Shot Peening Processes to obtain Nanocrystalline surfaces in metal alloys:
H. Bai et alii, Frattura ed Integrità Strutturale, 56 (2021) 16-45; DOI: 10.3221/IGF-ESIS.56.02
16
Experimental investigation of cracking behaviors of ductile and
brittle rock-like materials
Hao Bai, Wei Du*
Sichuan Expressway Construction & Development Group Co., LTD, Chengdu, China
secdcbh@126.com
582126107@qq.com
Yundong Shou*, Lichuan Chen
National Breeding Base of Technology and Innovation Platform for Automatic-monitoring of Geologic Hazards (Chongqing
Engineering Research Center of Automatic Monitoring for Geological Hazards), Chongqing, China
Wuhan University, China
shouyundong@whu.edu.cn, https://orcid.org/0000-0001-7424-4006
chen_lichuan@163.com
Filippo Berto
Norwegian University of Science and Technology, Norway
filippo.berto@ntnu.no
ABSTRACT. The cracking characteristics of ductile rocks were studied by
similar materials with sand, barite, epoxide resin, polyamide, silicone rubber
and alcohol, while the cracking characteristics of brittle rocks were
investigated by similar material with sand, barite, rosin and alcohol. In this
paper, to enhance the application range of the rock-like materials in the field
of geotechnical engineering model tests, the values of the elastic modulus and
the compressive strength of the artificial rock-like materials are changed in a
wide range by adjusting the amount of cementitious materials (epoxide resin,
polyamide, rosin, etc). The elastic modulus, compressive strength and cracking
characteristics were obtained from the complete axial stress–strain curves of
the specimens made of similar materials, which were cast using the different
mixture ratios. These experimental data can provide quantitative investigation
on mixture ratios of similar materials of rocks to model the geotechnical
engineering. Furthermore, the effect of mixture ratios on mechanical
properties and crack propagation pattern of specimens were also investigated
by the specimens with pre-existing flaws under uniaxial compressive tests.
KEYWORDS. Rock-like materials; Material composition; Ductility; Brittleness;
Crack evolution.
Citation: Bai, H., Du, W., Berto, F.,
Experimental investigation of cracking
behaviors of ductile and brittle rock-like
materials, Frattura ed Integrità Strutturale, 56
(2021) 16-45.
Received: 02.01.2021
Accepted: 17.01.2021
Published: 01.04.2021
Copyright: © 2021 This is an open access
article under the terms of the CC-BY 4.0,
which permits unrestricted use, distribution,
and reproduction in any medium, provided the
original author and source are credited.
https://youtu.be/PKi-k_hsMbg
H. Bai et alii, Frattura ed Integrità Strutturale, 56 (2021) 16-45; DOI: 10.3221/IGF-ESIS.56.02
17
INTRODUCTION
he similar simulation test in rocks on the basis of the similarity theory of modeling test is an explorative method to
study the mechanical properties of geotechnical materials. The mechanical phenomena and the stress-strain variation
characteristics of prototype are analyzed through the observation of stress and strain on similar models casted by
using single or multiple materials, which provides a more reasonable scientific basis for the design of the geotechnical
engineering and the selection of the construction scheme.
In similar model experimental studies, the ratio of similar materials and the casting method of test models have a great
influence on the physical and mechanical properties of the material, which plays a decisive role in the success of similar
simulation tests. For a long period of time, the geotechnical similar simulation test has been an important means of solving
complex engineering problems. It can not only study the normal stress state of engineering, but also acquire the ultimate
load and failure modes of engineering. Meanwhile, compared with the numerical calculation, the results given by similar
simulation tests are more intuitive and can give people a deeper impression, and are widely used in geotechnical engineering
research.
The cracking mechanisms of rocks have been studied experimentally on rock-like materials or rock materials, and rock-like
materials are widely used because the flaws are easy to be fabricated. The first experimental study on rock-like specimens
that contained flaws under uniaxial compression condition was conducted by Brace and Bombolakis [1]. Since then, many
studies have examined the fracture processes of pre-cracked rock-like materials subjected to compression. Experimental
studies have been performed on many different types of rock-like materials, including glass [2,3], Columbia Resin [4],
polymethyl methacrylate [5,6], cement mortar [7], sandstone-like composite material [8-11], and gypsum [12-18]. To
investigate the initiation, propagation, and coalescence of cracks in real rock materials, some experiments and numerical
simulation on rock such as granite [19-21], marble [17-18,22] and mudstone [23] have also been conducted. Zhou et al. [24]
and Bi et al. [25] proposed General Particle Dynamics to simulate the crack initiation, growth and coalescence in rock or
rock-like materials. Wang et al. [26-27] developed the conjugated bond-based peridynamics to investigate the cracking
behaviors in rock or rock-like materials. Zhou et al. [28-29] established micromechanics-based model to study the damage
mechanism of rocks. Zhou et al.[30] investigated the initiation, growth and coalescence of 3D crack in rock-like rocks. the
cracking behaviors in rock or rock-like materials. Zhou et al. [30] and Zhang et al. [31-34] studied progressive failure of
brittle rocks with non-isometric flaws. Such rock-like materials and real rock materials have not only common characteristics
for crack evolution, but also differences caused by the material properties, loading methods, and specimen geometry [35-
36].
Moreover, since rock is a very complex and anisotropic material whose mechanical properties vary widely, ranging from
hard rock with very high mechanical properties to soft rock with very low mechanical properties [30-36]. However, there is
scarce study on the cracking behaviors and mechanical properties of ductile and brittle rock-like materials.
To simulate different kinds of rock with a wide range of intensity variation, a new type of rock-like material with wide-
ranging and stable mechanical properties must be developed. In this paper, the certain raw materials were selected according
to the mechanical properties of ductile and brittle rocks and the mechanical laws of ductile and brittle rock-like materials
were obtained by experimental analysis of materials with different ratios, which provides a reference for the ratio of rock-
like materials in experiments. In addition, two rock-like materials were applied to crack propagation experiment, and the
influence rules of different ratios of rock-like materials on crack propagation modes and mechanical properties of the
specimens were obtained.
EXPERIMENTAL STUDIES
Specimen preparation
he composition of the raw materials used to make similar models can be basically divided into three categories
according to their use: the first one is filling material acted as the skeleton, the second one is cementing material that
plays a role in bonding, and the third one is auxiliary admixture served as regulation of physical and mechanical
properties. In similar simulation experiments, in order to make the similar model satisfy requirements of the volumetric
weight similarity ratio, it is more common to use barite, gypsum, sand, iron powder as the filling material. There are also
many cementitious materials commonly used as bonding materials like gypsum, white latex, epoxide resin, polyamide,
cement, rosin, etc. At the same time, for the purpose of adjusting the physical and mechanical properties of rock-like
materials to better simulate the actual rock, it is essential to add additional auxiliary agents, such as silicone rubber, lime,
T
T
H. Bai et alii, Frattura ed Integrità Strutturale, 56 (2021) 16-45; DOI: 10.3221/IGF-ESIS.56.02
18
neoprene, glycerin (humectant), borax (retarder) mica powder, softwood chips, etc. Furthermore, to make rock-like materials
isotropic and homogeneous after hardening molding, it is also necessary to incorporate a certain amount of organic solvent,
including frequently-used gasoline, engine oil, alcohol, etc. And its purpose is to dissolve organic substances such as silicone
rubber, so that the components can be more uniformly mixed.
In this paper, the experiment was designed to prepare rock-like materials which could simulate ductile and brittle rocks.
Initially some raw materials are selected as rock-like materials. After that tentative raw materials are added for trial matching.
Eventually, the preparative rock-like materials are tested in uniaxial compression in order to figure out whether the full
stress-strain curve of the rock-like materials is similar to the corresponding curve of actual rocks.
When simulating the raw material composition of ductile rock-like materials, it was finally decided to use sand and barite
as filling materials. Moreover, epoxide resin and polyamide were used as cementitious materials, silicone rubber and rosin
were used as auxiliary adjusting agents, and alcohol was used as organic solvent. The force-displacement curve of whole
process in uniaxial compression test for ductile rock-like material is shown in Fig. 1. With regard to brittle rock-like
materials, sand and barite were used as filling materials, rosin was used as cementitious material, silicone rubber, epoxide
resin and polyamide were used as auxiliary adjusting agents, and alcohol was used as organic solvent. Fig. 1 and Fig. 2 are
the force-displacement curve of whole process in uniaxial compression test for ductile and brittle rock-like materials,
respectively.
Figure 1: Force-displacement curve of the uniaxial compression UCS test for ductile rock-like materials.
Figure 2: Force-displacement curve of UCS test for brittle rock-like materials.
H. Bai et alii, Frattura ed Integrità Strutturale, 56 (2021) 16-45; DOI: 10.3221/IGF-ESIS.56.02
19
To obtain the experimental phenomena and make data reliable, two specimens for each ratio of materials were made and
relevant test data was processed averagely. The ratio relationship of raw material is shown in Tabs. 1 and 2.
Number Raw materials Weight ratio
Percentage of variable
components
A1 Sand, barite, epoxy, polyamide and alcohol 500:300:4:4:40 59% (sand)
A2 Sand, barite, epoxy, polyamide and alcohol 600:300:4:4:40 63.3% (sand)
A3 Sand, barite, epoxy, polyamide and alcohol 700:300:4:4:40 66.8% (sand)
A4 Sand, barite, epoxy, polyamide and alcohol 800:300:4:4:40 69.7% (sand)
B1 Sand, barite, epoxy, polyamide and alcohol 500:300:4:4:40 35.4% (barite)
B2 Sand, barite, epoxy, polyamide and alcohol 500:350:4:4:40 39% (barite)
B3 Sand, barite, epoxy, polyamide and alcohol 500:400:4:4:40 42.7% (barite)
B4 Sand, barite, epoxy, polyamide and alcohol 500:450:4:4:40 45.1% (barite)
C1 Sand, barite, epoxy, polyamide and alcohol 500:300:4:4:40 0.9% (epoxy and polyamide)
C2 Sand, barite, epoxy, polyamide and alcohol 500:300:6:6:40 1.4% (epoxy and polyamide)
C3 Sand, barite, epoxy, polyamide and alcohol 500:300:8:8:40 1.9%(epoxy and polyamide)
C4 Sand, barite, epoxy, polyamide and alcohol 500:300:10:10:40 2.3%(epoxy and polyamide)
D1 Sand, barite, epoxy, polyamide and alcohol 500:300:4:4:40 0% (silicone rubber)
D2
Sand, barite, epoxy, polyamide, alcohol and silicone
rubber
500:300:4:4:40:5 0.6% (silicone rubber)
D3
Sand, barite, epoxy, polyamide, alcohol and silicone
rubber
500:300:4:4:40:10 1.2% (silicone rubber)
D4
Sand, barite, epoxy, polyamide, alcohol and silicone
rubber
500:300:4:4:40:15 1.7% (silicone rubber)
E1 Sand, barite, epoxy, polyamide and alcohol 500:300:4:4:40 0% (rosin)
E2 Sand, barite, epoxy, polyamide, alcohol and rosin 500:300:4:4:40:2 0.2% (rosin)
E3 Sand, barite, epoxy, polyamide, alcohol and rosin 500:300:4:4:40:4 0.5% (rosin)
E4 Sand, barite, epoxy, polyamide, alcohol and rosin 500:300:4:4:40:6 0.7% (rosin)
F1
Sand, barite, epoxy, polyamide, alcohol and silicone
rubber
500:300:4:4:40:5 0% (rosin)
F2
Sand, barite, epoxy, polyamide, alcohol silicone
rubber and rosin
500:300:4:4:40:5:2 0.2% (rosin)
F3
Sand, barite, epoxy, polyamide, alcohol silicone
rubber and rosin
500:300:4:4:40:5:4 0.5% (rosin)
F4
Sand, barite, epoxy, polyamide, alcohol silicone
rubber and rosin
500:300:4:4:40:5:6 0.7% (rosin)
Table 1: The raw materials and ratio of ductile rock-like materials.
In the process of fabricating specimens, the raw materials were first weighed according to the ratio of each rock-like
materials. At the same time, the mold was cleaned and assembled, and the inner surface of the mold was coated with an
appropriate amount of lubricating oil so that the mold could be removed later. Subsequently the sand and barite powder
were mixed evenly, and the rosin powder or the epoxide resin-polyamide was dissolved in alcohol to form an alcohol
solution (which was thoroughly stirred and slightly heated with hot water to accelerate dissolution), then the alcohol solution
was then added evenly to the already mixed mixture. Since silicone rubber was not easily dissolved in alcohol, it could only
be slowly dispersed in the agitated material during agitation. Finally, the mixture was poured into the mold and tamped (the
hammer was stopped when there was no obvious sinking during the hammering process). The specimens after pouring
molding is shown in Fig. 3.
H. Bai et alii, Frattura ed Integrità Strutturale, 56 (2021) 16-45; DOI: 10.3221/IGF-ESIS.56.02
20
Number Raw materials Weight ratio
Percentage of variable
components
A1' Sand, barite, rosin and alcohol 200:200:5:15 47.6% (sand)
A2' Sand, barite, rosin and alcohol 250:200:5:15 53.2% (sand)
A3' Sand, barite, rosin and alcohol 300:200:5:15 57.7% (sand)
A4' Sand, barite, rosin and alcohol 350:200:5:15 61.4% (sand)
B1' Sand, barite, rosin and alcohol 200:200:5:15 47.6% (barite)
B2' Sand, barite, rosin and alcohol 200:250:5:15 53.2% (barite)
B3' Sand, barite, rosin and alcohol 200:300:5:15 57.7% (barite)
B4' Sand, barite, rosin and alcohol 200:350:5:15 61.4% (barite)
C1' Sand, barite, rosin and alcohol 200:200:5:15 1.2% (rosin)
C2' Sand, barite, rosin and alcohol 200:200:7:15 1.7% (rosin)
C3' Sand, barite, rosin and alcohol 200:200:9:15 2.1% (rosin)
C4' Sand, barite, rosin and alcohol 200:200:11:15 2.6% (rosin)
D1' Sand, barite, rosin and alcohol 200:200:5:15 0% (epoxy and polyamide)
D2' Sand, barite, rosin, alcohol, epoxy and polyamide 200:200:5:15:1:1 0.47% (epoxy and polyamide)
D3' Sand, barite, rosin, alcohol, epoxy and polyamide 200:200:5:15:2:2 0.94% (epoxy and polyamide)
D4' Sand, barite, rosin, alcohol, epoxy and polyamide 200:200:5:15:3:3 1.4% (epoxy and polyamide)
E1' Sand, barite, rosin and alcohol 200:200:5:15 0% (silicone rubber)
E2' Sand, barite, rosin, alcohol and silicone rubber 200:200:5:15:2 0.47% (silicone rubber)
E3' Sand, barite, rosin, alcohol and silicone rubber 200:200:5:15:4 0.94% (silicone rubber)
E4' Sand, barite, rosin, alcohol and silicone rubber 200:200:5:15:6 1.4% (silicone rubber)
Table 2: The raw materials and proportion of brittle rock-like material.
Figure 3: Prepared specimens.
H. Bai et alii, Frattura ed Integrità Strutturale, 56 (2021) 16-45; DOI: 10.3221/IGF-ESIS.56.02
21
Testing System
In this paper, an electronic universal testing machine was used to carry out the uniaxial compression test of specimens. The
test machine has two loading modes (load control and displacement control) which can automatically collect data throughout
the test. In order to prevent the damage of the test machine caused by the sudden destruction of specimen and to ensure
integrity of the stress-strain curve obtained by experiments, the loading mode of displacement control was selected in the
experiments. The device used for testing the fracture toughness of rock-like materials consists of a loading device (electronic
universal testing machine) and a bracket device (for supporting cylindrical specimens to meet the three-point bending
loading requirements).
In the process of processing the specimen, 1 mm wide crack was first machined on the specimen, then the crack tip was
ground with a diamond wire saw to a diameter of 0.5 mm. In the test, the crack length is 10 mm (generally, the ratio of the
crack length to the specimen diameter is 0.15 to 0.5), and the crack tip angle is 30° (the crack tip angle is generally required
to be small enough to produce a relatively strong I-type stress filed), the ratio of span to diameter is 1.5 (the ratio of span
and diameter of the specimen is relatively small when the material strength is low, generally 1.5 to 4). After the specimen
was processed, the specimen was placed in the exact position of the test holder and was tested under loading by the electronic
universal testing machine. During the loading process, the crack propagation and failure modes of the specimen were
observed and recorded, and finally the maximum load at the time of crack propagation was recorded. The crack geometry
and loading diagram of the specimen are shown in Fig. 4.
Figure 4: Crack geometry and loading schematic.
ANALYSIS OF EXPERIMENT RESULTS
Analysis of experimental results of ductile rock-like materials
Effect of raw materials on stress-strain curves and brittleness indexes of ductile rock-like materials
enerally, the complete stress-strain curve of rocks can be used to qualitatively analyze the brittleness of rock.
Therefore, based on the brittleness index of the full stress-strain curve, another brittleness index, namely “brittle
modulus”, is obtained. Eqn. (1) is the calculation expression of the brittle modulus.
−
=
−
0
0
0
c
c
E (1)
were
0E is the brittle modulus,
c is peak strength,
+
= 10 2
c , 0 is the strain corresponding to0 ,
c is the strain corresponding to c .
Fig. 5 and Fig. 6 are respectively diagrams of the stress-strain curves and brittle modulus changes of ductile rock-like
materials under different raw material ratios. Combining the failure process of the specimen and analyzing the curve change
in the figure, it can be seen that:
G
H. Bai et alii, Frattura ed Integrità Strutturale, 56 (2021) 16-45; DOI: 10.3221/IGF-ESIS.56.02
22
① when the amount of sand increases, the difference in the damage of the specimen is little. The reason may be that a large
amount of cementitious material and barite has a certain ductility when the sand content is low, and the shear failure of the
sand also has a certain ductility when the sand content is high.
② When the barite content is relatively low, the specimen exhibits a certain ductility, and as the barite content increases,
the ductility of the specimen is more pronounced. The reason is probably due to the fact that the cementitious materials,
epoxide resin and polyamide, have a certain ductility, and the barite material itself also has good ductility when it is failed.
When the barite content is relatively high, the specimen is mainly failed by the shear failure of sand and barite, and the barite
itself has better ductility when it is failed.
③ When the content of epoxide resin and polyamide is relatively low, the specimen has a certain ductility, and as the content
of epoxide resin and polyamide increases, the ductility of the specimen is more obvious. The reason should be that the
cementitious materials, epoxide resin and polyamide, have good ductility when they are dried and hardened.
④ When the silicone rubber is not added, the specimen has a certain ductility, and the ductility of the specimen is more
obvious as the amount of added silicone rubber increases. The reason is that the silicone rubber after coagulation hardening
has a good ductility, which increases the ductility of the specimen.
⑤ In the absence of silicone rubber, when the amount of rosin is 0, the specimen exhibits certain ductile failure properties,
and as the amount of added rosin increases, the specimen no longer has good ductility, but exhibits brittle failure properties.
The reason should be that the hardened rosin exhibits a distinct brittle character when it is failed, and ultimately changes
the ductile failure properties of rock-like material itself. ⑥Under the condition of containing silicone rubber, when the
amount of rosin is 0, the specimen also exhibits certain ductile failure properties, and as the amount of added rosin increases,
the ductility of the specimen is not severely reduced. But only when the rosin is added in a large amount, the ductility of
specimen is slightly reduced. The reason should be that rock-like materials added with silicone rubber without rosin have
good ductility, and the addition of a small amount of rosin is not sufficient to change their ductility.
It can also be seen from figures that:
① As the amount of sand decreases, the strain corresponding to the maximum stress tends to increase, which may be related
to the strain of epoxide resin and polyamide after hardening. With the decrease of sand content, the residual strength of
rock-like materials tends to increase, which may be due to the high residual strength of both epoxy and polyamide, as well
as barite.
② As the barite content increases, there are some differences in the residual strength of rock-like materials. This is most
likely due to the high residual strength of both epoxy and polyamide, as well as barite.
③ As the content of epoxide resin and polyamide increases, the strain corresponding to the maximum stress tends to
increase slightly, because epoxide resin and polyamide will have a larger strain when broken. Moreover, the residual strength
of the specimen tends to increase when the content of epoxide resin and polyamide is high, because epoxide resin and
polyamide also have high residual strength.
④ When the amount of added silicone rubber increases, the residual strength of the specimen slightly decreases, which is
likely to be related to the high residual strength of the silicone rubber.
⑤ As the amount of rosin added increases, the strain corresponding to the maximum stress tends to decrease, which may
be related to the less strain of the rosin. In the absence of silicone rubber, the residual strength of the specimen does not
change substantially when the amount of added rosin changes. In the case of silicone rubber, the residual strength of the
specimen slightly changes when the amount of rosin added increases, which may be related to the high residual strength of
rock-like materials without rosin.
Effect of raw materials on stress-strain curves and brittleness indexes of ductile rock-like materials
The elastic modulus can be obtained by the stress-strain curve of rock-like material. Fig. 7 shows the relationship between
the content of each raw material and the elastic modulus.
It can be clearly seen from the Fig. 7 that the elastic modulus of the ductile rock-like material can be increased by increasing
the content of epoxide resin and polyamide, and adding an appropriate amount of rosin. The elastic modulus of rock-like
materials increases when rosin is added, which may have a great relationship with the elastic modulus of rosin.
In the experiment, when the amount of sand and barite powder in the raw material component cannot be changed, the
purpose of lowering the elastic modulus of the material can be achieved by adding the auxiliary admixture silicone rubber.
From the effect of the raw material on the stress-strain curve, it can be known that if the elastic modulus of the ductile rock-
like material is to be enhanced and the ductile rock-like material has a certain brittleness, the epoxide resin and polyamide
should not be added excessively, but an appropriate amount of the auxiliary regulator rosin should be added.
H. Bai et alii, Frattura ed Integrità Strutturale, 56 (2021) 16-45; DOI: 10.3221/IGF-ESIS.56.02
23
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Sand for 59%
Sand for 63.3%
Sand for 66.8%
Sand for 69.7%
A
x
ia
l
st
re
ss
(
M
P
a
)
Axial strain (%)
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Barite powder for 35.4%
Barite powder for 39%
Barite powder for 42.7%
Barite powder for 45.1%
A
x
ia
l
st
re
ss
(
M
P
a
)
Axial strain (%)
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
Epoxy resin-Polyamide for 0.9%
Epoxy resin-Polyamide for 1.4%
Epoxy resin-Polyamide for 1.9%
Epoxy resin-Polyamide for 2.3%
A
x
ia
l
st
re
ss
(
M
P
a
)
Axial strain (%)
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Silicone rubber for 0%
Silicone rubber for 0.6%
Silicone rubber for 1.2%
Silicone rubber for 1.7%
A
x
ia
l
st
re
ss
(
M
P
a
)
Axial strain (%)
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
0.0
0.3
0.6
0.9
1.2
1.5
1.8
Rosin for 0%
Rosin for 0.2%
Rosin for 0.5%
Rosin for 0.7%
A
x
ia
l
st
re
ss
(
M
P
a
)
Axial strain (%)
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Rosin for 0%
Rosin for 0.2%
Rosin for 0.5%
Rosin for 0.7%
A
x
ia
l
st
re
ss
(
M
P
a
)
Axial strain (%)
Figure 5: Stress-strain curve of ductile rock-like materials with different raw material ratios.
H. Bai et alii, Frattura ed Integrità Strutturale, 56 (2021) 16-45; DOI: 10.3221/IGF-ESIS.56.02
24
60.0 62.5 65.0 67.5 70.0
72
80
88
96
B
ri
tt
le
m
o
d
u
lu
s
(M
P
a
)
Sand content (%)
35.0 37.5 40.0 42.5 45.0
40
48
56
64
72
B
ri
tt
le
m
o
d
u
lu
s
(M
P
a
)
Barite content (%)
1.0 1.5 2.0 2.5
50
55
60
65
70
75
B
ri
tt
le
m
o
d
u
lu
s
(M
P
a
)
Content of epoxide resin and polyamide (%)
0.0 0.5 1.0 1.5 2.0
20
40
60
80
B
ri
tt
le
m
o
d
u
lu
s
(M
P
a
)
Content of silicone rubber (%)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
80
100
120
140
160
B
ri
tt
le
m
o
d
u
lu
s
(M
P
a
)
Rosin content (without silicone rubber) (%)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
50
100
150
200
B
ri
tt
le
m
o
d
u
lu
s
(M
P
a
)
Rosin content (adding silicone rubber) (%)
Figure 6: Brittle modulus of ductile rock-like materials with different raw material ratios.
H. Bai et alii, Frattura ed Integrità Strutturale, 56 (2021) 16-45; DOI: 10.3221/IGF-ESIS.56.02
25
60.0 62.5 65.0 67.5 70.0
120
140
160
180
E
la
st
ic
m
o
d
u
lu
s
(M
P
a
)
Sand content (%)
35.0 37.5 40.0 42.5 45.0
100
120
140
160
180
E
la
st
ic
m
o
d
u
lu
s
(M
P
a
)
Barite content (%)
1.00 1.25 1.50 1.75 2.00 2.25 2.50
180
190
200
210
E
la
st
ic
m
o
d
u
lu
s
(M
P
a
)
Epoxide resin and Polyamide content (%)
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75
50
100
150
200
E
la
st
ic
m
o
d
u
lu
s
(M
P
a
)
Content of silicone rubber (%)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
150
200
250
300
350
E
la
st
ic
m
o
d
u
lu
s
(M
P
a
)
Rosin content (without silicone rubber) (%)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
120
140
160
180
200
220
E
la
st
ic
m
o
d
u
lu
s
(M
P
a
)
Rosin content (adding silicone rubber) (%)
Figure 7: Relations between raw materials contents and elastic modulus of ductile rock-like materials.
H. Bai et alii, Frattura ed Integrità Strutturale, 56 (2021) 16-45; DOI: 10.3221/IGF-ESIS.56.02
26
60.0 62.5 65.0 67.5 70.0
0.8
0.9
1.0
1.1
1.2
U
n
ia
x
ia
l
c
o
m
p
re
ss
iv
e
s
tr
e
n
g
th
(
M
P
a
)
Sand content (%)
35.0 37.5 40.0 42.5 45.0
0.85
0.90
0.95
1.00
1.05
1.10
1.15
U
n
ia
x
ia
l
c
o
m
p
re
ss
iv
e
s
tr
e
n
g
th
(
M
P
a
)
Barite content (%)
1.00 1.25 1.50 1.75 2.00 2.25 2.50
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
U
n
ia
x
ia
l
c
o
m
p
re
ss
iv
e
s
tr
e
n
g
th
(
M
P
a
)
Content of epoxide resin and polyamide (%)
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75
0.7
0.8
0.9
1.0
1.1
U
n
ia
x
ia
l
c
o
m
p
re
ss
iv
e
s
tr
e
n
g
th
(
M
P
a
)
Content of silicone rubber (%)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
U
n
ia
x
ia
l
c
o
m
p
re
ss
iv
e
s
tr
e
n
g
th
(
M
P
a
)
Rosin content (without silicone rubber) (%)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
U
n
ia
x
ia
l
c
o
m
p
re
ss
iv
e
s
tr
e
n
g
th
(
M
P
a
)
Rosin content (adding silicone rubber) (%)
Figure 8: Relationships between raw materials contents and uniaxial compressive strength of ductile rock-like materials.
H. Bai et alii, Frattura ed Integrità Strutturale, 56 (2021) 16-45; DOI: 10.3221/IGF-ESIS.56.02
27
Effect of raw materials on uniaxial compressive strength of ductile rock-like materials
The uniaxial compressive strength of the rock-like materials, that is, the peak stress on the curve, can be obtained by the
stress-strain curve. Fig. 8 shows the relation between the content of each raw material and the uniaxial compressive strength.
It can be clearly seen from Fig. 8 that the uniaxial compressive strength of ductile rock-like materials can be enhanced by
increasing the content of epoxide resin and polyamide and adding an appropriate amount of the auxiliary regulator rosin.
To reduce the uniaxial compressive strength of ductile rock-like materials, it is possible to increase the content of sand and
barite, and to add an appropriate amount of auxiliary regulator silicone rubber.
In the experiment, when the content of sand and barite powder cannot be changed, the purpose of reducing the uniaxial
compressive strength of the ductile rock-like material can be achieved by adding the auxiliary admixture silicone rubber.
From the effect of the raw material on the stress-strain curve, it can be known that if the uniaxial compressive strength of
the ductile rock-like material is to be enhanced and the ductile rock-like material has a certain brittleness, the epoxide resin
and polyamide cannot be excessively added, but an appropriate amount of the auxiliary regulator rosin should be added.
Effect of raw materials on fracture toughness of ductile rock-like materials
Referring to the relevant literature [37], the formula for fracture toughness of rock-like materials is shown in Eqns. 2 and 3.
= − + − +
−
2 3 4
2
[3.75 11.98 24.4( ) 25.69( ) 10.02( ) ]
( )
IC
PS a a a a a
K
D D D DD D a
(2)
where P represents the maximum load at the time of loading, S is the span, D denotes the diameter, which is 0.05 m, and a
is the crack length, which is 0.02 m.
Substituting a and D into Eqn. 2 yields
= 2675 ( a m )ICK PS P
(3)
By substituting relevant experimental data into Eqn. 3, the fracture toughness of ductile rock-like materials can be obtained.
The relationship between the fracture toughness and the content of each raw material is shown in Fig. 9.
It can be clearly seen from Fig. 9 that the fracture toughness of ductile rock-like materials can be enhanced by increasing
the content of epoxide resin and polyamide and adding an appropriate amount of auxiliary regulator rosin. At the same time,
it can be seen that for the purpose of improving the fracture toughness of rock-like materials, the addition of silicone rubber
and rosin is not as good as the case of adding rosin alone. To reduce the fracture toughness of ductile rock-like materials,
the content of sand and barite can be increased, and an appropriate amount of auxiliary regulator silicone rubber can be
added.
In the experiment, when the content of sand and barite powder cannot be changed, the purpose of reducing the fracture
toughness of the ductile rock-like material can be achieved by adding the auxiliary admixture silicone rubber. From the
effect of the raw material on the stress-strain curve, it is also known that if the fracture toughness of the ductile rock-like
material is to be improved and the ductile rock-like material has a certain brittleness, the epoxide resin and polyamide should
not be excessively added, but an appropriate amount of the auxiliary regulator rosin should be added.
Analysis of experimental results of brittle rock-like materials
Effect of raw materials on stress-strain curves and brittleness indexes of brittle rock-like materials
The uniaxial compressive stress-strain curve and brittle modulus of brittle rock-like materials can be obtained by the same
treatment method. Fig. 10 and Fig. 11 show respectively stress-strain curves and brittle modulus changes for brittle rock-
like materials at different raw material ratios.
It can be seen from the curves in the figures:
① When the sand content is relatively low, the specimen exhibits relatively brittle fracture properties, and the brittle fracture
characteristics of the specimen are no longer obvious as the sand content increases. Because when the sand content is low,
the damage of the specimen is mainly the brittle failure of the rosin. When the sand content is relatively high, the specimen
is mainly failed by the shear failure of the sand. In addition, it can be seen that as the sand content increases, the strain
corresponding to the maximum stress tends to increase.
H. Bai et alii, Frattura ed Integrità Strutturale, 56 (2021) 16-45; DOI: 10.3221/IGF-ESIS.56.02
28
60 65 70
0.024
0.026
0.028
0.030
0.032
F
ra
c
tu
re
t
o
u
g
h
n
e
ss
(
M
P
a
·m
1
/2
)
Sand content (%)
35 40 45
0.026
0.028
0.030
0.032
F
ra
c
tu
re
t
o
u
g
h
n
e
ss
(
M
P
a
·m
1
/2
)
Barite content (%)
1.0 1.5 2.0 2.5
0.030
0.035
0.040
0.045
F
ra
c
tu
re
t
o
u
g
h
n
e
ss
(
M
P
a
·m
1
/2
)
Content of epoxide resin and polyamide (%)
0.0 0.5 1.0 1.5 2.0
0.026
0.028
0.030
0.032
F
ra
c
tu
re
t
o
u
g
h
n
e
ss
(
M
P
a
·m
1
/2
)
Content of silicone rubber (%)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0.030
0.035
0.040
0.045
F
ra
c
tu
re
t
o
u
g
h
n
e
ss
(
M
P
a
·m
1
/2
)
Rosin content (without silicone rubber) (%)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.028
0.030
0.032
0.034
0.036
0.038
F
ra
c
tu
re
t
o
u
g
h
n
e
ss
(
M
P
a
·m
1
/2
)
Rosin content (adding silicone rubber) (%)
Figure 9: Relationships between raw materials contents and fracture toughness of ductile rock-like materials.
H. Bai et alii, Frattura ed Integrità Strutturale, 56 (2021) 16-45; DOI: 10.3221/IGF-ESIS.56.02
29
0.0 0.5 1.0 1.5 2.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Sand for 47.6%
Sand for 53.2%
Sand for 57.7%
Sand for 61.4%
S
tr
e
ss
(
M
P
a
)
Strain (%)
0.0 0.5 1.0 1.5 2.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Barite powder for 47.6%
Barite powder for 53.2%
Barite powder for 57.7%
Barite powder for 61.4%
S
tr
e
ss
(
M
P
a
)
Strain (%)
0.0 0.3 0.6 0.9 1.2 1.5
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
Rosin for 1.2%
Rosin for 1.7%
Rosin for 2.1%
Rosin for 2.6%
S
tr
e
ss
(
M
P
a
)
Strain (%)
0.0 0.4 0.8 1.2 1.6 2.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
Epoxy resin-Polyamide for 0%
Epoxy resin-Polyamide for 0.47%
Epoxy resin-Polyamide for 0.94%
Epoxy resin-Polyamide for 1.4%
S
tr
e
ss
(
M
P
a
)
Strain (%)
0.0 0.4 0.8 1.2 1.6 2.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Silicone rubber for 0%
Silicone rubber for 0.47%
Silicone rubber for 0.94%
Silicone rubber for 1.4%
S
tr
e
ss
(
M
P
a
)
Strain (%)
Figure 10: Stress-strain curve of brittle rock-like materials with different raw material ratios.
H. Bai et alii, Frattura ed Integrità Strutturale, 56 (2021) 16-45; DOI: 10.3221/IGF-ESIS.56.02
30
45 50 55 60 65
60
80
100
120
140
160
B
ri
tt
le
m
o
d
u
lu
s
(M
P
a
)
Sand content (%)
45 50 55 60
40
60
80
100
120
140
160
B
ri
tt
le
m
o
d
u
lu
s
(M
P
a
)
Barite content (%)
1.0 1.5 2.0 2.5
150
200
250
300
350
B
ri
tt
le
m
o
d
u
lu
s
(M
P
a
)
Rosin content (%)
0.0 0.5 1.0 1.5
60
80
100
120
140
160
B
ri
tt
le
m
o
d
u
lu
s
(M
P
a
)
Epoxide resin-polyamide content (%)
0.0 0.5 1.0 1.5
60
80
100
120
140
160
B
ri
tt
le
m
o
d
u
lu
s
(M
P
a
)
Silicone rubber content (%)
Figure 11: Brittle modulus of brittle rock-like materials with different raw material ratios.
H. Bai et alii, Frattura ed Integrità Strutturale, 56 (2021) 16-45; DOI: 10.3221/IGF-ESIS.56.02
31
② When the barite content is relatively low, the specimen exhibits relatively obvious brittle fracture properties. With the
increase of barite content, the brittle fracture characteristics of the specimen are no longer obvious. This is because when
the barite content is relatively low, the damage of the specimen is mainly the brittle failure of the rosin. When the barite
content is relatively high, the damage of the specimen is mainly reflected by the shear failure of sand and barite, and the
barite material itself has relatively good ductility. It can also be found that as the barite content increases, the strain
corresponding to the maximum stress tends to increase.
③ When the content of rosin is relatively high, the specimen exhibits obvious brittle fracture properties, and the brittle
fracture characteristics of the specimen are no longer obvious with the decrease of rosin content. This is also because when
the rosin content is relatively high, the damage of the specimen is mainly the brittle failure of the rosin. When the content
of rosin is relatively low, the damage of the specimen is mainly reflected by the shear failure of sand and barite, and the
barite itself has better ductility. It can be seen that as the amount of added epoxide resin and polyamide increases, the strain
corresponding to the maximum stress tends to increase, which may be related to the greater strain of epoxide resin and
polyamide during failure. Moreover, it can also be seen that as the content of epoxide resin and polyamide increases, the
residual strength of the specimen increases, which may be related to the good ductility of epoxide resin and polyamide.
④ When rock-like materials do not contain the epoxide resin and polyamide, the specimen exhibits relatively obvious brittle
fracture properties, and the brittle fracture characteristics of the specimen are no longer obvious as the amount of epoxide
resin and polyamide added increases. The reason may be that epoxide resin and polyamide have good ductility during failure,
thereby improving the brittle fracture property of the rosin itself.
⑤ When the silicone rubber is not added, the specimen exhibits relatively obvious brittle fracture properties. With the
increase of the silicone rubber content, the brittle fracture characteristics of the specimen are no longer obvious. The reason
may be that the silicone rubber has good ductility, thereby improving the brittle fracture properties of the rosin itself. It can
also be seen that as the amount of added silicone rubber increases, the strain corresponding to the maximum stress tends
to increase, which may be related to the greater strain of the silicone rubber during failure. In addition, it can be seen that
there is no significant difference in the residual strength of the specimen when the amount of added silicone rubber is
increased, which may be related to the ductility of the hardened silicone rubber.
Effect of raw materials on elastic modulus of brittle rock-like materials
Similarly, the relationship between the content of each raw material and the elastic modulus is shown in Fig. 12. It can be
seen that in order to increase the elastic modulus of brittle rock-like materials, it can only be achieved by increasing the
content of the rosin in the raw materials. When the rosin content increases, the elastic modulus of rock-like materials
increases significantly, which may have a great relationship with the elastic modulus of rosin itself.
In the experiment, when the content of sand and barite powder cannot be changed, the purpose of lowering the elastic
modulus of the material can be achieved by adding the auxiliary admixture epoxide resin, polyamide, or silicone rubber. It
can also be seen from Fig. 12 that silicone rubber has a better effect of lowering the elastic modulus of the material relative
to the epoxide resin and the polyamide.
Effect of raw materials on uniaxial compressive strength of brittle rock-like materials
The uniaxial compressive strength of brittle rock-like material was obtained by the stress-strain curve, and the relationship
between the content of each raw material and the uniaxial compressive strength was as shown in Fig. 13.
It can be clearly seen from the figure that the uniaxial compressive strength of the brittle rock-like material can be enhanced
by increasing the content of the rosin and adding an appropriate amount of the auxiliary regulator epoxide resin and
polyamide. To reduce the uniaxial compressive strength of brittle rock-like materials, the content of sand and barite can be
increased, and an appropriate amount of auxiliary regulator silicone rubber can be added.
In the experiment, when the content of sand and barite powder cannot be changed, the purpose of reducing the uniaxial
compressive strength of the brittle rock-like material can be achieved by adding the auxiliary admixture silicone rubber.
From the effect of the raw material on the stress-strain curve, it can be known that if the uniaxial compressive strength of
the brittle rock-like material is to be increased and the brittle rock-like material has a certain ductility, the rosin should not
be added too much, but an appropriate amount of the auxiliary regulator epoxide resin and polyamide should be added.
Effect of raw materials on fracture toughness of brittle rock-like materials
Similarly, the fracture toughness of the brittle rock-like material can also be obtained by substituting the relevant test data
into Eqn. 3. The relationship between the fracture toughness and the content of each raw material is shown in Fig. 14. It
can be clearly seen that in order to improve the fracture toughness of brittle rock-like materials, it is possible to increase the
H. Bai et alii, Frattura ed Integrità Strutturale, 56 (2021) 16-45; DOI: 10.3221/IGF-ESIS.56.02
32
content of rosin and add an appropriate amount of auxiliary regulator epoxide resin and polyamide. It has also been found
that the addition of epoxide resin and polyamide to improve the fracture toughness of rock-like materials is better. To
reduce the fracture toughness of brittle rock-like materials, the content of sand and barite in the raw materials should be
increased, and an appropriate amount of auxiliary regulator silicone rubber can be added.
45 50 55 60
140
160
180
200
220
E
la
st
ic
m
o
d
u
lu
s
(M
P
a
)
Sand content (%)
45 50 55 60
140
160
180
200
220
E
la
st
ic
m
o
d
u
lu
s
(M
P
a
)
Barite content (%)
1.0 1.5 2.0 2.5
200
250
300
350
400
E
la
st
ic
m
o
d
u
lu
s
(M
P
a
)
Rosin content (%)
0.0 0.5 1.0 1.5
160
170
180
190
200
210
220
E
la
st
ic
m
o
d
u
lu
s
(M
P
a
)
Content of epoxide resin and polyamide (%)
0.0 0.5 1.0 1.5
130
140
150
160
170
180
190
200
210
E
la
st
ic
m
o
d
u
lu
s
(M
P
a
)
Silicone rubber content (%)
Figure 12: Relationships between raw materials contents and elastic modulus of brittle rock-like materials.
H. Bai et alii, Frattura ed Integrità Strutturale, 56 (2021) 16-45; DOI: 10.3221/IGF-ESIS.56.02
33
47.5 50.0 52.5 55.0 57.5 60.0 62.5
0.9
1.0
1.1
1.2
U
n
ia
x
ia
l
c
o
m
p
re
ss
iv
e
s
tr
e
n
g
th
(
M
P
a
)
Sand content (%)
45 50 55 60
0.9
1.0
1.1
1.2
U
n
ia
x
ia
l
c
o
m
p
re
ss
iv
e
s
tr
e
n
g
th
(
M
P
a
)
Barite content (%)
1.0 1.5 2.0 2.5
1.1
1.2
1.3
1.4
1.5
1.6
1.7
U
n
ia
x
ia
l
c
o
m
p
re
ss
iv
e
s
tr
e
n
g
th
(
M
P
a
)
Rosin content (%)
0.0 0.5 1.0 1.5
1.15
1.20
1.25
1.30
1.35
1.40
1.45
U
n
ia
x
ia
l
c
o
m
p
re
ss
iv
e
s
tr
e
n
g
th
(
M
P
a
)
Content of epoxide resin and polyamide (%)
0.0 0.5 1.0 1.5
0.9
1.0
1.1
1.2
U
n
ia
x
ia
l
c
o
m
p
re
ss
iv
e
s
tr
e
n
g
th
(
M
P
a
)
Silicone rubber content (%)
Figure 13: Relationships between raw materials contents and uniaxial compressive strength of brittle rock-like materials.
H. Bai et alii, Frattura ed Integrità Strutturale, 56 (2021) 16-45; DOI: 10.3221/IGF-ESIS.56.02
34
45 50 55 60 65
0.026
0.028
0.030
0.032
0.034
F
ra
c
tu
re
t
o
u
g
h
n
e
ss
(M
P
a
·m
1
/2
)
Sand content (%)
45 50 55 60 65
0.026
0.028
0.030
0.032
0.034
F
ra
c
tu
re
t
o
u
g
h
n
e
ss
(M
P
a
·m
1
/2
)
Barite content (%)
1.0 1.5 2.0 2.5
0.032
0.034
0.036
0.038
0.040
0.042
F
ra
c
tu
re
t
o
u
g
h
n
e
ss
(M
P
a
·m
1
/2
)
Rosin content (%)
0.0 0.5 1.0 1.5
0.032
0.034
0.036
0.038
F
ra
c
tu
re
t
o
u
g
h
n
e
ss
(M
P
a
·m
1
/2
)
Epoxide resin-polyamide content (%)
0.0 0.5 1.0 1.5
0.026
0.028
0.030
0.032
0.034
F
ra
c
tu
re
t
o
u
g
h
n
e
ss
(M
P
a
·m
1
/2
)
Content of silicone rubber (%)
Figure 14: Relationships between raw materials contents and fracture toughness of brittle rock-like materials.
H. Bai et alii, Frattura ed Integrità Strutturale, 56 (2021) 16-45; DOI: 10.3221/IGF-ESIS.56.02
35
In the experiment, when the content of sand and barite powder cannot be changed, the purpose of reducing the fracture
toughness of the brittle rock-like material can be achieved by adding the auxiliary admixture silicone rubber. From the effect
of the raw material on the stress-strain curve, it can be known that if the fracture toughness of the brittle rock-like material
is to be increased and the brittle rock-like material has a certain ductility, the rosin should not be added too much, but an
appropriate amount of the auxiliary regulator epoxide resin and polyamide should be added.
APPLICATION OF ROCK-LIKE MATERIALS IN CRACK PROPAGATION EXPERIMENTS
Experimental design
n this experiment, crack propagation studies were carried out on specimens with the same original crack arrangement.
According to the previous test results, the raw material ratios of the crack propagation experiment was finally
determined, which was divided into the ratio of ductility group and the ratio of brittleness group, as shown in Tab. 3
and Tab. 4.
Number Raw materials Ratio Epoxide resin - polyamide content (%)
G1 Sand, barite, epoxy, polyamide and alcohol 300:300:4:4:40 1.23
G2 Sand, barite, epoxy, polyamide and alcohol 300:300:6:6:40 1.84
G3 Sand, barite, epoxy, polyamide and alcohol 300:300:8:8:40 2.47
G4 Sand, barite, epoxy, polyamide and alcohol 300:300:10:10:40 3.11
G5 Sand, barite, epoxy, polyamide and alcohol 300:300:12:12:40 3.61
Table 3: Ductility group ratio.
Number Raw materials Ratio Rosin content (%)
H1 Sand, barite, rosin and alcohol 200:200:5:15 1.19
H2 Sand, barite, rosin and alcohol 200:200:7:15 1.66
H3 Sand, barite, rosin and alcohol 200:200:9:15 2.12
H4 Sand, barite, rosin and alcohol 200:200:11:15 2.58
H5 Sand, barite, rosin and alcohol 200:200:13:15 3.04
Table 4: Brittleness group ratio.
The initial crack layout of this experiment is shown in Fig. 15 (2a shows the crack length, c shows the crack unconnected
rate, s indicates the crack pitch, and α indicates the crack inclination angle), and the specimen has a pre-crack opening degree
of 0.8 mm. The dimension of the specimen are 140mm high, 90mm wide and 40mm thick. In the experiment, the
geotechnical experimental servo test machine from Chongqing University was used as the experimental device, which can
control the loading mode by using a computer program and collect test data synchronously. Different ways of loading can
be performed by setting a computer program, and the loading rate can also be adjusted.
This experiment was to observe the whole process of cracking of cracked specimens, and the crack initiation, expansion
and coalescence speed were relatively fast. Therefore, in order to achieve the ideal image acquisition effect, the RDT/16
high-speed dynamic recording system was applied in the experiment. The loading mode of displacement control was selected
where the loading rate was 1mm/min, and the shooting speed of the high-speed dynamic recording system during loading
was 25 images per second.
I
H. Bai et alii, Frattura ed Integrità Strutturale, 56 (2021) 16-45; DOI: 10.3221/IGF-ESIS.56.02
36
Figure 15: Crack layout.
Characteristics of the crack propagation process
Comparative analysis of crack initiation modes
Tab. 5 is a comparison table of the crack initiation modes of the ductile group. The content of epoxide resin and polyamide
is gradually reduced from left to right, that is, the brittleness of the material is gradually increased.
By comparing and analyzing Tab. 5, it can be seen that as the content of epoxide resin and polyamide decreases gradually,
the new crack initiation mode gradually changes from the state where the initial wing crack and shear crack coexist to only
the wing crack. Through the observation of the experimental loading process and the analysis of the experimental data, it is
found that there is no significant difference in the vertical compression displacement of each specimen when the new crack
starts to sprout.
G5 G4 G3 G2 G1
a- wing crack
b- shear crack
c- wing crack
d- shear crack
a- shear crack
b- wing crack
c- wing crack
d- shear crack
a- shear crack
b- shear crack
c- wing crack
d- wing crack
a- wing crack
b- wing crack
c- wing crack
d- wing crack
a- wing crack
b- wing crack
c- wing crack
d- wing crack
Table 5: Crack initiation mode of the ductile group.
G5
G5
G4
G4
G3
G3
G2
G2
G1
G1
20mm 20mm 20mm 20mm 20mm
H. Bai et alii, Frattura ed Integrità Strutturale, 56 (2021) 16-45; DOI: 10.3221/IGF-ESIS.56.02
37
Tab. 6 is a comparison table of the crack initiation modes of the brittle group. The rosin content increases from left to right,
that is, the brittleness of the material increases gradually.
By comparing and analyzing Tab. 6, it can be seen that as the rosin content increases gradually, the new crack initiation
mode is almost all wing crack. Observing the experimental loading process and analyzing the experimental data, it is found
that when the new crack begins to sprout, the vertical compression displacement of the specimen with more rosin content
is smaller.
H1 H2 H3 H4 H5
a- wing crack
b- wing crack
c- wing crack
d- wing crack
a- wing crack
b- wing crack
c- wing crack
d- wing crack
a- wing crack
b- wing crack
c- wing crack
d- wing crack
a- wing crack
b- wing crack
c- wing crack
d- wing crack
a- wing crack
b- wing crack
c- wing crack
d- wing crack
Table 6: Crack initiation mode of the brittle group.
According to the comprehensive analysis of the two tables, as the brittleness of the material increases gradually, the new
crack initiation mode of the rock-like material gradually changes from shear crack to wing crack. At the same time, when
the new crack starts to sprout, the vertical compression displacement of the specimen gradually decreases.
Comparative analysis of crack coalescence failure mode
Tab. 7 is a comparison table of the crack coalescence failure modes of the ductile group. The content of epoxide resin and
polyamide gradually reduces from left to right, that is, the brittleness of the material gradually increases.
By comparing and analyzing Tab. 7, it can be seen that as the content of epoxide resin and polyamide reduces gradually, the
crack coalescence failure mode gradually changes from the initial composite failure of tensile and shear to the tensile failure.
Observing the experimental loading process and analyzing the experimental data, it can be found that when the cracks
coalesce, the vertical compression displacement of the specimen with lower content of epoxide resin and polyamide is
smaller.
Tab. 8 is a comparison table of the crack coalescence failure modes of brittle group. The content of rosin is gradually
increased from left to right, that is, the brittleness of the material is gradually increased.
By comparing and analyzing Tab. 8, it can be seen that as the content of rosin increases gradually, the crack coalescence
failure mode is almost all tensile failure. Observing the experimental loading process and analyzing the experimental data, it
can be found that when the cracks coalesce, the vertical compression displacement of the specimen with more rosin content
is smaller.
According to the comprehensive analysis of the two tables, as the brittleness of the material increases gradually, the crack
coalescence failure mode of the rock-like material gradually changes from the composite failure of tensile and shear to tensile
H1
H1
H2
H2
H3
H3
H4
H4
H5
H5
20mm 20mm 20mm 20mm 20mm
H. Bai et alii, Frattura ed Integrità Strutturale, 56 (2021) 16-45; DOI: 10.3221/IGF-ESIS.56.02
38
failure. At the same time, the vertical compression displacement of the specimen gradually decreases when the cracks
coalesce.
G5 G4 G3 G2 G1
composite failure
of tensile-shear
composite failure
of tensile-shear
composite failure
of tensile-shear
composite failure
of tensile-shear
tensile failure
Table 7: Sketch of crack coalescence of ductile group.
H1 H2 H3 H4 H5
Tensile failure Tensile failure Tensile failure Tensile failure Tensile failure
Table 8: Sketch of crack coalescence.
Analysis of mechanical properties of rock-like materials
Analysis of crack initiation stress
① Crack initiation stress of ductile group
Crack initiation stress refers to the value of instantaneous stress when the initial crack of the specimen is expanded to form
a new crack. Under the action of uniaxial compression load, the two initial pre-cracks in the specimen do not necessarily
produce new cracks at the same time, that is, the initial crack initiation stress of the two initial pre-cracks may be different.
Comparing the photos taken by the high-speed camera at different times with the stresses and strains recorded by the
uniaxial compression servo system, then the time, strain and stress of cracking of each initial pre-crack can be determined.
The crack initiation stress and its average value of the two initial pre-cracks are shown in Tab. 9 and Tab. 10. The relationship
between the crack initiation stress and the ratio of different raw materials is shown in Fig. 16.
It is found that each specimen produces new cracks in the experiment. Moreover, it can be found that changing the content
of epoxide resin-polyamide or rosin, the crack initiation stress of the first crack in the specimen is not significantly different
from the crack initiation stress of the second crack. The reason may be that the cracking of the first crack causes stress
redistribution, which in turn causes rapid cracking of the other crack. By comparing and analyzing the crack initiation stress
of the specimen with different content of epoxide resin-polyamide or rosin, it is found that the initial pre-crack in the
specimen with less content of epoxide resin-polyamide or rosin is more susceptible to cracking.
G5 G4 G3 G2 G1
H1 H2 H3 H4 H5
20mm 20mm 20mm 20mm 20mm
20mm 20mm 20mm 20mm 20mm
H. Bai et alii, Frattura ed Integrità Strutturale, 56 (2021) 16-45; DOI: 10.3221/IGF-ESIS.56.02
39
Number
Crack initiation stress of
crack①
Crack initiation stress of
crack②
Average value of crack
initiation stress
G1 0.61 0.71 0.66
G2 0.78 0.72 0.75
G3 0.82 0.94 0.88
G4 1.07 1.11 1.09
G5 1.38 1.34 1.36
Table 9: Crack initiation stress of ductile group (MPa).
Number
Crack initiation stress of
crack①
Crack initiation stress of
crack②
Average value of crack
initiation stress
H1 0.63 0.55 0.59
H2 0.86 0.76 0.81
H3 0.93 0.97 0.95
H4 1.11 1.13 1.12
H5 1.19 1.15 1.17
Table 10: Crack initiation stress of brittle group (MPa).
1.0 1.5 2.0 2.5 3.0 3.5 4.0
0.4
0.6
0.8
1.0
1.2
1.4
1.6
crack①
crack②
C
ra
c
k
i
n
it
ia
ti
o
n
s
tr
e
ss
(
M
P
a
)
Content of epoxide resin and polyamide (%)
1.0 1.5 2.0 2.5 3.0 3.5
0.4
0.6
0.8
1.0
1.2
1.4
crack①
crack②
C
ra
c
k
i
n
it
ia
ti
o
n
s
tr
e
ss
(
M
P
a
)
Rosin content (%)
Figure 16: The crack initiation stress of two cracks in specimens.
Analysis of peak strain
① Peak strain of ductile group
The peak strain of the specimen with different epoxide resin-polyamide content was obtained by processing the experiment
data, as shown in Tab. 11. The relationship between the peak strain of the specimen and the content of epoxide resin-
polyamide is shown in Fig. 17.
It can be seen from the figure that the minimum peak strain of the specimen is 0.80% and the maximum peak strain is
1.55%. Therefore, it can be considered that the change of the content of epoxide resin-polyamide has a relatively striking
influence on the peak strain of the specimen. At the same time, with the increase of epoxide resin-polyamide content, the
H. Bai et alii, Frattura ed Integrità Strutturale, 56 (2021) 16-45; DOI: 10.3221/IGF-ESIS.56.02
40
peak strain of the specimen shows an increasing trend. Meanwhile the peak strain increases rapidly from the beginning, and
then increases slowly.
Epoxide resin - polyamide content (%) 1.23 1.84 2.47 3.11 3.61
Peak strain (%) 0.80 1.04 1.23 1.47 1.55
Table 11: Peak strain of ductile group.
1.0 1.5 2.0 2.5 3.0 3.5 4.0
0.8
1.0
1.2
1.4
1.6
P
e
a
k
S
tr
a
in
(
%
)
Content of epoxide resin and polyamide (%)
Figure 17: The relationship between peak strain and epoxide resin-polyamide content.
② Peak strain of brittle group
The peak strain of the specimen with different rosin content was obtained by processing the experiment data, as shown in
Tab. 12. The relationship between the peak strain of the specimen and the rosin content is shown in Fig. 18.
It can be seen from the figure that the minimum peak strain of the specimen is 0.41% and the maximum peak strain is
0.70%. Therefore, it can be considered that the change of the rosin content has modest influence on the peak strain of the
specimen but is not very obvious. At the same time, with the rosin content increases, the peak strain of the specimen shows
a decreasing trend, and the strain decreases rapidly from the start and then decreases slowly.
Rosin content (%) 1.19 1.65 2.13 2.56 3.05
Peak strain (%) 0.70 0.64 0.51 0.44 0.41
Table 12: Peak strain of brittle group.
1.0 1.5 2.0 2.5 3.0
0.4
0.5
0.6
0.7
P
e
a
k
S
tr
a
in
(
%
)
Epoxide resin-polyamide content (%)
Figure 18: The relationship between peak strain and rosin content.
H. Bai et alii, Frattura ed Integrità Strutturale, 56 (2021) 16-45; DOI: 10.3221/IGF-ESIS.56.02
41
By comparing the peak strains of the ductile group and the brittle group, it can be known that the content of the
cementitious material has a certain influence on the peak strain of the material. Moreover, with the brittleness of the material
increases, the peak strain of the material gradually decreases.
Analysis of crack connection mode and connection stress
Tab. 13 is a table of crack connection modes of ductile group. The epoxide resin-polyamide content gradually reduces from
left to right, that is, the brittleness of the material gradually increases. By analyzing Tab. 13, it shows that as the epoxide
resin-polyamide content decreases gradually, the crack connection mode has no obvious regularity, and the wing crack
connection is the main connection mode. At the same time, it can be found that as the epoxide resin-polyamide content
reduces, and correspondingly the crack connection stress gradually reduces.
G5 G4 G3 G2 G1
Initial crack ① is
connected to wing
crack “c”.
Wing crack “b” is
connected to wing
crack “c”.
Shear crack “b” is
connected to wing
crack “c”.
Wing crack “b” is
connected to initial
crack ②.
Wing crack “b” is
connected to wing
crack “c”.
Connection stress
is 1.54 MPa
Connection stress
is 1.30 MPa
Connection stress
is 1.05 MPa
Connection stress
is 0.89 MPa
Connection stress
is 0.74 MPa
Table 13: Crack connection mode of ductile group.
Tab. 14 is a table of crack connection modes of brittle group. The rosin content gradually increases from left to right, that
is, the brittleness of the material gradually increases. Through the analysis of Tab. 14, it indicates that as the rosin content
increases gradually, the crack connection mode has no obvious regularity, and the wing crack connection is the main
connection mode. At the same time, it can be found that as the rosin content increases, the crack connection stress gradually
increases accordingly.
In order to compare the relative magnitude relationship between crack initiation stress, connection stress and peak intensity,
a comparative analysis of the three is performed, as shown in Fig. 19. It can be found that as the epoxide resin-polyamide
content increases gradually, that is, the ductility of the material gradually increases, the crack connection stress gradually
approaches the peak strength. At the same time, as the rosin content increases gradually, that is, the brittleness of the material
increases gradually, the crack connection stress gradually approaches the initiation stress.
Future developments will be addressed to improve the mechanical strength in case of more complex geometrical
discontinuities [38-39]. A specific focus on the cyclic behavior will be addressed to improve the total final fatigue life at
room [40-42] and high temperature [43] as made for traditional materials. This will allow to improve locally the strength to
counterbalance local geometrical effects that can occur in a real 3D component [44-49].
G5 G4 G3 G2 G1
G5 G4 G3 G2 G1
20mm 20mm 20mm 20mm 20mm
H. Bai et alii, Frattura ed Integrità Strutturale, 56 (2021) 16-45; DOI: 10.3221/IGF-ESIS.56.02
42
H1 H2 H3 H4 H5
Wing crack “b” is
connected to wing
crack “c”.
Wing crack “b” is
connected to wing
crack “c”.
Wing crack “b” is
connected to initial
crack ②.
Wing crack “b” is
connected to wing
crack “c”.
Wing crack “b” is
connected to wing
crack “c”.
Connection stress
is 0.73 MPa
Connection stress
is 0.90 MPa
Connection stress
is 1.06 MPa
Connection stress
is 1.17 MPa
Connection stress
is 1.22 MPa
Table 14: Crack connection mode of brittle group.
1.0 1.5 2.0 2.5 3.0 3.5 4.0
0.6
0.8
1.0
1.2
1.4
1.6
S
tr
e
ss
(
M
P
a
)
Epoxide resin-polyamide content (%)
Peak intensity
Crack connection stress
Crack initiation stress
1.0 1.5 2.0 2.5 3.0
0.6
0.8
1.0
1.2
1.4
S
tr
e
ss
(
M
P
a
)
Rosin content (%)
Peak intensity
Crack connection stress
Crack initiation stress
Figure 19: The relationship between peak intensity, connection stress and initiation stress.
CONCLUSIONS
ased on the mechanical properties of ductile and brittle rocks, certain raw materials were selected and the mechanical
laws of ductile and brittle rock-like materials were obtained. And two rock-like materials were applied to the
experiment of crack propagation. The main conclusions can be summarized as follows:
For the simulation of ductile rock-like materials, sand and barite powder as filler materials, epoxide resin and polyamide as
cementitious materials, and alcohol as organic solvent can be chosen. When the content of the cementitious material
increases, the uniaxial compressive strength and fracture toughness of the ductile rock-like material significantly improve,
B
H1 H2 H3 H4 H5
H1 H2 H3 H4 H5
20mm 20mm 20mm 20mm 20mm
H. Bai et alii, Frattura ed Integrità Strutturale, 56 (2021) 16-45; DOI: 10.3221/IGF-ESIS.56.02
43
and the change of elastic modulus is not obvious. When the content of other raw materials cannot be changed, the addition
of auxiliary material silicone rubber is mainly to reduce the elastic modulus and strength of this ductile rock-like material,
and the addition of rosin is mainly to improve the elastic modulus and brittleness of ductile rock-like materials. Similarly,
using sand and barite powder as a filling material, rosin as a cementitious material, and alcohol as an organic solvent brittle
rock-like materials can be better simulated. When the content of the cementitious material increases, the elastic modulus
and the uniaxial compressive strength of brittle rock-like materials significantly improve, and the fracture toughness even
improves more obviously. When the content of other raw materials cannot be changed, the auxiliary materials epoxide resin
and polyamide are mainly added to make the brittle rock-like materials have certain ductility, and the addition of silicone
rubber is mainly to reduce the elastic modulus and brittleness of brittle rock-like materials.
Through the crack propagation model experiment of rock-like materials, it is found that as the brittleness of the material
increases, the new crack initiation mode of the rock-like material gradually changes from shear crack to wing crack, and the
vertical compression displacement of the specimen will gradually decrease when the new crack starts to sprout. When the
cracks coalesce, the wing crack connection is the main connection mode, and the vertical compression displacement of the
specimen with low content of epoxide resin and polyamide in the ductile group or high content of rosin in the brittle group
is smaller. It can be also known that the damage of the ductile group specimen is mainly based on the tensile-shear composite
failure mode, while the damage of the brittle group specimen is mostly the tensile failure mode. Moreover, for the specimens
of ductile group, as the content of epoxide resin and polyamide increases gradually, the crack connection stress increases
and gradually approaches the peak strength. For the specimens of brittle group, as the rosin content increases gradually, the
crack connection stress increases but gradually approaches the initiation stress.
ACKNOWLEDGEMENTS
he work is supported by the National Natural Science Foundation of China (Nos. 41807251, 52027814, 51809198, 51839009 and
51679017), Fundamental Research Funds for the Central Universities (No. 2042018kf0008).
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