
H=Pmax
Ac(1)
where P
max
is the maximum loading, N; and A
c
is contacting area, m
2
. For the ideal Bose
indenter, it can be obtained by:
Ac=24.5hc2(2)
Ecan be calculated by:
Er=√πS
2β√Ac
(3)
Materials 2022,15, 7143 6 of 19
where Sis the contact stiffness that is the slope of the initial unloading stage,
β
is the
parameter related to the shape of the indenter and the βof the ideal indenter is 1.034.
Kcis calculated by the energy method [33]:
Kc=pGcEr(4)
where Eris the modified elastic modulus, GPa; and Gcis the critical energy release rate.
In the calculation of G
c
, the total energy in the indentation deformation is composed
of elastic energy and plastic energy, and the plastic energy consists of pure plastic energy
and the energy induced by fracture.
W=We+Wp=We+Wpp +Wf(5)
where W
f
represents the energy used to result in a fracture in the indentation defor-
mation, and W
pp
is pure plastic energy. Based on above research, it can be obtained
(Cheng et al. 2002):
Wpp
W=1−[1−3(hf/hmax)2+2(hf/hmax )2
1−(hf/hmax)2](6)
Then,
Gc=∂Wf
∂Ac
=Wf
Ac(7)
In the fracture mechanic, the K
c
can be determined by the length of the crack that re-
sulted from residual indentation under set loading, which is shown as follows
(Lee et al. 2012):
Kc=Pmax
l3/2 ∏(E
H,v,φ,l
hc
)(8)
where lis the length of the crack, vis Poisson’s ratio and
φ
is the shape parameter of
the indenter:
Kcl3/2
Pmax
=∏(E
H,v,φ,l
hc
)(9)
Substituting Equations (1) and (2) to Equation (9) yields:
Kcl3/2
H·Ac
=Kcl3/2
H·24.5h2
c
=∏(E
H,v,φ,l
hc
)(10)
Kc
H·l1/2 =∏(E
H,v,φ,hc
l)(11)
K2
c
H2·l·H
E=K2
c
HEl =∏(v,φ,hc
l)(12)
Then, the B1can be regarded as:
B1=HEl
K2
c
(13)
In the nanoindentation test, the length of the crack can be tested with a high precision
electronic scanner, and the grid indentation results in a great deal of experimental work.
Hence, the length of crack lis replaced by h
s
, which is the test data directly from the
indentation experiment:
hs=εPmax
S(14)
Materials 2022,15, 7143 7 of 19
The horizontal projection of the deformation caused by the indentation at the edge is
the crack length l. Due to the geometric similarity between hsand l, it can be obtained:
hs∝l(15)
So, the brittleness index Bis defined by:
B=HEhs
K2
c
(16)
Substituting Equations (1), (4) and (7) to Equation (16) yields:
B=EHhs
Kc2=EhsPmax/Ac
EWf/Ac
=Pmax hs
Wf
=2Ws
Wf
(17)
where W
s
is the elastic recoverable energy of the contacting area of the indenter. The
W
s
/W
f
represents the size of the friability of the indentation point, which further proves
the applicability of B.
3. Results
3.1. Mineralogy Information
In order to obtain the mineral component of the shale sample, the XRD tests were
performed on the fragments within the experimental shale sample. As shown in Table 1,
the mineral component of shale was composed of quartz, potash feldspar, plagioclase,
calcite, dolomite, clay minerals, pyrite and illite.
Table 1. Mineralogical composition of shale sample.
Mineral Composition Content/%
Quartz 12.5
K-Feldspar 3.0
Plagioclase 21.9
Calcite 23.2
Dolomite 25.9
Pyrite 1.4
Illite 7.34
Kaolinite 0.3
Chlorite 0.68
Kaolinite–montmorillonite 3.78
It should be noted that the proportion of carbonate minerals was 49.1% and accounted
for the largest part. There are two traditional shale brittleness assessment methods based
on mineral composition. The carbonate mineral was regarded as the brittleness mineral
and the carbonate mineral was eliminated from the evaluation of brittleness. In this test,
the micro-mechanical property was directly used to evaluate the brittleness of the shale.
3.2. Mineral Petrological Detection
As shown in Figure 4, the surface of shale mostly consisted of dolomite particles,
scattered quartz particles and feldspar. The grains were filled with clay containing illite,
chlorite and a small amount of biotite, which corresponded to the results of the XRD tests.
In grid 1, the quartz, feldspar, carbonate rock mineral and clay mineral content were 13.79%,
14.09%, 48.16% and 17.43%, respectively. In grid 2, the quartz, feldspar, carbonate rock
mineral and clay mineral content were 9.52%, 14.38%, 50.72% and 18.53%, respectively. In
grid 3, the quartz, feldspar, carbonate rock mineral and clay mineral content were 12.49%,
16.31%, 47.26% and 17.43%, respectively. In grid 4, the quartz, feldspar, carbonate rock
mineral and clay mineral content were 8.43%, 17.3%, 51.52% and 15.37%, respectively.
Among the four grids, the quartz content in grid 1 was the largest, which was 5.36% higher
Materials 2022,15, 7143 8 of 19
than that in grid 4. Grid 4 had the highest feldspar content, which was 3.21% higher than
grid 1 with the lowest feldspar content. The carbonate mineral content was the highest in
grid 4, which was 4.26% higher than that in grid 3. The highest clay mineral content in
grid 2 was 3.16% higher than that in grid 4. The difference in mineral content in the four
grids was less than 6%, but the distribution of minerals was different, which resulted in the
variations in the micro-properties of the shale.
Figure 4.
Mineral distribution under QEMSCAN: (
a
) nanoindentation grid 1, (
b
) nanoindentation
grid 2, (c) nanoindentation grid 3, (d) nanoindentation grid 4.
3.3. SEM
Figure 5shows the SEM images of the shale samples under different horizons, with
magnifications of 1200
×
, 2000
×
, 5000
×
and 8000
×
times, respectively. At 1200 magnifica-
tion, the mineral particles were scattered on the surface of the shale, along with sporadic
organic matter. In addition, the obvious micro-pores and pores formed after mineral exfoli-
Materials 2022,15, 7143 9 of 19
ation could be seen. When the magnification was 2000
×
times, the mineral contour was
clear, and the clay minerals filled in the middle of the mineral particles could be observed
clearly. The micro-pores in the clay minerals were more obvious, making the clay minerals
honeycomb. When the magnification was 5000
×
times, the mineral shape was clearer.
Combined with the mineral distribution obtained by QEMSCAN, the square dolomite
particles could be clearly identified, but quartz, feldspar and other particles could not be
identified in this mode. In addition to the initial pores on the surface of the shale, there were
also many pores caused by the whole or partial exfoliation of massive minerals. Beyond
that, there were also microscopic fissures developed at the edges of the mineral grains and
pores throughout the mineral grains. At 8000 magnifications, the bonds between minerals
could be seen more clearly. In the middle of the lumpy mineral grains, clay minerals and
organic matter filled them.
Figure 5.
SEM images in different fields of shale: (
a
) 1200
×
magnification, (
b
) 2000
×
magnification,
(c) 5000×magnification, (d) 8000×magnification.
3.4. Analysis of Load–Displacement Curves
Each indentation point corresponds to a loading–displacement curve, which represents
the mechanical behavior of the mineral composition at the indentation point. Under
nanoindentation loading, the displacement loading curve presented a similar shape. As
shown in Figure 6, the displacement increased gradually with the increasing load in the
loading stage. During the keep loading stage, the displacement continued to increase.
The elastic deformation recovered and left residual deformation h
f
in the unloading stage.
Materials 2022,15, 7143 10 of 19
Under the same loading rate and peak load, the trends of the displacement load curves
were roughly similar. However, the curve was slightly different due to diversity minerals,
and the mechanical parameters were obtained through the analysis of the curve. Among
the four grids, the maximum residual indentation depths were 260 nm, 328 nm, 325 nm and
286 nm, respectively, and the minimum residual indentation depths were 50 nm, 52 nm,
45 nm and 48 nm, respectively. It can be seen that h
max
varied greatly, which owed to
the different mineral compositions and shale micro-structures. The obvious “pop in” and
“elbow” phenomena can be seen in curves, and the phenomenon of “pop in” was relatively
common. Such a sudden increase in displacement may have resulted from the micro- and
nanoscale pores. These may have been original or may have been micro-cracks produced
by the indenter in pressing. “Pop in” mostly occurred at the indentation points with a
large indentation depth, and the indentation points were mostly clay minerals. It can be
seen from the SEM in Section 3.3 that there were many micro-pores developed in the clay
minerals. When the indenter met these pores in the process of pressing, displacement
mutation occurred. The elbow phenomenon occurred during the unloading process and
was characterized by abrupt changes in the unloading slope. The occurrence of this
phenomenon may have been the result of the phase transitions that occurred in the slow
lifting of the indenter. This phenomenon can be explained by SEM in Section 3.3, and on the
plane, the clay minerals were used as substrates to fill between the large grains. However,
in the longitudinal direction, when the indenters experienced a transition from matrix to
brittle minerals in the unloading process, the “elbow” phenomenon occurred. It is worth
noting that the indentation size was smaller than the grain size of the mineral, and the
“elbow” phenomenon mostly appeared in grids 3 and 4.
Figure 6.
Load–displacement curve: (
a
) nanoindentation grid 1, (
b
) nanoindentation grid 2, (
c
) nanoin-
dentation grid 3, (
d
) nanoindentation grid 4. Blue represents high elasticity and red represents low
elasticity.
3.5. Mechanical Properties
The micro-mechanical properties of the shale were obtained by a series of nanoinden-
tation experiments, i.e., E,Hand K
c
. To better analyze the relationships among E,Hand K
c
,
the analysis of the normal distribution on these were conducted by Equation (18).
yE=A
√2πσ exp"−1
2x−µ
σ2#(18)
Materials 2022,15, 7143 11 of 19
where
σ
is standard deviation and represents the amplitude of the distribution of data and
µ
is the mathematical expectation and characterizes the position of the normal distribution
of the data.
3.5.1. Elastic Modulus
The frequency distribution of Eis displayed in Figure 7and the fitting correlation coef-
ficients of grid 1, 2, 3 and 4 were 0.6759, 0.5786, 0.6218 and 0.5106, respectively. The varying
ranges of Eof grid 1, 2, 3 and 4 were 3.58~12.07 GPa, 4.45~14.24 GPa,
3.82~16.48 GPa
and
2.74~17.16 GPa, respectively. The mean elastic modulus
E
of the four grids were 8.24, 8.54,
10.92 and 10.82 GPa, respectively, and the corresponding mathematical expectations were
8.24, 8.54, 11.14 and 10.95, respectively. It can be seen that the indenters varying from 7 to
10 GPa of Eaccounted for 52% in grid 1 and that
E
was the greatest in grid 3. However, the
variance of grid 4 was much higher than that of grid 3, which can be accounted for with
the discrete data in grid 4.
Figure 7.
Frequency distribution histogram of elastic modulus. The closer the value of R
2
is to 1, the
better the fit of the regression line to the observed values; on the contrary, the smaller the value of R
2
,
the worse the fit of the regression line to the observed values.
3.5.2. Hardness
The frequency distribution of His displayed in Figure 8and the fitting correlation
coefficients of grid 1, 2, 3 and 4 were 0.6087, 0.4961, 0.5266 and 0.5491, respectively. Except
for grid 1, the other distributions in grid 2, 3 and 4 had an obvious negative skew distribu-
tion, and the concentration areas of Hwere significant with range of 0.1 GPa. The varying
areas of Hof grid 1, 2, 3 and 4 were 0.122~0.476 GPa, 0.115~0.496 GPa, 0.081~0.546 GPa and
0.146~0.604 GPa, respectively. The average Hof grid 1, 2, 3 and 4 were 0.325, 0.342, 0.4 and
0.396 GPa, respectively. The concentration ranges of grid 1, 2, 3 and 4 were
0.4~0.5 GPa
,
0.4~0.5 GPa, 0.45~0.55 GPa and 0.45~0.55 GPa, respectively, and the proportions of the
indenters were 27%, 48%, 46% and 40%, respectively. Grid 4 had the largest hardness
distribution interval and the largest average hardness. The mathematical expectations of
grid 1, 2, 3 and 4 were 0.33, 0.43, 0.47 and 0.52, respectively, which were higher than
H
owing to the high hardness minerals in the clay.
Materials 2022,15, 7143 12 of 19
Figure 8.
Frequency distribution histogram of H. The closer the value of R
2
is to 1, the better the fit of
the regression line to the observed values; on the contrary, the smaller the value of R
2
, the worse the
fit of the regression line to the observed values.
3.5.3. Fracture Toughness
Frequency distributions of K
c
are displayed in Figure 9and the fitting correlation coef-
ficients of grid 1, 2, 3 and 4 were 0.6102, 0.6069, 0.7951 and 0.6893, respectively. The varying
ranges of K
c
of grid 1, 2, 3 and 4 were 5.36~15.55 GPa, 5.6~15.71 GPa,
6.43~18.44 GPa
and
4.85~21.56 GPa, respectively. The mean fracture toughness
Kc
of four grids were 10.41,
11.23, 13.24 and 12.78 MPa
·
m
1/2
, respectively, and that of grid 3 was the largest. The
mathematical expectations of the four grids were 10.08, 11.31, 13.24 and 12.78, respectively.
The mathematical expectation of grid 2 and grid 4 was same as the mean value. The
mathematical expectation of grid 1 was less than its average value, and a positive skewness
distribution was presented, while that of grid 3 was greater than its average value, which
presented a negative skewness distribution.
Figure 9.
Frequency distribution histogram of K
c
. The closer the value of R
2
is to 1, the better the fit
of the regression line to the observed values; on the contrary, the smaller the value of R
2
, the worse
the fit of the regression line to the observed values.
Materials 2022,15, 7143 13 of 19
3.6. Relationships among Various Mechanical Properties
Figure 10 gives the relationships among various mechanical properties of the four
grids after statistics, and the mechanical property distributions mostly followed the normal
distribution. The frequency distributions of E,Hand K
c
are displayed on the diagonal. The
correlation coefficients between Eand K
c
were higher than 0.8, which indicates a great fit.
The correlation coefficient of Hwas a little worse with the value of 0.7348, but it was higher
than that of the dispersed mesh. The mean values of E,Hand K
c
were 9.64 GPa, 0.365 GPa
and 11.91 MPa
·
m
1/2
, respectively. The correlations among the mechanical properties are
demonstrated in Figure 11.
Figure 10.
The correlation between Hand K
c
was the lowest, and the correlation coefficient was
0.5067. In addition, the correlation coefficient between Eand K
c
was 0.6839. It can be observed
that data points present discrete distribution, which was probably caused by mineral heterogeneity,
micro−cracks and micro−pores.
Figure 11. Frequency index B.
Materials 2022,15, 7143 14 of 19
4. Discussions
4.1. Evaluation of Micro-Brittleness Index
The micro-brittleness of the four grids can be obtained based on the Equation (16),
and it reflects the friability of the indenter. By analyzing the brittleness index of numerous
indenters, as displayed in Figure 11, the varying ranges of the brittleness index of the four
grids were 11.31~58.67, 9.16~57.07, 7.46~65.69 and 10.52~61.32, respectively. Additionally,
the mean micro-brittleness index
B
of the four grids was 26.38, 24.12, 25.97 and 26.87,
respectively. The friability of grid 4 was the best based on the above analysis on the
brittleness index. However, the analysis was invalid due to it ignoring the integrity and
heterogeneity of the shale. Hence, a deep analysis is necessary in next section.
By investigating the distributions of the brittleness index in the four grids, it can be
seen that the distribution of the brittleness index presented an obvious bimodal distribution,
which could be divided into a low brittleness region and a high brittleness region. The
boundary value of the low and high brittleness region in the four grids were 38, 40, 40
and 45, respectively. The mean brittleness indices of the low brittleness regions were 20.96,
21.05, 23.09 and 23.6, respectively. The mean brittleness indices of the high brittleness
regions were 49.47, 51.77, 55.08 and 55.61, respectively. Additionally, the proportions of
the high brittleness index were 19%, 10%, 9% and 14%, respectively. It can be concluded
that the mean value of the brittleness index was small in grid 1, while the proportion of the
high brittleness index was the largest, indicating that the friability of grid 1 was positive
and higher than the other grids.
4.2. Distribution of Micro-Brittleness Index
The micro-brittleness index of a single point was obtained by pressing in and out of
the nanoindentation head. In Section 4.1, the related statistical analysis was performed
on the micro-brittleness index of a single point and the evaluation of the friability was
finished. However, shale is strong heterogeneity material, and it is difficult to represent
the overall characteristics of shale only through the analysis of a single point. Even if the
mesh statistics are the same, the micro-brittleness will be different due to the various mesh
distribution. In this paper, the indenter was moved along a serpentine path of the array
by a selected starting point. By giving the array length and spacing between adjacent
indentations, the brittleness index was matched with the spatial position of the indentation.
This spatial distribution provides a way to determine the micro-brittleness distribution on
the shale surface.
Figure 12 shows the reference origin software and the method used was the difference
method. As shown in the left of Figure 12, the brittleness index was drawn as a hotspot
map according to its position, and the strong heterogeneity of the shale was observed. The
color of the grid represents the level of the brittleness index. The red color represents a
high brittleness index, which is scattered in the indentation grid, just as quartz grains are
scattered in shale. The existence of high brittleness indentation points improves the overall
friability. However, it is difficult to transfer the crack to the next point when two high brittle
indentation points are far away from each other. The cloud diagram of the brittleness index
distribution was obtained with step fuzzy processing in the right of Figure 12. When the
crack extends to this point, it must extend to the high brittleness area. The high brittleness
zones are connected to each other to form fracture propagation channels.
The content of the high brittleness indentation points was 19% in grid 1, which was
higher than the other three indentation points. However, the concentration of the high
brittleness indentation points led to a small number of crack expansion channels. When
the crack expanded to grid 1, it was extremely easy to be absorbed by the low brittleness
zone, resulting in the ability loss of the crack extension. Therefore, the high content of
high brittleness in grid 1 was unvaluable for friability. In grid 3, there were a few high
brittleness indentation points (9%), but these high brittleness indentation points were
scattered and connected with each other to form multiple channels, which were conducive
to the propagation of cracks. The brittleness index distribution of the four grids was
Materials 2022,15, 7143 15 of 19
analyzed. There were two channels for grid 1, four channels for grid 2 and grid 3 and five
channels for grid 4. Therefore, grid 4 had the best friability based on the distributions of
the brittleness index.
Figure 12.
Friability surface distribution: (
a
) nanoindentation grid 1, (
b
) nanoindentation grid 2,
(c) nanoindentation
grid 3, (
d
) nanoindentation grid 4. The red dashed lines in Figure 12 are connec-
tions between highly brittle regions that form crack propagation channels.
Materials 2022,15, 7143 16 of 19
4.3. The Relationship between Micro-Brittleness Index and Mineral Distribution
In previous studies, the same mineral was considered to have specific mechanical
properties. However, different mineral cementations have a strong influence on their
mechanical properties. Nanoindentation tests were carried out by the grid indentation
method, and an indentation point was placed in a grid with various mineral connections.
The categories of the main minerals in the grid were compared with the brittleness index
obtained by indentation tests. Figure 13 shows the corresponding relationship between
the minerals and the brittleness index. In grid 1, the quartz content, feldspar content,
carbonate mineral content and clay mineral content was 14.09%, 13.79%, 48.16% and
17.43%, respectively. The indentation grid of the quartz-dominated grid accounted for 19%,
basically corresponding to the high brittleness region. However, the brittleness index of the
grid points by the feldspar-dominated and carbonate- dominated grids was in the middle.
The grid points by the clay-dominated grid had a low brittleness index, but they also had
a high brittleness index owing to the existence of brittle particles in the clay minerals. In
grid 2, the quartz content was 9.52%, which corresponded to the high brittleness. The
content of feldspar, carbonate minerals and clay minerals was 14.38%, 18.53% and 50.72%,
respectively. In grid 3, the content of quartz, feldspar, carbonate minerals and clay minerals
was 12.49%, 16.31%, 47.26% and 15.86%, respectively. The content of high brittleness was
9%, which was less than the quartz, and this was due to the low brittleness of some of the
quartz surrounded by clay. In grid 4, the content of the quartz, feldspar, carbonate minerals
and clay minerals was 8.43%, 17.3%, 51.52% and 15.37%, respectively. The proportion of
high brittleness was 14%, which was much higher than that of quartz. This was because
quartz particles are small and most of them were cemented with carbonate minerals, were
part of the carbonate minerals and showed high hardness.
Figure 13. Cont.
Materials 2022,15, 7143 17 of 19
Figure 13.
The relationship between brittleness index and minerals: (
a
) nanoindentation grid 1,
(b) nanoindentation grid 2, (c) nanoindentation grid 3, (d) nanoindentation grid 4.
It can be seen that quartz played a very important role in the evaluation of microscopic
brittleness. Quartz is highly brittle, and when it is cemented with other minerals, the
overall brittleness is improved. Quartz takes on different shapes, most of which are round
shapes. These quartz particles are relatively large and are formed during the diagenesis
process. They co-deposited with carbonate minerals and cemented with clay minerals to
form shale. In addition, many clusters of quartz can be observed. These small particles of
quartz are produced in clay minerals. They may not be formed by diagenesis, but by the
precipitation of siliceous material during the transformation of clay to form quartz. This is
why some clay minerals also exhibit a high brittleness.
5. Conclusions
In this paper, nanoindentation technology was used to study the micro-mechanical
properties of shale. Meanwhile, the indentation deformation was introduced through
dimensional analysis and then the micro-brittleness index was proposed. Compared with
the traditional dimensional method, the nanoindentation method was dimensionless, which
could well characterize the physical meaning. The mineral composition, pore structure
characteristics and surface mineral distribution of shale were characterized by XRD, SEM
and QEMSCAN. The four regions of shale were compared in an analysis to explore the
characteristics and distributions of shale micro-brittleness. The main conclusions are
as follows:
(1)
The micro-brittleness index of the shale ranged from 7.46 to 65.69 and the average
brittleness index was 25.837. The distribution of the brittleness index presented an
obvious bimodal distribution. The shale was divided into low brittleness and high
brittleness around 40. It had a positive effect on the overall friability of shale although
the proportion of these high brittle minerals was only about 15%.
Materials 2022,15, 7143 18 of 19
(2)
The brittleness distribution of the shale surface was obtained via the grid indentation
method, and the distribution of the brittleness index presented a strong heterogeneity.
The indentation points with a high brittleness index were scattered in the indentation
grid. When the two highly brittle indentation points were closer, they were connected
to each other to form a channel for crack propagation. When the content of the high
brittle indentation points was high but too concentrated, it was not conducive to
crack propagation.
(3)
The distribution of the minerals obtained by QEMSCAN was meshed and then
compared with the indentation grid to obtain the corresponding relationships between
the brittleness index and minerals. The pattern of most indentation points was quartz
with a high brittleness and clay with a low brittleness. However, there existed a
variety of situations due to the various cementations between the minerals. When
quartz was cemented with clay minerals, the brittleness decreased. When a small
amount of quartz was cemented with carbonate, the indentation point showed a
higher brittleness index. At the same time, the clay region also presented a high
brittleness due to the presence of many small brittle particles in the clay minerals.
Author Contributions:
Conceptualization, L.Y., D.Y., Z.H. and Y.M.; methodology, L.Y.; software,
Y.M.; validation, D.Y., Z.H., S.L., J.C. and M.H.; investigation, L.Y., S.L. and M.H.; writing—original
draft preparation, L.Y.; writing—review and editing, L.Y. and J.C. All authors have read and agreed
to the published version of the manuscript.
Funding:
The research was funded by the National Natural Science Foundation of China (41941018),
the major Science and Technology Project in Yunnan Province (202002AF080003), the Fundamental
Research Funds for the Central Universities and funded by Institute for Deep Underground Science
and Engineering (XD2021022).
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: All the data is available within the manuscript.
Conflicts of Interest: The authors declare no competing financial interest.
References
1. Akinbinu, V.A. Relationship of brittleness and fragmentation in brittle compression. Eng. Geol. 2017,221, 82–90. [CrossRef]
2.
Moghadam, A.L.; Harris, N.B.; Ayranci, K.; Gomez, J.S.; Angulo, N.A.; Chalaturnyk, R.C. Brittleness in the Devonian Horn River
shale, British Columbia, Canada. J. Nat. Gas Sci. Eng. 2018,62, 247–258. [CrossRef]
3.
Cai, M. Prediction and prevention of rockburst in metal mines—A case study of Sanshandao gold mine. J. Rock Mech. Geotech.
Eng. 2016,8, 204–211. [CrossRef]
4.
Cała, M.; Cyran, K.; Kawa, M.; Kolano, M.; Wałach, D. Identification of microstructural properties of shale by combined use
of X-Ray micro-CT and nanoindentation tests. In Proceedings of the ISRM European Rock Mechanics Symposium EUROCK,
Ostrava, Czech Republic, 20–22 June 2017; pp. 735–743.
5.
Chen, J.; Zhang, G.; Chen, H.; Yin, X. The construction of shale rock physics effective model and prediction of rock brittleness. In
Proceedings of the 2014 SEG Annual Meeting, SEG Technical Program Expanded Abstracts, Denver, CO, USA,
26–31 October 2014
.
6. Gong, X.; Sun, C.C. A new tablet brittleness index. Eur. J. Pharm. Biopharm. 2015,93, 260–266. [CrossRef] [PubMed]
7.
Huo, Z.; Zhang, J.; Li, P.; Tang, X.; Yang, X.; Qiu, Q.; Dong, Z.; Li, Z. An improved evaluation method for the brittleness index of
shale and its application—A case study from the southern north China basin. J. Nat. Gas Sci. Eng. 2018,59, 47–55. [CrossRef]
8.
Kaunda, R.B.; Asbury, B. Prediction of rock brittleness using nondestructive methods for hard rock tunneling. J. Rock Mech.
Geotech. Eng. 2016,8, 533–540. [CrossRef]
9.
Khandelwal, M.; Faradonbeh, R.S.; Monjezi, M.; Armaghani, D.J.; Yagiz, S. Function development for appraising brittleness of
intact rocks using genetic programming and nonlinear multiple regression models. Eng. Comput. 2016,32, 13–21. [CrossRef]
10.
Lee, J.H.; Gao, Y.F.; Johanns, K.E.; Pharr, G.M. Cohesive interface simulations of indentation cracking as a fracture toughness
measurement method for brittle materials. Acta Mater. 2012,60, 5448–5467. [CrossRef]
11.
Li, C.; Ostadhassan, M.; Abarghani, A.; Fogden, A.; Kong, L. Multi-scale evaluation of mechanical properties of the Bakken shale.
J. Mater. Sci. 2019,54, 2133–2151. [CrossRef]
12.
Liu, Z.; Sun, Z. New brittleness indexes and their application in shale/clay gas reservoir prediction. Petrol. Explor. Dev.
2015
,42,
129–137. [CrossRef]
Materials 2022,15, 7143 19 of 19
13.
Ma, Z.; Gamage, R.P.; Zhang, C. Application of nanoindentation technology in rocks: A review. Geomech. Geophys. Geo-Energy
Geo-Resour. 2020,6, 1–27. [CrossRef]
14. Zhang, T.H.; Yang, Y.M. Development and application of nano-hardness technology. Adv. Mech. 2002,03, 349–364.
15. UIm, F.J.; Abousleiman, Y. The nanogranular nature of shale. Acta Geotech. 2006,1, 77–88.
16.
Zhou, H.; Meng, F.Z.; Zhang, C.Q.; Xu, R.C.; Lu, J.J. Quantitative evaluation method of rock brittleness characteristics based on
stress-strain curve. Chin. J. Rock Mech. Eng. 2014,33, 1114–1122.
17.
Chen, G.Q.; Zhao, C.; Wei, T.; Wang, J.C. Evaluation method of rock brittleness characteristics based on total stress-strain curve
and crack initiation stress. Chin. J. Rock Mech. Eng. 2018,37, 51–59.
18.
Liu, H.F.; Zheng, K.; Zhu, C.Q.; Meng, Q.H.; Wu, W.J. Evaluation of brittleness characteristics of reef limestone based on
stress-strain curve. Geomechanics 2021,42, 673–680.
19.
Mao, B. Why are brittleness and fracability not equivalent in designing hydraulic fracturing in tight shale gas reservoirs. Petrol.
Explor. Dev. 2016,2, 1–19.
20.
Meng, F.Z.; Wong, L.; Zhou, H. Rock brittleness indices and their applications to different fields of rock engineering: A review. J.
Rock Mech. Geotech. 2021,13, 221–247. [CrossRef]
21.
Ozfirat, M.K.; Yenice, H.; Simir, F.; Yarali, O. A new approach to rock brittleness and its usability at prediction of drillability. J. Afr.
Earth. Sci. 2016,119, 94–101. [CrossRef]
22.
Shi, X.; Jiang, S.; Yang, L.; Tang, M.; Xiao, D. Modeling the viscoelasticity of shale by nanoindentation creep tests. Int. J. Rock Mech.
Min. Sci. 2020,127, 104210. [CrossRef]
23.
Slim, M. Creep properties of source rocks using indentation: The role of organic matter on texture and creep rates. Ph.D. Thesis,
Massachusetts Institute of Technology, Department of Earth, Atmospheric, and Planetary Sciences, Cambridge, MA, USA, 2016.
24.
Tian, Z.; Wei, W.; Zhou, S.; Wood, D.A.; Cai, J. Experimental and fractal characterization of the microstructure of shales from
Sichuan Basin, China. Energy Fuels 2021,35, 3899–3914. [CrossRef]
25.
Wang, D.; Ge, H.; Wang, X.; Wang, J.; Meng, F.; Suo, Y.; Han, P. A novel experimental approach for fracability evaluation in
tight-gas reservoirs. J. Nat. Gas Sci. Eng. 2015,23, 239–249. [CrossRef]
26.
Wang, S.; Liu, K.; Han, J.; Ling, K.; Jia, B. Investigation of properties alternation during super-critical CO
2
injection in shale. Appl.
Sci. 2019,9, 1686. [CrossRef]
27.
Wong, L.; Meng, F.; Guo, T.; Shi, X. The role of load control modes in determination of mechanical properties of granite. Rock
Mech. Rock Eng. 2019,53, 539–552. [CrossRef]
28.
Xu, J.; Tang, X.; Wang, Z.; Feng, Y.; Bian, K. Investigating the softening of weak interlayers during landslides using nanoindentation
experiments and simulations. Eng. Geol. 2020,277, 105801. [CrossRef]
29.
Shen, W.J.; Ma, T.R.; Li, X.Z.; Sun, B.J.; Hu, Y.; Xu, J.C. Fully coupled modeling of two-phase fluid flow and geomechanics in
ultra-deep natural gas reservoirs. Phys. Fluids 2022,34, 1–10. [CrossRef]
30.
Zhao, X.; Zhou, L.; Pu, X.; Jin, F.; Jiang, W.; Xiao, D.; Han, W.; Shi, Z. Development and exploration practice of the concept of
hydrocarbon accumulation in rifted-basin troughs: A case study of Paleogene Kongdian Formation in Cangdong sag, Bohai Bay
Basin. Petrol. Explor. Dev. 2018,45, 1166–1176. [CrossRef]
31.
Zhou, H.; Chen, J.; Lu, J.; Jiang, Y.; Meng, F. A new rock brittleness evaluation index based on the internal friction angle and class
I stress–strain curve. Rock Mech. Rock Eng. 2018,51, 2309–2316. [CrossRef]
32.
Oliver, W.C.; Pharr, G.M. Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding
and refinements to methodology. J. Mater. Res. 2004,19, 3–20. [CrossRef]
33.
Cheng, Y.T.; Li, Z.; Cheng, C.M. Scaling relationships for indentation measurements. Philos. Mag. A
2002
,82, 1821–1829.
[CrossRef]
