experimentalstudyoffracturecharacterizationsofrocksunder...
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Research ArticleExperimental Study of Fracture Characterizations of Rocks underDynamic Tension Test with Image Processing
Dihao Ai Yuechao Zhao Beijing Xie and Chengwu Li
College of Resources and Safety Engineering China University of Mining and Technology Beijing 100083 China
Correspondence should be addressed to Chengwu Li lcwcumtbeducn
Received 28 April 2019 Accepted 17 June 2019 Published 1 July 2019
Academic Editor Stefano Manzoni
Copyright copy 2019 Dihao Ai et al +is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
To investigate the fracture characterizations of rocks under high strain rate tensile failure a series of dynamic Brazilian tests wasconducted using Split Hopkinson pressure bar (SHPB) and a high-speed digital camera at a frame rate of 50000 frames persecond (FPS) with a resolution of 272times 512 pixels was adopted to capture the real-time images and visualize the failure processesUsing the extracted cracks and image processing technique the relationship between loading condition (impact velocity) crackpropagation process (crack velocity crack fractal characteristic and crack morphological features) and dynamic mechanicalproperties (absorbed energy and strain-stress parameters) was explored and analyzed +e experimental results indicate that (1)impact velocity plays a critical role in both crack propagation process and dynamic mechanical properties (2) the crack fractaldimension is positively correlated with crack propagation velocity and has a linear relationship with the proposed morphologicalfeature of crack (3) mean strain rate and max strain of rocks under SHPB loading both decrease with the increase of crackpropagation velocity and (4) the energy absorbed by the rocks increases with increasing impact velocity and has a strong negativecorrelation with a proposed novel crack descriptor Experimental studies pertaining to the measurement of crack propagationpath and velocity in particular some crack feature extraction approaches present a promising way to reveal the fracture processand failure mechanisms of rock-like materials
1 Introduction
Fully understanding the dynamic rock mechanics is ofgreat importance in dealing with a wide range of civilengineering applications eg earthquakes mining sub-way tunnel excavation blasting events and protectiveconstruction project [1 2] +e properties of rocks underdynamic loading tests always are very different from thoseof static tests due to the transient nature of high strain rateloading therefore several testing methods for determiningthe dynamic properties and fracture behavior of rocks havebeen conducted over the past few decades eg Braziliandisc (BD) [3 4] semicircular bending (SCB) [5 6]notched semicircular bending (NSCB) [7ndash9] crackedchevron notched BD (CCNBD) [10] cracked chevronNSCB (CCNSCB) [11] flattened BD (FBD) [12] and holedcracked FBD (HCFBD) [13] Additionally the dynamicmechanical behavior of rock materials under different testconditions has been extensively studied eg dynamic
uniaxial compressive test dynamic triaxial compressivetest dynamic tensile test and dynamic shear test Forexample Lundberg [14] performed some compressiontests on rock-like materials using the SHPB techniqueIsheyskiy and Marinin [15] investigated the strength ofblasted rocks accounting for fracture zones and exploredthe relationship between uniaxial compressive strength ofaverage rock and energy consumption Gary and Bailly[16] applied some improved loading technique to de-termine the triaxial compressive strength of rock-likematerials Zhao et al [17] investigated the dynamic shearstrengths of rock-like materials using a pneumatichy-draulic machine
Moreover it has been generally recognized that rock androck-like materials are much weaker in tension than com-pression +erefore accurate determination of dynamicresponse and fracture properties of rocks under high strainrate tensile failure is important In general dynamic tensiontesting methods are being continuously improved from the
HindawiShock and VibrationVolume 2019 Article ID 6352609 14 pageshttpsdoiorg10115520196352609
original quasistatic ones to precisely determine the dynamictensile strength which can be approximately classified intotwo categories direct tensile and indirect tensile testingmethods [1] Compared with the direct testing method tomeasure the tensile strength of rock material an indirecttesting method provides a more convenient and accuratealternative not only for the specimen preparation but also forthe experimental design [18]
More specifically the primary testing methods todetermine the dynamic tensile strength of rock are ba-sically extended from corresponding quasistatic ones andmainly include BD or FBD method bending [19] or SCBmethod [5] spalling method [20ndash22] etc SpecificallyZhou et al [3] and Zhao et al [4] conducted several testson rock specimens with BD configuration using a SHPBand investigated the dynamic indirect tensile strength ofrocks under different loading conditions Dai et al [5 6]explored the rate dependence of tensile strength of rocksunder SHPB impact loading using SCB Biolzi and Labuz[23] investigated the deformation of a rock specimen inthe classical four-point bend (FPB) fracture tests Wanget al [24] also assessed the FPB method for testing thetensile strength and fracture toughness of rocks by usingthe SHPB apparatus Klepaczko and Brara [20] performeda dynamic tensile test for concreate using spallingmethod In addition to the above indirect tension testAsprone et al [25] investigated the dynamic behavior ofrock-like materials using the dynamic DT (Direct ten-sion) method Among these the BD test is widely used formeasuring the static and dynamic fracture toughness ofrock and rock-like materials under the Split Hopkinsonpressure bar (SHPB) loading SHPB is a highly reliableapparatus and widely utilized to quantify the dynamicproperties of rocks under high strain rates since it wasinvented by Kolsky in 1949 [26] and many efforts havebeen made to improve the measurement results [27 28]Moreover these experiments always are conducted toexplore the dynamic mechanical properties of rocks aswell as crack initiation propagation and coalescenceunder different SHPB loading rates [11 29ndash31] For ex-ample Zhang and Zhao [32] performed an experimentalinvestigation about quasistatic and dynamic fracturebehavior of rock materials by a servohydraulic and SHPBloading system Bertram and Kalthoff [33] investigatedthe Mode-I propagation processes for limestone materialunder different crack speeds and explained the charac-teristics of the crack propagation path of brittle materialsbased on the experimental results Also in Mode-I rockfracture process Dai et al [11] and Chen et al [34]employed SHPB and laser gap gauge to study the dynamicfracture properties of rock-like materials with CCNSCBand SCB configuration respectively Forquin [35] pro-posed a crack velocity measurement method using opticalcorrelation technique for concrete and rock-like mate-rials under dynamic tensile loading test Zhao et al [36]also adopted a high-speed digital camera to record thecrack propagation process of coal materials under SHPBimpact loading and explored its fractal characteristicsGomez et al [37] performed a photoelastic dynamic
splitting experiment and studied the dynamic behavior ofconcrete and granite with tensile damage
Since dynamic fracture of rockmaterial is a very complexbehavior some traditional contact measurement approacheslike resistance strain gauges cannot provide enough in-formation to reveal the dynamic fracture process of rock+erefore many noncontact and optical measurementtechniques have been adopted and developed as a promisingway in the experiment to record the fracture process andfurther reveal the fracture process and failure mechanisms ofrock materials [38] +ese techniques can be approximatelyclassified into following groups ie CT (computed to-mography) [39 40] SEM (scanning electron microscope)[41 42] X-ray phase contrast imaging (PCI) [43 44] LGG(laser gap gauge) [34 45] DIC (digital image correlation)[46ndash48] and DIT (dynamic infrared tomography) [49]Among them using the high-speed amp high-resolutioncamera is the most convenient way to capture the fractureprocess of rock material
Nevertheless with regard to the crack evolutioncharacteristics and failure process the investigation ismore challenging than that of stress-strain on the rockspecimen in SHPB experiments since there are no effectivecharacteristic parameters that can quantitatively describecrack propagation To the best of our knowledge researchstudies into the relationship between crack propagationand mechanical properties are relatively few +ereforewe proposed a data processing method based on Ratsnakegraphic annotation software [50] and Halcon machinevision software [51] to extract crack propagation featureswhich are further compared with the dynamic mechanicalproperties of rocks +e main aim of this study is to vi-sualize the relationship between crack propagation pro-cess and mechanical properties of rock using extractedmulticracks and then to investigate and reveal the futurefracture behavior of the rock materials
2 Experiment Procedures
21 Experimental Design and Rock Specimens +e dynamicBrazilian tensile test is conducted using the SHPB systemat China University of Mining and Technology Beijing(CUMTB) and the schematic and physical map of theexperimental setup are shown in Figures 1 and 2respectively
+e SHPB system mainly consists of power system barsstrain wave collector and high frame rate camera In orderto satisfy the one-dimensional stress wave propagation wavethe length of the bars should be 30 times of the bar diameter[3] +erefore the length and the diameter of the barsutilized in the experiment are 2000mm and 50mm and thelength and diameter of the bullet are 400mm and 50mm Inaddition all the bars used in the SHPB test are 35CrMn steelmaterial with 7800 kgm3 density 206GPa Youngrsquos mod-ulus and 028 Poissonrsquos ratio
To visualize the fracture process and further revealfracture mechanism FASTCAM SA5 (16G) camera wasemployed to capture the fractured images of rock whichadopts the CMOS sensor with a 20 μm pixel delivering an
2 Shock and Vibration
ISO light sensitivity of 10000 monochrome and 4000colors When the frame rate is set to 1000000 FPS theresolution of the captured image is only 16 times 64 pixels onthe other hand when the resolution is set to 1024 times1024the maximum frame rate is only 7000 FPS which cannotcapture the fracture process of a rock specimen underSHPB impact loading erefore the camera is set to272 times 512 pixels resolution at a frame rate of 50000 FPS inthe experiment
e rock samples utilized in the experiment aremanufactured by sandstone selected from a quarry in theFangshan area of Beijing China According to the ISRMsuggestion for BD specimens preparation the rock
specimens were cut from the same rock block withoutobvious bedding and manufactured to a cylinder with adimension of 50mm in diameter and 25mm in lengthMoreover two ends of the rock specimen were nelyground to be at within an accuracy of plusmn005mm andperpendicular to the longitudinal axis no morethan plusmn025deg At last the surface of the rock samples issmooth by Vaseline lubricant
22 SHPB Test SHPB is an ideal apparatus for testing thedynamic response of materials and its principle is basedon the one-dimensional (1D) stress wave propagation Toaccurately calculate the dynamic properties of rock ma-terial under SHPB loading the following three assump-tions also require to be satised [1] (1) propagation ofelastic waves in the bars satised 1D stress wave theorywhich determined by the bar dimensions (2) neglectingthe friction and inertia eects on the rock specimen whichcan be fullled approximately with the suggested testingprocedures (3) specimen reaches stress equilibrium For aclassic SHPB test when the bullet impacts the incidentbar a compressive pulse is generated and propagatestowards the rock sample With the above recorded in-cident εi(t) reected εr(t) and transmitted εt(t) strainsignals the stress σ(t) strain ε(t) and strain rate _ε(t) ofrock material under dierent impact velocities can beexpressed as
Laser beams
εi
εr
εt
Nitrogen
Bullet
Damper
Strain gauge
Light source
Specimen
Incident bar
TTL out
High frame rate camera
Transmission barAbsorption bar
Waveform record system
Strain amplifier
Speed test system
TTL in
Incident waveReflected waveTransmitted wave
εiεrεt
Figure 1 Schematic map of the SHPB experimental system
Figure 2 Physical map of the SHPB experimental system
Shock and Vibration 3
σ(t) AE
2ASεi(t) + εr(t) + εt(t)1113858 1113859 (1)
ε(t) C
LS1113946
t
0εi(t)minus εr(t)minus εt(t)1113858 1113859dt (2)
_ε(t) C
LSεi(t)minus εr(t)minus εt(t)1113858 1113859 (3)
where A and AS are the cross-sectional area of the bar androck specimen respectively E is Youngrsquos modulus of the barC is the longitudinal stress wave speed of the bar and LSdenotes the length of rock specimen
Also the dynamic forces on the incident and transmittedends P1 and P2 can be computed as
P1 AE εi + εr( 1113857
P2 AEεt(4)
3 Methodology
Figure 3 shows the framework of our proposed methodwhich mainly consists of two parts ie crack feature ex-traction and dynamic mechanical properties calculationFirstly the video of the fracture process of rock specimens issplit into several images which will be postprocessed by thecrack extraction module To achieve the accurate extractionof cracks a novel and efficient image annotation softwaretool Ratsnake [50] is adopted to identify and extract crackson rock surface accurately According to the principles ofconnected domain approach used in semantic image seg-mentation application images of extracted cracks of rockspecimens under SHPB impact loading are obtained +enby Halcon [51] machine vision software a number of novelcrack features have been proposed and calculated to describethe fracture process of rock under different loading rates Atthe same time dynamic mechanical properties also havebeen computed based on the above formulas Finally acorrelation matrix was constructed based on Pearsonrsquoscorrelation coefficient
As illustrated in Figure 4 the correlation matrix heat-map has been calculated based on the experimental data tovisualize the relationship between loading condition crackpropagation process and dynamic mechanical properties ofrocks under different SHPB impact velocities
Given paired data (x1 y1) (xn yn)1113864 1113865 consisting ofn pairs Pearsonrsquos correlation coefficient rxy is defined as
rxy 1113936
ni1 xi minusx( 1113857 yi minusy( 1113857
1113936ni1 xi minus x( 1113857
21113969
1113936ni1 yi minusy( 1113857
21113969 (5)
where n is the sample size xi yi are the individual pointsindexed with i and x y are the sample mean values of x andy points
In the correlation matrix heat-map larger positivevalues were represented by dark red colors denoting astrong positive correlation between two variables whilelarger negative values were represented by dark blue colors
which indicate a strong negative correlation between twovariables
4 Results and Discussion
41 Crack Propagation Process
411 Crack Propagation Velocity Over the past few de-cades there have been some investigations for crackpropagation velocities of rock materials under dynamicloading which provide a promising way to explore thefracture mechanisms of rock materials [1 18] Howeverrelatively few crack extraction approaches based on imageprocessing have been conducted on rock specimens to de-scribe the failure process and explore the fracture mecha-nism due to the technical difficulties associated with crackfeature extraction and computation
In this study the crack propagation velocity V and VAPwere calculated according to the crack length and crack area(the number of crack pixels) [52] as shown in Figures 5 and 6
To visualize the relationship between these two crackvelocity variables Figure 7 plots VAP
as a function of V aswell as the fitting curve It can be seen that VAP
increasesalmost linearly with the increased of V under SHPBloading
412 Crack Fractal Characteristic Since cracks on rocksurface are an important index to measure the state of rockmaterial and fractals exhibit the ability for measuring thecomplex topological pattern many significant endeavorshave been made to investigate the fractality of cracks to themechanics of fracture [53 54]
In mathematics a fractal dimension is used to evaluatethe fractal patterns by quantifying their complexity as a ratioof the change in detail to the change in scale [55] Unliketopological dimensions the fractal dimension can takenoninteger values Particularly there are many formalmathematical definitions for fractal dimension eg box-counting dimension information dimension and correla-tion dimension Among them the box-counting dimensionis calculated by counting how this number changes as itmakes the grid finer by applying a box-counting algorithmIn more detail by the box-counting dimension computationmethod the fractal dimension of an object can be computedas [56]
N C middot SD
(6)
where D is fractal dimension S the scale of the object(cracks) N the number of boxes of scale S required to coverthe object (cracks) and C a constant number Taking thelogarithm it can be rewritten
lnN lnC + D middot ln S (7)
+erefore the box-counting dimensionD can be definedas
D minuslimsrarr0
lnN
ln S (8)
4 Shock and Vibration
Figure 8 presents an illustration for crack coverageusing dierent scale boxes (S 8 16 32 64) whileFigure 9(a) plots the linear tting results of lnN and ln Swhich shows the fractal dimension is 114 for current crackson rock surface Based on the plots of lnN and ln S the
fractal dimension of the crack can be accumulated byformula (8)
In general the higher fractal dimension indicates a morecurved and intricate crack propagation path ereforeaccording to the above method the fractal dimension of
ρXY
= cov(x y)σxσy
3167ms3246ms3577ms3511ms3869ms4307ms4385ms4443ms4687ms5150ms5502ms
Set gridsCrack
annotation
Export mask binary image
Set connection domain
Input image
Output cracks
helliphellip
helliphellip
Crack central coordinate
Crack area and crack number
Crack fractal dimension
Crack statistical information
Crack morphological features
Crack extraction
Time
Time
Y
X
X
Y
Impact velocity
Absorbed energy
Max strain
Max stress
Mean strain rate
Crack fracture video
Images of extracted cracks
Dynamic fractureprocess investigation
(a)
(b)
(c)
(f) (g)
(d) (e)
(h)
6
5
4
Stre
ss (M
Pa)
3
2
1
0
00 25 50 75Strain (times10ndash3)
100 125 150 175
100
100
100
100
100
100
100
100
100
100
062
062
068
068
044
044
ndash078
ndash078
ndash029
ndash029
050
050
ndash062
067
ndash062
ndash049
ndash049
ndash02608
04
00
ndash04
ndash08ndash026 ndash065 ndash060 ndash019 010 ndash005 ndash063 ndash025
ndash074 ndash062 ndash022 018 004 ndash026
ndash010 ndash014 ndash021 053 ndash004 ndash027 ndash029 ndash025
023 035 014 ndash051 ndash016 ndash026ndash027 ndash063
005 ndash029 ndash023 039 004ndash004ndash016 ndash005
039ndash038ndash014 ndash040 018053ndash051 010
ndash040 ndash023072037
083
ndash022ndash021014 ndash019
072 ndash038 ndash029 ndash062ndash014035 ndash060
083 037 ndash014 005 ndash074ndash010023 ndash065
ndash029
067
Figure 3 An overview of the proposed approach for the investigation of dynamic fracture process of rock materials under SHPB impactloading (a) an input video of rock fracture process (b) an algorithm for multicracks extraction (c) crack extraction results for a fractureprocess video (d) dynamic strain-stress response of rock specimens (e) the formula of Pearsonrsquos correlation coeiexclcient (f ) matrix of crackevolution features (g) matrix of dynamic mechanical properties (h) a correlation matrix heat-map of relationship between crack evolutionfeatures and dynamic mechanical properties
Loadingcondition
Crackpropagation
process
Dynamicmechanicalproperties
Impact velocity v
v
V
V
VAP
VAP
VAnis
VAnis
VComp
VComp
WS
WS
σmax
σmax
εmax
εmax
VD
VD
Crack propagation velocity
Crack fractals characteristic
Crack morphological features
Dynamic fracture energy
Strain-stress parameters
ε
100
100
100
100
100
100
100
100
100
100
062
062
068
068
044
044
ndash078
ndash078
ndash029
ndash029
050
050
ndash062
067
ndash062
ndash049
ndash049
ndash026
ndash026 ndash065 ndash060 ndash019 010 ndash005 ndash063 ndash025
ndash074 ndash062 ndash022 018 004 ndash026
ndash010 ndash014 ndash021 053 ndash004 ndash027 ndash029 ndash025
023 035 014 ndash051 ndash016 ndash026ndash027 ndash063
005 ndash029 ndash023 039 004ndash004ndash016 ndash005
039ndash038ndash014 ndash040 018053ndash051 010
ndash040 ndash023072037
083
ndash022ndash021014 ndash019
072 ndash038 ndash029 ndash062ndash014035 ndash060
083 037 ndash014 005 ndash074ndash010023 ndash065
ndash029
067ε
08
04
00
ndash04
ndash08
Figure 4 An illustration of the correlation matrix heat-map with loading condition crack propagation process and dynamic mechanicalproperties
Shock and Vibration 5
cracks in each frame of the rock fracture process has beenincreasing Figure 9(b) gives a quantitative description of thecrack propagation process of rock specimens under dierentimpact velocities It can be observed from it that the fractaldimension of cracks increases gradually during the fractureprocess of rocks and the value of the fractal dimension ofcracks on rock surface ranges from 08 to 12
Figure 10 shows the relationship between crack prop-agation velocity and fractal dimension velocity It has beenfound that both crack propagation velocities V and VAPincrease with increasingVD for rocks under dierent impactvelocities
413 Crack Morphological Features In addition toadopting the crack area AP and fractal dimension D toquantitatively describe the crack characteristics twomorphological features that can further analyze the crackevolution path and failure process are also proposed basedon image processing technique Figure 11 demonstrates acrack morphological process for crack initiation propa-gation and coalescence In order to present a quantitativedescription of the distribution and shape factor of cracksAnisometry and Compactness which derived from imagemorphology are proposed In specic Anisometry isderived from the geometric moments for each crack anddened as
Anisometry Ra
Rb (9)
where Ra denotes the main radius of maximum ellipse of thecrack and Rb represents the secondary radius of the ellipseSimilarly Compactness is also a shape factor which valueranges from 0 to 1 and can be expressed as
Compactness max 1 Cprime( )
Cprime L2
4 middot F middot π
(10)
where L is the total length of the contour and F is the area ofthe region
As shown in Figure 12(a) VComp is decreasing withthe increase of VD as a whole It can also be seen fromFigure 12(b) that the values of VAnis decrease almostlinearly with the increase of impact velocity which in-dicates that longitudinal crack length produced bythe rock is less than transversersquos under higher impactvelocity
414 Distribution of Cracks It has been generally rec-ognized that for a valid and typical dynamic Brazilian
5mm
0μs
(a)
75μs
a = 175mm
(b)
Figure 5 An illustration of crack propagation velocity computation using crack length
6000
A P (p
ixel
s) 4000
2000
0
0 100Time (micros)
200
Crack initiation
Crack coalescence
Crack propagi
nation
300
APFitting curve of AP
Figure 6 An illustration of crack propagation velocity compu-tation using crack area
Fitting curve of V and VAP
3 times 107
2 times 107
1 times 107
0
V AP (p
ixel
ss)
100V (ms)
200 300 400 500 600 700
Figure 7 Relationship between V and VAPof rock specimens
under SHPB loading
6 Shock and Vibration
test crack should be first appeared along the impactdirection somewhere near the center of the specimen andthen propagates bilaterally to the loading endsAccording to the row and column index of the crackcenter Figure 13 shows the coordinate distribution ofcrack center in the process of rock failure It can beobserved from Figure 13 that most of the rock disc cracksnear the center of the specimen and the fracture prop-agation direction are bilateral to the loading ends and
some cracks also appeared at the contact side of rock andbars +e result indicates that the failure patterns ofdynamic Brazil test under SHPB loading approximatelyinclude tensile failure and shear failure Accordingly thecracks near the center of rocks are mainly caused by thetensile failure which is the main axial crack parallel to theloading direction and other cracks are caused by theshear failure that is a result of secondary fractures due tothe further compression
ndash1
Fitting curve
D = 114 R2 = 099
ndash2
InS ndash3
ndash4
ndash5
2 3InN
4 5
(a)
12
10
D08
06
04
02
00200 300 400 500
BXY1 (4687ms)BXY2 (5150ms)BXY3 (4443ms)BXY4 (4385ms)BXY5 (3377ms)BXY6 (3167ms)
BXY7 (3511ms)BXY8 (3246ms)BXY9 (3689ms)BXY10 (4307ms)BXY11 (5502ms)
600 7001000Time (micros)
(b)
Figure 9 (a) Number of covered boxes versus box size (b) fractal characteristics of crack for rock material under different velocities
200
Scale = 64
100
00 100 200 300 400 500
(a)
Scale = 32
200
100
00 100 200 300 400 500
(b)
Scale = 16
200
100
00 100 200 300 400 500
(c)
Scale = 8
200
100
00 100 200 300 400 500
(d)
Figure 8 An illustration of different box scales to fully cover cracks
Shock and Vibration 7
42 Dynamic Mechanical Properties Figure 14 illustratesthe incident εi(t) reected εr(t) and transmitted εt(t)strain signals of rock specimens under dierent impactvelocities during SHPB dynamic loading test According
to the three-wave analysis method the mechanicalproperties of rocks under SHPB loading are determinedIn this study the absorbed energy and stress-strain pa-rameters are calculated and further compared with crack
100V
(ms
)
200
300
400
500
600
700
000 001VD (Dframe)
002 003 004 005 006 007
Fitting curve of VD and VAP
VAP
Fitting curve of VD and VV
4 times 107
3 times 107
2 times 107
1 times 107
0
V AP (p
ixel
ss)
Figure 10 Relationship between V VAP and VD in the SHPB experiment
Crack initiation
(a) (b)
Crack propagination
(c) (d)
Crack coalescence
(e)
F
LRb
Ra
(f )
Figure 11 An illustration of crack morphological features (a) (c) and (e) are original images represent crack initiation propagation andcoalescence respectively (b) (d) and (f) are extracted cracks from corresponded images
8 Shock and Vibration
propagation features to explore the relationship betweenthem
421 Dynamic Fracture Energy It has been generally rec-ognized that the fracture of rock under loading rates is theprocess of accumulation and dissipation of energy [57] Inspecific the consumed energy under SHPB dynamic loadingcan be well quantified based on the first law of thermody-namics [34] During the SHPB dynamic loading test theenergy of the incident wave WI the energy of the reflectedwave WR and the energy of the transmitted wave WT can becomputed as
WI A middot C
E1113946 εi(t)
2dt
WR A middot C
E1113946 εr(t)
2dt
WT A middot C
E1113946 εt(t)
2dt
(11)
where A is the cross-sectional area C is the longitudinalwave speed and E is Youngrsquos modulus of the bars
Assuming that all the energy loss at the specimen and barinterfaces can be negligible the energy absorbed by the rockspecimen WS can be expressed as
Fitting curve of VD and VComp
10
12
14
16
18
20
22
24
26
28V C
omp (
com
pfr
ame)
001 002 003 004 005 006 007000VD (Dframe)
(a)
Fitting curve of v and VAnis
35 40 45 50 5530v (ms)
8
10
12
14
16
18
20
22
24
V Ani
s (an
isfr
ame)
(b)
Figure 12 (a) Relationship between VComp and VD (b) relationship between VAnis and V
Impact velocity
Incident bar Transmission bar
Rock specimen250
200
Imag
e hei
ght (
pixe
ls)
150
100
50
0
BXY1BXY2BXY3
BXY4BXY5BXY6
BXY7BXY8BXY9
BXY10BXY11
200 300 400 5001000Image width (pixels)
Figure 13 Crack distribution for rocks under different impact velocities
Shock and Vibration 9
WS WI minusWR minusWT (12)
Figure 15 shows the total energy absorbed versus theimpact velocity for the rock specimens It indicates that the
energy absorbed by the rock specimen increases with in-creasing impact velocity
Moreover substantial efforts have been devoted to per-forming quantitative measurements on fracture surface and it
εi-4687msεi-5150msεi-4443msεi-4385msεi-3377msεi-3167msεi-3511msεi-3246msεi-3869msεi-4307msεi-5502ms
εt-4687msεt-5150msεt-4443msεt-4385msεt-3377msεt-3167msεt-3511msεt-3246msεt-3869msεt-4307msεt-5502ms
εr-4687msεr-5150msεr-4443msεr-4385msεr-3377msεr-3167msεr-3511msεr-3246msεr-3869msεr-4307msεr-5502ms
140 160 180 200 220 240 260 280120100
3
2
1
0
ndash1V
olta
ge (V
)ndash2
ndash3
Time (μs)
Figure 14 Incident reflected and transmitted signals of rocks under different impact velocities
18
WS (
J)
16
14
12
10
8
6
4
2
030 35 40 45 50 55
v (ms)
Fitting curve of v and WS
Figure 15 Relationship between v and WS
10 Shock and Vibration
has been well recognized that surface roughness in rock-likematerials exhibits self-similarity properties at least over a givenrange of length scales In other words the fracture surfacetopography of rock-like materials reveals inherent details as-sociated with energy dissipation mechanisms that govern thefracturing process +erefore the relationship between fractaldimension and absorbed energy was first calculated and theresult is shown in Figure 16(a) However it can be found thatthere is no obvious relationship between the two variables
On the other hand Figure 16(b) presents the total energyabsorbed WS versus the crack feature VAnis for the rockspecimens It can be seen that there is a linearly negativecorrelation between the two variables the greater the WSthe smaller the VAnis
422 Strain-Stress Parameters According to the incidentεi(t) reflected εr(t) and transmitted εt(t) strain signalsillustrated in Figure 14 and formulas (1)ndash(3) the max stressmax strain and mean strain rate of rocks under differentimpact velocities were calculated Combining with the crackcharacteristic parameters in the above section the re-lationship between the crack propagation process and dy-namic mechanical properties was analyzed
Figure 17 shows the max strain and mean strain rateversus the crack propagation velocity V while Figure 18shows the max strain and mean strain rate versus the crackpropagation velocity VAP
It can be seen that with theincrease of the V both the max strain and mean strain rateare gradually decreased and mean strain rate basically
000
001
002
003
004
005
006
007V D
(Dfr
ame)
2 4 6 8 10 12 14 16 180WS (J)
(a)
Fitting curve of WS and VAnis
2 4 6 8 10 12 14 16 180WS (J)
8
10
12
14
16
18
20
22
24
V Ani
s (an
isfr
ame)
(b)
Figure 16 (a) Relationship between WS and VD (b) relationship between WS and VAnis
Fitting curve of V and ε
66
68
70
72
74
76
78
εmiddot (sndash1
)
200 300 400 500
600 700100V (ms)
(a)
Fitting curve of V and εmax
200 300 400 500 600 700100V (ms)
25
30
35
40
45
50
55
60
65
70
ε max
(10ndash3
)
(b)
Figure 17 Curves of strain parameters with crack propagation velocity V and associated results after linear fitting (a) _ε as a function of V(b) εmax as a function of V
Shock and Vibration 11
remains the same when V ranges from 350ms to 650msSimilarly the max strain and mean strain rate also linearlydecrease with the increase of crack propagation velocityVAP
5 Conclusion
In this study the Brazil test of rock specimens was per-formed under different impact velocities using the SHPBsystem to explore fracture characterizations of rocks underdynamic loads Based on image processing technique crackpropagation process was quantitatively described from threeperspectives the crack propagation velocity crack fractalcharacteristic and crack morphological features Accordingto the recorded strain wave signals the dynamic mechanicalproperties of rocks were also calculated and the relationshipbetween impact velocity and crack propagation process wasexplored and analyzed +e main conclusions are listed asfollows
(1) Crack propagation velocities V and VAPboth in-
crease with increase of the crack fractals velocity VD
(2) +e proposed two crack features Compactness andAnisometery have a capacity of describing thefracture process of rock In specific VAnis linearlydecreases with the increase of impact velocity v whileVComp exhibits a negative relationship with crackfractals velocity VD
(3) +e energy absorbed by the rocks increases with theincrease of impact velocity v but shows a linearnegative trend with VAnis
(4) +e mean strain rate and max strain both decreasewith increase of crack propagation velocity whichshows that there is a certain relationship between thecrack propagation process and dynamic mechanicalproperties of rocks under dynamic loading
In the future work we will conduct the static tensile testsusing the BD specimen on the same rock material andcompare the static and dynamic results in terms of me-chanical properties and crack propagation process
Nomenclature
_ε Mean strain rate (sminus1)σmax Max stress (MPa)εmax Max strain (10minus3)A Cross-sectional area of the bar (mm2)A Crack length (mm)Ap Crack quantification area (pixels)AS Cross-sectional area of the specimen (mm2)Anis Crack feature descriptormdashanisometryC Longitudinal stress wave speed of the bar (ms)Comp Crack feature descriptormdashcompactnessD Fractal dimensionE Youngrsquos modulus of the bar (GPa)LS Length of rock specimen (mm)P1 P2 Dynamic forces on incident and transmitted ends
(N)rxy Pearsonrsquos correlation coefficientV Crack propagation velocity (ms)v Impact velocity (ms)VD Fractal dimension velocity (Dframe)VAP
Crack propagation velocity (pixelss)VAnis Anisometry velocity (anisframe)VComp Compactness velocity (compframe)WS Absorbed energy (J)
Data Availability
+e data utilized in this study are available from the cor-responding author upon request
00 50 times 106 10 times 107 15 times 107
Fitting curve of VAP and ε
20 times 107 25 times 107 30 times 107 35 times 107
VAP (pixelss)
66
68
70
72
74
76
78ε (
sndash1)
(a)
70
65
60
55
50
44
40
30
25
35
ε max
(10ndash3
)
Fitting curve of VAP and εmax
00 50 times 106 10 times 107 15 times 107 20 times 107 25 times 107 30 times 107 35 times 107
VAP (pixelss)
(b)
Figure 18 Curves of strain parameters with crack propagation velocity VAPand associated results after linear fitting (a) _ε as a function of
VAP (b) εmax as a function of VAP
12 Shock and Vibration
Conflicts of Interest
+e authors declare that they have no conflicts of interest
Acknowledgments
+is research was financially supported by the NationalNatural Science Foundation of China (nos 51274206 and51404277) +is support is greatly acknowledged andappreciated
References
[1] K Xia and W Yao ldquoDynamic rock tests using split Hop-kinson (Kolsky) bar systemmdasha reviewrdquo Journal of RockMechanics and Geotechnical Engineering vol 7 no 1pp 27ndash59 2015
[2] F Gong H Ye and Y Luo ldquo+e effect of high loading rate onthe behaviour and mechanical properties of coal-rock com-bined bodyrdquo Shock and Vibration vol 2018 Article ID4374530 9 pages 2018
[3] Y X Zhou K Xia X B Li et al ldquoSuggested methods fordetermining the dynamic strength parameters and mode-ifracture toughness of rock materialsrdquo International Journal ofRock Mechanics and Mining Sciences vol 49 no 1pp 105ndash112 2012
[4] Y Zhao G-F Zhao Y Jiang D Elsworth and Y HuangldquoEffects of bedding on the dynamic indirect tensile strength ofcoal Laboratory experiments and numerical simulationrdquoInternational Journal of Coal Geology vol 132 pp 81ndash932014
[5] F Dai K Xia and S N Luo ldquoSemicircular bend testing withsplit Hopkinson pressure bar for measuring dynamic tensilestrength of brittle solidsrdquo Review of Scientific Instrumentsvol 79 no 12 article 123903 2008
[6] F Dai K Xia and L Tang ldquoRate dependence of the flexuraltensile strength of Laurentian graniterdquo International Journalof Rock Mechanics and Mining Sciences vol 47 no 3pp 469ndash475 2010
[7] Y Wang ldquoRock dynamic fracture characteristics based onNSCB impact methodrdquo Shock and Vibration vol 2018 Ar-ticle ID 3105384 13 pages 2018
[8] Q B Zhang and J Zhao ldquoEffect of loading rate on fracturetoughness and failure micromechanisms in marblerdquo Engi-neering Fracture Mechanics vol 102 pp 288ndash309 2013
[9] M D Kuruppu Y Obara M R Ayatollahi K P Chong andT Funatsu ldquoISRM-suggested method for determining themode i static fracture toughness using semi-circular bendspecimenrdquo Rock Mechanics and Rock Engineering vol 47no 1 pp 267ndash274 2014
[10] M RM Aliha andM R Ayatollahi ldquoRock fracture toughnessstudy using cracked chevron notched Brazilian disc specimenunder pure modes I and II loadingmdasha statistical approachrdquoeoretical and Applied Fracture Mechanics vol 69 no 2pp 17ndash25 2014
[11] F Dai K Xia H Zheng and Y X Wang ldquoDetermination ofdynamic rock mode-i fracture parameters using crackedchevron notched semi-circular bend specimenrdquo EngineeringFracture Mechanics vol 78 no 15 pp 2633ndash2644 2011
[12] T Tang Z P Bazant S Yang and D Zollinger ldquoVariable-notch one-size test method for fracture energy and processzone lengthrdquo Engineering Fracture Mechanics vol 55 no 3pp 383ndash404 1996
[13] Q Z Wang S Zhang and H P Xie ldquoRock dynamic fracturetoughness tested with holed-cracked flattened Brazilian discsdiametrically impacted by SHPB and its size effectrdquo Experi-mental Mechanics vol 50 no 7 pp 877ndash885 2010
[14] B Lundberg ldquoA split Hopkinson bar study of energy ab-sorption in dynamic rock fragmentationrdquo InternationalJournal of Rock Mechanics and Mining Sciences amp Geo-mechanics Abstracts vol 13 no 6 pp 187ndash197 1976
[15] V Isheyskiy and M Marinin ldquoDetermination of rock massweakening coefficient after blasting in various fracture zonesrdquoEngineering Solid Mechanics vol 5 no 3 pp 199ndash204 2017
[16] G Gary and P Bailly ldquoBehaviour of quasi-brittle material athigh strain rate Experiment and modellingrdquo EuropeanJournal of Mechanics-ASolids vol 17 no 3 pp 403ndash4201998
[17] J Zhao H B Li and Y H ZhaoDynamic Strength Tests of theBukit Timah Granite Nanyang Technological UniversitySingapore 1998
[18] Q B Zhang and J Zhao ldquoA review of dynamic experimentaltechniques andmechanical behaviour of rockmaterialsrdquo RockMechanics and Rock Engineering vol 47 no 4 pp 1411ndash14782014
[19] J Zhao and H B Li ldquoExperimental determination of dynamictensile properties of a graniterdquo International Journal of RockMechanics and Mining Sciences vol 37 no 5 pp 861ndash8662000
[20] J R Klepaczko and A Brara ldquoAn experimental method fordynamic tensile testing of concrete by spallingrdquo InternationalJournal of Impact Engineering vol 25 no 4 pp 387ndash4092001
[21] S Kubota Y Ogata Y Wada G Simangunsong H Shimadaand K Matsui ldquoEstimation of dynamic tensile strength ofsandstonerdquo International Journal of Rock Mechanics andMining Sciences vol 45 no 3 pp 397ndash406 2008
[22] B Erzar and P Forquin ldquoAn experimental method to de-termine the tensile strength of concrete at high rates of strainrdquoExperimental Mechanics vol 50 no 7 pp 941ndash955 2010
[23] L Biolzi and J Labuz ldquoInstabilities in fracture of elastic-softening structuresrdquo Fracture of Engineering Materials andStructures vol 6 no 8 pp 821ndash826 1991
[24] Q ZWangW Li and H P Xie ldquoDynamic split tensile test offlattened Brazilian disc of rock with SHPB setuprdquo Mechanicsof Materials vol 41 no 3 pp 252ndash260 2009
[25] D Asprone E Cadoni A Prota and G Manfredi ldquoDynamicbehavior of a mediterranean natural stone under tensileloadingrdquo International Journal of Rock Mechanics and MiningSciences vol 46 no 3 pp 514ndash520 2009
[26] H Kolsky ldquoAn investigation of the mechanical properties ofmaterials at very high rates of loadingrdquo Proceedings of thePhysical Society Section B vol 62 no 11 pp 676ndash700 1949
[27] U S Lindholm ldquoSome experiments with the split Hopkinsonpressure barrdquo Journal of the Mechanics and Physics of Solidsvol 12 no 5 pp 317ndash335 1964
[28] G Subhash and G Ravichandran Split-Hopkinson PressureBar Testing of Ceramics pp 497ndash504 ASM InternationalMaterials Park OH USA 2000
[29] X Li T Zhou D Li and Z Wang ldquoExperimental and nu-merical investigations on feasibility and validity of prismaticrock specimen in SHPBrdquo Shock and Vibration vol 2016Article ID 7198980 13 pages 2016
[30] M R Ayatollahi and M Sistaninia ldquoMode __ fracture study ofrocks using Brazilian disk specimensrdquo International Journal ofRock Mechanics and Mining Sciences vol 48 no 5pp 819ndash826 2011
Shock and Vibration 13
[31] Q Z Wang X P Gou and H Fan ldquo+e minimum di-mensionless stress intensity factor and its upper bound forCCNBD fracture toughness specimen analyzed with straightthrough crack assumptionrdquo Engineering Fracture Mechanicsvol 82 pp 1ndash8 2012
[32] Q B Zhang and J Zhao ldquoQuasi-static and dynamic fracturebehaviour of rock materials phenomena and mechanismsrdquoInternational Journal of Fracture vol 189 no 1 pp 1ndash322014
[33] A Bertram and J F Kalthoff ldquoCrack propagation toughnessof rock for the range of low to very high crack speedsrdquo KeyEngineering Materials vol 251-252 pp 423ndash430 2003
[34] R Chen K Xia F Dai F Lu and S N Luo ldquoDeterminationof dynamic fracture parameters using a semi-circular bendtechnique in split Hopkinson pressure bar testingrdquo Engi-neering Fracture Mechanics vol 76 no 9 pp 1268ndash12762009
[35] P Forquin ldquoAn optical correlation technique for character-izing the crack velocity in concreterdquo e European PhysicalJournal Special Topics vol 206 no 1 pp 89ndash95 2012
[36] Y Zhao S Gong C Zhang Z Zhang and Y Jiang ldquoFractalcharacteristics of crack propagation in coal under impactloadingrdquo Fractals vol 26 no 2 article 1840014 2018
[37] J T Gomez A Shukla and A Sharma ldquoStatic and dynamicbehavior of concrete and granite in tension with damagerdquoeoretical and Applied Fracture Mechanics vol 36 no 1pp 37ndash49 2001
[38] Q B Zhang and J Zhao ldquoDetermination of mechanicalproperties and full-field strain measurements of rock materialunder dynamic loadsrdquo International Journal of Rock Me-chanics and Mining Sciences vol 60 pp 423ndash439 2013
[39] W Yao Y Xu H-W Liu and K Xia ldquoQuantification ofthermally induced damage and its effect on dynamic fracturetoughness of two mortarsrdquo Engineering Fracture Mechanicsvol 169 pp 74ndash88 2017
[40] T S Yun Y J Jeong K Y Kim and K-B Min ldquoEvaluation ofrock anisotropy using 3D X-ray computed tomographyrdquoEngineering Geology vol 163 pp 11ndash19 2013
[41] T Yin X Li K Xia and S Huang ldquoEffect of thermaltreatment on the dynamic fracture toughness of Laurentiangraniterdquo Rock Mechanics and Rock Engineering vol 45 no 6pp 1087ndash1094 2012
[42] S Huang K Xia F Yan and X Feng ldquoAn experimental studyof the rate dependence of tensile strength softening ofLongyou sandstonerdquo Rock Mechanics and Rock Engineeringvol 43 no 6 pp 677ndash683 2010
[43] S N Luo B J Jensen D E Hooks et al ldquoGas gun shockexperiments with single-pulse X-ray phase contrast imagingand diffraction at the advanced photon sourcerdquo Review ofScientific Instruments vol 83 no 7 article 073903 2012
[44] M Hudspeth B Claus S Dubelman et al ldquoHigh speedsynchrotron X-ray phase contrast imaging of dynamic ma-terial response to split Hopkinson bar loadingrdquo Review ofScientific Instruments vol 84 no 2 article 025102 2013
[45] Y Li and K T Ramesh ldquoAn optical technique for mea-surement of material properties in the tension Kolsky barrdquoInternational Journal of Impact Engineering vol 34 no 4pp 784ndash798 2007
[46] G Gao S Huang K Xia and Z Li ldquoApplication of digitalimage correlation (DIC) in dynamic notched semi-circularbend (NSCB) testsrdquo Experimental Mechanics vol 55 no 1pp 95ndash104 2015
[47] B Pan K Qian H Xie and A Asundi ldquoTwo-dimensionaldigital image correlation for in-plane displacement and strain
measurement a reviewrdquo Measurement Science and Technol-ogy vol 20 no 6 article 062001 2009
[48] F Amiot M Bornert P Doumalin et al ldquoAssessment ofdigital image correlation measurement accuracy in the ulti-mate error regime main results of a collaborative bench-markrdquo Strain vol 49 no 6 pp 483ndash496 2013
[49] W Shi Y Wu and L Wu ldquoQuantitative analysis of theprojectile impact on rock using infrared thermographyrdquoInternational Journal of Impact Engineering vol 34 no 5pp 990ndash1002 2007
[50] D K Iakovidis T Goudas C V Smailis and I MaglogiannisldquoRatsnake a versatile image annotation tool with applicationto computer-aided diagnosisrdquo e Scientific World Journalvol 2014 Article ID 286856 12 pages 2014
[51] B A Han H Y Xiang Z Li and J J Huang ldquoDefects de-tection of sheet metal parts based on HALCON and regionmorphologyrdquo Applied Mechanics and Materials vol 365-366pp 729ndash732 2013
[52] D Ai Y Zhao Q Wang and C Li ldquoExperimental andnumerical investigation of crack propagation and dynamicproperties of rock in SHPB indirect tension testrdquo In-ternational Journal of Impact Engineering vol 126 pp 135ndash146 2019
[53] H Xie and D J Sanderson ldquoFractal effects of crack propa-gation on dynamic stress intensity factors and crack veloci-tiesrdquo International Journal of Fracture vol 74 no 1pp 29ndash42 1996
[54] F Dai R Chen and K Xia ldquoA semi-circular bend techniquefor determining dynamic fracture toughnessrdquo ExperimentalMechanics vol 50 no 6 pp 783ndash791 2010
[55] D Chakerian and B B Mandelbrot ldquo+e fractal geometry ofnaturerdquo College Mathematics Journal vol 15 no 2pp 175ndash177 1984
[56] K Falconer ldquoFractal geometry mathematical foundationsand applicationsrdquo Biometrics vol 46 no 3 pp 886-887 1990
[57] T-B Yin K Peng L Wang P Wang X-Y Yin andY-L Zhang ldquoStudy on impact damage and energy dissipationof coal rock exposed to high temperaturesrdquo Shock and Vi-bration vol 2016 Article ID 5121932 10 pages 2016
14 Shock and Vibration
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original quasistatic ones to precisely determine the dynamictensile strength which can be approximately classified intotwo categories direct tensile and indirect tensile testingmethods [1] Compared with the direct testing method tomeasure the tensile strength of rock material an indirecttesting method provides a more convenient and accuratealternative not only for the specimen preparation but also forthe experimental design [18]
More specifically the primary testing methods todetermine the dynamic tensile strength of rock are ba-sically extended from corresponding quasistatic ones andmainly include BD or FBD method bending [19] or SCBmethod [5] spalling method [20ndash22] etc SpecificallyZhou et al [3] and Zhao et al [4] conducted several testson rock specimens with BD configuration using a SHPBand investigated the dynamic indirect tensile strength ofrocks under different loading conditions Dai et al [5 6]explored the rate dependence of tensile strength of rocksunder SHPB impact loading using SCB Biolzi and Labuz[23] investigated the deformation of a rock specimen inthe classical four-point bend (FPB) fracture tests Wanget al [24] also assessed the FPB method for testing thetensile strength and fracture toughness of rocks by usingthe SHPB apparatus Klepaczko and Brara [20] performeda dynamic tensile test for concreate using spallingmethod In addition to the above indirect tension testAsprone et al [25] investigated the dynamic behavior ofrock-like materials using the dynamic DT (Direct ten-sion) method Among these the BD test is widely used formeasuring the static and dynamic fracture toughness ofrock and rock-like materials under the Split Hopkinsonpressure bar (SHPB) loading SHPB is a highly reliableapparatus and widely utilized to quantify the dynamicproperties of rocks under high strain rates since it wasinvented by Kolsky in 1949 [26] and many efforts havebeen made to improve the measurement results [27 28]Moreover these experiments always are conducted toexplore the dynamic mechanical properties of rocks aswell as crack initiation propagation and coalescenceunder different SHPB loading rates [11 29ndash31] For ex-ample Zhang and Zhao [32] performed an experimentalinvestigation about quasistatic and dynamic fracturebehavior of rock materials by a servohydraulic and SHPBloading system Bertram and Kalthoff [33] investigatedthe Mode-I propagation processes for limestone materialunder different crack speeds and explained the charac-teristics of the crack propagation path of brittle materialsbased on the experimental results Also in Mode-I rockfracture process Dai et al [11] and Chen et al [34]employed SHPB and laser gap gauge to study the dynamicfracture properties of rock-like materials with CCNSCBand SCB configuration respectively Forquin [35] pro-posed a crack velocity measurement method using opticalcorrelation technique for concrete and rock-like mate-rials under dynamic tensile loading test Zhao et al [36]also adopted a high-speed digital camera to record thecrack propagation process of coal materials under SHPBimpact loading and explored its fractal characteristicsGomez et al [37] performed a photoelastic dynamic
splitting experiment and studied the dynamic behavior ofconcrete and granite with tensile damage
Since dynamic fracture of rockmaterial is a very complexbehavior some traditional contact measurement approacheslike resistance strain gauges cannot provide enough in-formation to reveal the dynamic fracture process of rock+erefore many noncontact and optical measurementtechniques have been adopted and developed as a promisingway in the experiment to record the fracture process andfurther reveal the fracture process and failure mechanisms ofrock materials [38] +ese techniques can be approximatelyclassified into following groups ie CT (computed to-mography) [39 40] SEM (scanning electron microscope)[41 42] X-ray phase contrast imaging (PCI) [43 44] LGG(laser gap gauge) [34 45] DIC (digital image correlation)[46ndash48] and DIT (dynamic infrared tomography) [49]Among them using the high-speed amp high-resolutioncamera is the most convenient way to capture the fractureprocess of rock material
Nevertheless with regard to the crack evolutioncharacteristics and failure process the investigation ismore challenging than that of stress-strain on the rockspecimen in SHPB experiments since there are no effectivecharacteristic parameters that can quantitatively describecrack propagation To the best of our knowledge researchstudies into the relationship between crack propagationand mechanical properties are relatively few +ereforewe proposed a data processing method based on Ratsnakegraphic annotation software [50] and Halcon machinevision software [51] to extract crack propagation featureswhich are further compared with the dynamic mechanicalproperties of rocks +e main aim of this study is to vi-sualize the relationship between crack propagation pro-cess and mechanical properties of rock using extractedmulticracks and then to investigate and reveal the futurefracture behavior of the rock materials
2 Experiment Procedures
21 Experimental Design and Rock Specimens +e dynamicBrazilian tensile test is conducted using the SHPB systemat China University of Mining and Technology Beijing(CUMTB) and the schematic and physical map of theexperimental setup are shown in Figures 1 and 2respectively
+e SHPB system mainly consists of power system barsstrain wave collector and high frame rate camera In orderto satisfy the one-dimensional stress wave propagation wavethe length of the bars should be 30 times of the bar diameter[3] +erefore the length and the diameter of the barsutilized in the experiment are 2000mm and 50mm and thelength and diameter of the bullet are 400mm and 50mm Inaddition all the bars used in the SHPB test are 35CrMn steelmaterial with 7800 kgm3 density 206GPa Youngrsquos mod-ulus and 028 Poissonrsquos ratio
To visualize the fracture process and further revealfracture mechanism FASTCAM SA5 (16G) camera wasemployed to capture the fractured images of rock whichadopts the CMOS sensor with a 20 μm pixel delivering an
2 Shock and Vibration
ISO light sensitivity of 10000 monochrome and 4000colors When the frame rate is set to 1000000 FPS theresolution of the captured image is only 16 times 64 pixels onthe other hand when the resolution is set to 1024 times1024the maximum frame rate is only 7000 FPS which cannotcapture the fracture process of a rock specimen underSHPB impact loading erefore the camera is set to272 times 512 pixels resolution at a frame rate of 50000 FPS inthe experiment
e rock samples utilized in the experiment aremanufactured by sandstone selected from a quarry in theFangshan area of Beijing China According to the ISRMsuggestion for BD specimens preparation the rock
specimens were cut from the same rock block withoutobvious bedding and manufactured to a cylinder with adimension of 50mm in diameter and 25mm in lengthMoreover two ends of the rock specimen were nelyground to be at within an accuracy of plusmn005mm andperpendicular to the longitudinal axis no morethan plusmn025deg At last the surface of the rock samples issmooth by Vaseline lubricant
22 SHPB Test SHPB is an ideal apparatus for testing thedynamic response of materials and its principle is basedon the one-dimensional (1D) stress wave propagation Toaccurately calculate the dynamic properties of rock ma-terial under SHPB loading the following three assump-tions also require to be satised [1] (1) propagation ofelastic waves in the bars satised 1D stress wave theorywhich determined by the bar dimensions (2) neglectingthe friction and inertia eects on the rock specimen whichcan be fullled approximately with the suggested testingprocedures (3) specimen reaches stress equilibrium For aclassic SHPB test when the bullet impacts the incidentbar a compressive pulse is generated and propagatestowards the rock sample With the above recorded in-cident εi(t) reected εr(t) and transmitted εt(t) strainsignals the stress σ(t) strain ε(t) and strain rate _ε(t) ofrock material under dierent impact velocities can beexpressed as
Laser beams
εi
εr
εt
Nitrogen
Bullet
Damper
Strain gauge
Light source
Specimen
Incident bar
TTL out
High frame rate camera
Transmission barAbsorption bar
Waveform record system
Strain amplifier
Speed test system
TTL in
Incident waveReflected waveTransmitted wave
εiεrεt
Figure 1 Schematic map of the SHPB experimental system
Figure 2 Physical map of the SHPB experimental system
Shock and Vibration 3
σ(t) AE
2ASεi(t) + εr(t) + εt(t)1113858 1113859 (1)
ε(t) C
LS1113946
t
0εi(t)minus εr(t)minus εt(t)1113858 1113859dt (2)
_ε(t) C
LSεi(t)minus εr(t)minus εt(t)1113858 1113859 (3)
where A and AS are the cross-sectional area of the bar androck specimen respectively E is Youngrsquos modulus of the barC is the longitudinal stress wave speed of the bar and LSdenotes the length of rock specimen
Also the dynamic forces on the incident and transmittedends P1 and P2 can be computed as
P1 AE εi + εr( 1113857
P2 AEεt(4)
3 Methodology
Figure 3 shows the framework of our proposed methodwhich mainly consists of two parts ie crack feature ex-traction and dynamic mechanical properties calculationFirstly the video of the fracture process of rock specimens issplit into several images which will be postprocessed by thecrack extraction module To achieve the accurate extractionof cracks a novel and efficient image annotation softwaretool Ratsnake [50] is adopted to identify and extract crackson rock surface accurately According to the principles ofconnected domain approach used in semantic image seg-mentation application images of extracted cracks of rockspecimens under SHPB impact loading are obtained +enby Halcon [51] machine vision software a number of novelcrack features have been proposed and calculated to describethe fracture process of rock under different loading rates Atthe same time dynamic mechanical properties also havebeen computed based on the above formulas Finally acorrelation matrix was constructed based on Pearsonrsquoscorrelation coefficient
As illustrated in Figure 4 the correlation matrix heat-map has been calculated based on the experimental data tovisualize the relationship between loading condition crackpropagation process and dynamic mechanical properties ofrocks under different SHPB impact velocities
Given paired data (x1 y1) (xn yn)1113864 1113865 consisting ofn pairs Pearsonrsquos correlation coefficient rxy is defined as
rxy 1113936
ni1 xi minusx( 1113857 yi minusy( 1113857
1113936ni1 xi minus x( 1113857
21113969
1113936ni1 yi minusy( 1113857
21113969 (5)
where n is the sample size xi yi are the individual pointsindexed with i and x y are the sample mean values of x andy points
In the correlation matrix heat-map larger positivevalues were represented by dark red colors denoting astrong positive correlation between two variables whilelarger negative values were represented by dark blue colors
which indicate a strong negative correlation between twovariables
4 Results and Discussion
41 Crack Propagation Process
411 Crack Propagation Velocity Over the past few de-cades there have been some investigations for crackpropagation velocities of rock materials under dynamicloading which provide a promising way to explore thefracture mechanisms of rock materials [1 18] Howeverrelatively few crack extraction approaches based on imageprocessing have been conducted on rock specimens to de-scribe the failure process and explore the fracture mecha-nism due to the technical difficulties associated with crackfeature extraction and computation
In this study the crack propagation velocity V and VAPwere calculated according to the crack length and crack area(the number of crack pixels) [52] as shown in Figures 5 and 6
To visualize the relationship between these two crackvelocity variables Figure 7 plots VAP
as a function of V aswell as the fitting curve It can be seen that VAP
increasesalmost linearly with the increased of V under SHPBloading
412 Crack Fractal Characteristic Since cracks on rocksurface are an important index to measure the state of rockmaterial and fractals exhibit the ability for measuring thecomplex topological pattern many significant endeavorshave been made to investigate the fractality of cracks to themechanics of fracture [53 54]
In mathematics a fractal dimension is used to evaluatethe fractal patterns by quantifying their complexity as a ratioof the change in detail to the change in scale [55] Unliketopological dimensions the fractal dimension can takenoninteger values Particularly there are many formalmathematical definitions for fractal dimension eg box-counting dimension information dimension and correla-tion dimension Among them the box-counting dimensionis calculated by counting how this number changes as itmakes the grid finer by applying a box-counting algorithmIn more detail by the box-counting dimension computationmethod the fractal dimension of an object can be computedas [56]
N C middot SD
(6)
where D is fractal dimension S the scale of the object(cracks) N the number of boxes of scale S required to coverthe object (cracks) and C a constant number Taking thelogarithm it can be rewritten
lnN lnC + D middot ln S (7)
+erefore the box-counting dimensionD can be definedas
D minuslimsrarr0
lnN
ln S (8)
4 Shock and Vibration
Figure 8 presents an illustration for crack coverageusing dierent scale boxes (S 8 16 32 64) whileFigure 9(a) plots the linear tting results of lnN and ln Swhich shows the fractal dimension is 114 for current crackson rock surface Based on the plots of lnN and ln S the
fractal dimension of the crack can be accumulated byformula (8)
In general the higher fractal dimension indicates a morecurved and intricate crack propagation path ereforeaccording to the above method the fractal dimension of
ρXY
= cov(x y)σxσy
3167ms3246ms3577ms3511ms3869ms4307ms4385ms4443ms4687ms5150ms5502ms
Set gridsCrack
annotation
Export mask binary image
Set connection domain
Input image
Output cracks
helliphellip
helliphellip
Crack central coordinate
Crack area and crack number
Crack fractal dimension
Crack statistical information
Crack morphological features
Crack extraction
Time
Time
Y
X
X
Y
Impact velocity
Absorbed energy
Max strain
Max stress
Mean strain rate
Crack fracture video
Images of extracted cracks
Dynamic fractureprocess investigation
(a)
(b)
(c)
(f) (g)
(d) (e)
(h)
6
5
4
Stre
ss (M
Pa)
3
2
1
0
00 25 50 75Strain (times10ndash3)
100 125 150 175
100
100
100
100
100
100
100
100
100
100
062
062
068
068
044
044
ndash078
ndash078
ndash029
ndash029
050
050
ndash062
067
ndash062
ndash049
ndash049
ndash02608
04
00
ndash04
ndash08ndash026 ndash065 ndash060 ndash019 010 ndash005 ndash063 ndash025
ndash074 ndash062 ndash022 018 004 ndash026
ndash010 ndash014 ndash021 053 ndash004 ndash027 ndash029 ndash025
023 035 014 ndash051 ndash016 ndash026ndash027 ndash063
005 ndash029 ndash023 039 004ndash004ndash016 ndash005
039ndash038ndash014 ndash040 018053ndash051 010
ndash040 ndash023072037
083
ndash022ndash021014 ndash019
072 ndash038 ndash029 ndash062ndash014035 ndash060
083 037 ndash014 005 ndash074ndash010023 ndash065
ndash029
067
Figure 3 An overview of the proposed approach for the investigation of dynamic fracture process of rock materials under SHPB impactloading (a) an input video of rock fracture process (b) an algorithm for multicracks extraction (c) crack extraction results for a fractureprocess video (d) dynamic strain-stress response of rock specimens (e) the formula of Pearsonrsquos correlation coeiexclcient (f ) matrix of crackevolution features (g) matrix of dynamic mechanical properties (h) a correlation matrix heat-map of relationship between crack evolutionfeatures and dynamic mechanical properties
Loadingcondition
Crackpropagation
process
Dynamicmechanicalproperties
Impact velocity v
v
V
V
VAP
VAP
VAnis
VAnis
VComp
VComp
WS
WS
σmax
σmax
εmax
εmax
VD
VD
Crack propagation velocity
Crack fractals characteristic
Crack morphological features
Dynamic fracture energy
Strain-stress parameters
ε
100
100
100
100
100
100
100
100
100
100
062
062
068
068
044
044
ndash078
ndash078
ndash029
ndash029
050
050
ndash062
067
ndash062
ndash049
ndash049
ndash026
ndash026 ndash065 ndash060 ndash019 010 ndash005 ndash063 ndash025
ndash074 ndash062 ndash022 018 004 ndash026
ndash010 ndash014 ndash021 053 ndash004 ndash027 ndash029 ndash025
023 035 014 ndash051 ndash016 ndash026ndash027 ndash063
005 ndash029 ndash023 039 004ndash004ndash016 ndash005
039ndash038ndash014 ndash040 018053ndash051 010
ndash040 ndash023072037
083
ndash022ndash021014 ndash019
072 ndash038 ndash029 ndash062ndash014035 ndash060
083 037 ndash014 005 ndash074ndash010023 ndash065
ndash029
067ε
08
04
00
ndash04
ndash08
Figure 4 An illustration of the correlation matrix heat-map with loading condition crack propagation process and dynamic mechanicalproperties
Shock and Vibration 5
cracks in each frame of the rock fracture process has beenincreasing Figure 9(b) gives a quantitative description of thecrack propagation process of rock specimens under dierentimpact velocities It can be observed from it that the fractaldimension of cracks increases gradually during the fractureprocess of rocks and the value of the fractal dimension ofcracks on rock surface ranges from 08 to 12
Figure 10 shows the relationship between crack prop-agation velocity and fractal dimension velocity It has beenfound that both crack propagation velocities V and VAPincrease with increasingVD for rocks under dierent impactvelocities
413 Crack Morphological Features In addition toadopting the crack area AP and fractal dimension D toquantitatively describe the crack characteristics twomorphological features that can further analyze the crackevolution path and failure process are also proposed basedon image processing technique Figure 11 demonstrates acrack morphological process for crack initiation propa-gation and coalescence In order to present a quantitativedescription of the distribution and shape factor of cracksAnisometry and Compactness which derived from imagemorphology are proposed In specic Anisometry isderived from the geometric moments for each crack anddened as
Anisometry Ra
Rb (9)
where Ra denotes the main radius of maximum ellipse of thecrack and Rb represents the secondary radius of the ellipseSimilarly Compactness is also a shape factor which valueranges from 0 to 1 and can be expressed as
Compactness max 1 Cprime( )
Cprime L2
4 middot F middot π
(10)
where L is the total length of the contour and F is the area ofthe region
As shown in Figure 12(a) VComp is decreasing withthe increase of VD as a whole It can also be seen fromFigure 12(b) that the values of VAnis decrease almostlinearly with the increase of impact velocity which in-dicates that longitudinal crack length produced bythe rock is less than transversersquos under higher impactvelocity
414 Distribution of Cracks It has been generally rec-ognized that for a valid and typical dynamic Brazilian
5mm
0μs
(a)
75μs
a = 175mm
(b)
Figure 5 An illustration of crack propagation velocity computation using crack length
6000
A P (p
ixel
s) 4000
2000
0
0 100Time (micros)
200
Crack initiation
Crack coalescence
Crack propagi
nation
300
APFitting curve of AP
Figure 6 An illustration of crack propagation velocity compu-tation using crack area
Fitting curve of V and VAP
3 times 107
2 times 107
1 times 107
0
V AP (p
ixel
ss)
100V (ms)
200 300 400 500 600 700
Figure 7 Relationship between V and VAPof rock specimens
under SHPB loading
6 Shock and Vibration
test crack should be first appeared along the impactdirection somewhere near the center of the specimen andthen propagates bilaterally to the loading endsAccording to the row and column index of the crackcenter Figure 13 shows the coordinate distribution ofcrack center in the process of rock failure It can beobserved from Figure 13 that most of the rock disc cracksnear the center of the specimen and the fracture prop-agation direction are bilateral to the loading ends and
some cracks also appeared at the contact side of rock andbars +e result indicates that the failure patterns ofdynamic Brazil test under SHPB loading approximatelyinclude tensile failure and shear failure Accordingly thecracks near the center of rocks are mainly caused by thetensile failure which is the main axial crack parallel to theloading direction and other cracks are caused by theshear failure that is a result of secondary fractures due tothe further compression
ndash1
Fitting curve
D = 114 R2 = 099
ndash2
InS ndash3
ndash4
ndash5
2 3InN
4 5
(a)
12
10
D08
06
04
02
00200 300 400 500
BXY1 (4687ms)BXY2 (5150ms)BXY3 (4443ms)BXY4 (4385ms)BXY5 (3377ms)BXY6 (3167ms)
BXY7 (3511ms)BXY8 (3246ms)BXY9 (3689ms)BXY10 (4307ms)BXY11 (5502ms)
600 7001000Time (micros)
(b)
Figure 9 (a) Number of covered boxes versus box size (b) fractal characteristics of crack for rock material under different velocities
200
Scale = 64
100
00 100 200 300 400 500
(a)
Scale = 32
200
100
00 100 200 300 400 500
(b)
Scale = 16
200
100
00 100 200 300 400 500
(c)
Scale = 8
200
100
00 100 200 300 400 500
(d)
Figure 8 An illustration of different box scales to fully cover cracks
Shock and Vibration 7
42 Dynamic Mechanical Properties Figure 14 illustratesthe incident εi(t) reected εr(t) and transmitted εt(t)strain signals of rock specimens under dierent impactvelocities during SHPB dynamic loading test According
to the three-wave analysis method the mechanicalproperties of rocks under SHPB loading are determinedIn this study the absorbed energy and stress-strain pa-rameters are calculated and further compared with crack
100V
(ms
)
200
300
400
500
600
700
000 001VD (Dframe)
002 003 004 005 006 007
Fitting curve of VD and VAP
VAP
Fitting curve of VD and VV
4 times 107
3 times 107
2 times 107
1 times 107
0
V AP (p
ixel
ss)
Figure 10 Relationship between V VAP and VD in the SHPB experiment
Crack initiation
(a) (b)
Crack propagination
(c) (d)
Crack coalescence
(e)
F
LRb
Ra
(f )
Figure 11 An illustration of crack morphological features (a) (c) and (e) are original images represent crack initiation propagation andcoalescence respectively (b) (d) and (f) are extracted cracks from corresponded images
8 Shock and Vibration
propagation features to explore the relationship betweenthem
421 Dynamic Fracture Energy It has been generally rec-ognized that the fracture of rock under loading rates is theprocess of accumulation and dissipation of energy [57] Inspecific the consumed energy under SHPB dynamic loadingcan be well quantified based on the first law of thermody-namics [34] During the SHPB dynamic loading test theenergy of the incident wave WI the energy of the reflectedwave WR and the energy of the transmitted wave WT can becomputed as
WI A middot C
E1113946 εi(t)
2dt
WR A middot C
E1113946 εr(t)
2dt
WT A middot C
E1113946 εt(t)
2dt
(11)
where A is the cross-sectional area C is the longitudinalwave speed and E is Youngrsquos modulus of the bars
Assuming that all the energy loss at the specimen and barinterfaces can be negligible the energy absorbed by the rockspecimen WS can be expressed as
Fitting curve of VD and VComp
10
12
14
16
18
20
22
24
26
28V C
omp (
com
pfr
ame)
001 002 003 004 005 006 007000VD (Dframe)
(a)
Fitting curve of v and VAnis
35 40 45 50 5530v (ms)
8
10
12
14
16
18
20
22
24
V Ani
s (an
isfr
ame)
(b)
Figure 12 (a) Relationship between VComp and VD (b) relationship between VAnis and V
Impact velocity
Incident bar Transmission bar
Rock specimen250
200
Imag
e hei
ght (
pixe
ls)
150
100
50
0
BXY1BXY2BXY3
BXY4BXY5BXY6
BXY7BXY8BXY9
BXY10BXY11
200 300 400 5001000Image width (pixels)
Figure 13 Crack distribution for rocks under different impact velocities
Shock and Vibration 9
WS WI minusWR minusWT (12)
Figure 15 shows the total energy absorbed versus theimpact velocity for the rock specimens It indicates that the
energy absorbed by the rock specimen increases with in-creasing impact velocity
Moreover substantial efforts have been devoted to per-forming quantitative measurements on fracture surface and it
εi-4687msεi-5150msεi-4443msεi-4385msεi-3377msεi-3167msεi-3511msεi-3246msεi-3869msεi-4307msεi-5502ms
εt-4687msεt-5150msεt-4443msεt-4385msεt-3377msεt-3167msεt-3511msεt-3246msεt-3869msεt-4307msεt-5502ms
εr-4687msεr-5150msεr-4443msεr-4385msεr-3377msεr-3167msεr-3511msεr-3246msεr-3869msεr-4307msεr-5502ms
140 160 180 200 220 240 260 280120100
3
2
1
0
ndash1V
olta
ge (V
)ndash2
ndash3
Time (μs)
Figure 14 Incident reflected and transmitted signals of rocks under different impact velocities
18
WS (
J)
16
14
12
10
8
6
4
2
030 35 40 45 50 55
v (ms)
Fitting curve of v and WS
Figure 15 Relationship between v and WS
10 Shock and Vibration
has been well recognized that surface roughness in rock-likematerials exhibits self-similarity properties at least over a givenrange of length scales In other words the fracture surfacetopography of rock-like materials reveals inherent details as-sociated with energy dissipation mechanisms that govern thefracturing process +erefore the relationship between fractaldimension and absorbed energy was first calculated and theresult is shown in Figure 16(a) However it can be found thatthere is no obvious relationship between the two variables
On the other hand Figure 16(b) presents the total energyabsorbed WS versus the crack feature VAnis for the rockspecimens It can be seen that there is a linearly negativecorrelation between the two variables the greater the WSthe smaller the VAnis
422 Strain-Stress Parameters According to the incidentεi(t) reflected εr(t) and transmitted εt(t) strain signalsillustrated in Figure 14 and formulas (1)ndash(3) the max stressmax strain and mean strain rate of rocks under differentimpact velocities were calculated Combining with the crackcharacteristic parameters in the above section the re-lationship between the crack propagation process and dy-namic mechanical properties was analyzed
Figure 17 shows the max strain and mean strain rateversus the crack propagation velocity V while Figure 18shows the max strain and mean strain rate versus the crackpropagation velocity VAP
It can be seen that with theincrease of the V both the max strain and mean strain rateare gradually decreased and mean strain rate basically
000
001
002
003
004
005
006
007V D
(Dfr
ame)
2 4 6 8 10 12 14 16 180WS (J)
(a)
Fitting curve of WS and VAnis
2 4 6 8 10 12 14 16 180WS (J)
8
10
12
14
16
18
20
22
24
V Ani
s (an
isfr
ame)
(b)
Figure 16 (a) Relationship between WS and VD (b) relationship between WS and VAnis
Fitting curve of V and ε
66
68
70
72
74
76
78
εmiddot (sndash1
)
200 300 400 500
600 700100V (ms)
(a)
Fitting curve of V and εmax
200 300 400 500 600 700100V (ms)
25
30
35
40
45
50
55
60
65
70
ε max
(10ndash3
)
(b)
Figure 17 Curves of strain parameters with crack propagation velocity V and associated results after linear fitting (a) _ε as a function of V(b) εmax as a function of V
Shock and Vibration 11
remains the same when V ranges from 350ms to 650msSimilarly the max strain and mean strain rate also linearlydecrease with the increase of crack propagation velocityVAP
5 Conclusion
In this study the Brazil test of rock specimens was per-formed under different impact velocities using the SHPBsystem to explore fracture characterizations of rocks underdynamic loads Based on image processing technique crackpropagation process was quantitatively described from threeperspectives the crack propagation velocity crack fractalcharacteristic and crack morphological features Accordingto the recorded strain wave signals the dynamic mechanicalproperties of rocks were also calculated and the relationshipbetween impact velocity and crack propagation process wasexplored and analyzed +e main conclusions are listed asfollows
(1) Crack propagation velocities V and VAPboth in-
crease with increase of the crack fractals velocity VD
(2) +e proposed two crack features Compactness andAnisometery have a capacity of describing thefracture process of rock In specific VAnis linearlydecreases with the increase of impact velocity v whileVComp exhibits a negative relationship with crackfractals velocity VD
(3) +e energy absorbed by the rocks increases with theincrease of impact velocity v but shows a linearnegative trend with VAnis
(4) +e mean strain rate and max strain both decreasewith increase of crack propagation velocity whichshows that there is a certain relationship between thecrack propagation process and dynamic mechanicalproperties of rocks under dynamic loading
In the future work we will conduct the static tensile testsusing the BD specimen on the same rock material andcompare the static and dynamic results in terms of me-chanical properties and crack propagation process
Nomenclature
_ε Mean strain rate (sminus1)σmax Max stress (MPa)εmax Max strain (10minus3)A Cross-sectional area of the bar (mm2)A Crack length (mm)Ap Crack quantification area (pixels)AS Cross-sectional area of the specimen (mm2)Anis Crack feature descriptormdashanisometryC Longitudinal stress wave speed of the bar (ms)Comp Crack feature descriptormdashcompactnessD Fractal dimensionE Youngrsquos modulus of the bar (GPa)LS Length of rock specimen (mm)P1 P2 Dynamic forces on incident and transmitted ends
(N)rxy Pearsonrsquos correlation coefficientV Crack propagation velocity (ms)v Impact velocity (ms)VD Fractal dimension velocity (Dframe)VAP
Crack propagation velocity (pixelss)VAnis Anisometry velocity (anisframe)VComp Compactness velocity (compframe)WS Absorbed energy (J)
Data Availability
+e data utilized in this study are available from the cor-responding author upon request
00 50 times 106 10 times 107 15 times 107
Fitting curve of VAP and ε
20 times 107 25 times 107 30 times 107 35 times 107
VAP (pixelss)
66
68
70
72
74
76
78ε (
sndash1)
(a)
70
65
60
55
50
44
40
30
25
35
ε max
(10ndash3
)
Fitting curve of VAP and εmax
00 50 times 106 10 times 107 15 times 107 20 times 107 25 times 107 30 times 107 35 times 107
VAP (pixelss)
(b)
Figure 18 Curves of strain parameters with crack propagation velocity VAPand associated results after linear fitting (a) _ε as a function of
VAP (b) εmax as a function of VAP
12 Shock and Vibration
Conflicts of Interest
+e authors declare that they have no conflicts of interest
Acknowledgments
+is research was financially supported by the NationalNatural Science Foundation of China (nos 51274206 and51404277) +is support is greatly acknowledged andappreciated
References
[1] K Xia and W Yao ldquoDynamic rock tests using split Hop-kinson (Kolsky) bar systemmdasha reviewrdquo Journal of RockMechanics and Geotechnical Engineering vol 7 no 1pp 27ndash59 2015
[2] F Gong H Ye and Y Luo ldquo+e effect of high loading rate onthe behaviour and mechanical properties of coal-rock com-bined bodyrdquo Shock and Vibration vol 2018 Article ID4374530 9 pages 2018
[3] Y X Zhou K Xia X B Li et al ldquoSuggested methods fordetermining the dynamic strength parameters and mode-ifracture toughness of rock materialsrdquo International Journal ofRock Mechanics and Mining Sciences vol 49 no 1pp 105ndash112 2012
[4] Y Zhao G-F Zhao Y Jiang D Elsworth and Y HuangldquoEffects of bedding on the dynamic indirect tensile strength ofcoal Laboratory experiments and numerical simulationrdquoInternational Journal of Coal Geology vol 132 pp 81ndash932014
[5] F Dai K Xia and S N Luo ldquoSemicircular bend testing withsplit Hopkinson pressure bar for measuring dynamic tensilestrength of brittle solidsrdquo Review of Scientific Instrumentsvol 79 no 12 article 123903 2008
[6] F Dai K Xia and L Tang ldquoRate dependence of the flexuraltensile strength of Laurentian graniterdquo International Journalof Rock Mechanics and Mining Sciences vol 47 no 3pp 469ndash475 2010
[7] Y Wang ldquoRock dynamic fracture characteristics based onNSCB impact methodrdquo Shock and Vibration vol 2018 Ar-ticle ID 3105384 13 pages 2018
[8] Q B Zhang and J Zhao ldquoEffect of loading rate on fracturetoughness and failure micromechanisms in marblerdquo Engi-neering Fracture Mechanics vol 102 pp 288ndash309 2013
[9] M D Kuruppu Y Obara M R Ayatollahi K P Chong andT Funatsu ldquoISRM-suggested method for determining themode i static fracture toughness using semi-circular bendspecimenrdquo Rock Mechanics and Rock Engineering vol 47no 1 pp 267ndash274 2014
[10] M RM Aliha andM R Ayatollahi ldquoRock fracture toughnessstudy using cracked chevron notched Brazilian disc specimenunder pure modes I and II loadingmdasha statistical approachrdquoeoretical and Applied Fracture Mechanics vol 69 no 2pp 17ndash25 2014
[11] F Dai K Xia H Zheng and Y X Wang ldquoDetermination ofdynamic rock mode-i fracture parameters using crackedchevron notched semi-circular bend specimenrdquo EngineeringFracture Mechanics vol 78 no 15 pp 2633ndash2644 2011
[12] T Tang Z P Bazant S Yang and D Zollinger ldquoVariable-notch one-size test method for fracture energy and processzone lengthrdquo Engineering Fracture Mechanics vol 55 no 3pp 383ndash404 1996
[13] Q Z Wang S Zhang and H P Xie ldquoRock dynamic fracturetoughness tested with holed-cracked flattened Brazilian discsdiametrically impacted by SHPB and its size effectrdquo Experi-mental Mechanics vol 50 no 7 pp 877ndash885 2010
[14] B Lundberg ldquoA split Hopkinson bar study of energy ab-sorption in dynamic rock fragmentationrdquo InternationalJournal of Rock Mechanics and Mining Sciences amp Geo-mechanics Abstracts vol 13 no 6 pp 187ndash197 1976
[15] V Isheyskiy and M Marinin ldquoDetermination of rock massweakening coefficient after blasting in various fracture zonesrdquoEngineering Solid Mechanics vol 5 no 3 pp 199ndash204 2017
[16] G Gary and P Bailly ldquoBehaviour of quasi-brittle material athigh strain rate Experiment and modellingrdquo EuropeanJournal of Mechanics-ASolids vol 17 no 3 pp 403ndash4201998
[17] J Zhao H B Li and Y H ZhaoDynamic Strength Tests of theBukit Timah Granite Nanyang Technological UniversitySingapore 1998
[18] Q B Zhang and J Zhao ldquoA review of dynamic experimentaltechniques andmechanical behaviour of rockmaterialsrdquo RockMechanics and Rock Engineering vol 47 no 4 pp 1411ndash14782014
[19] J Zhao and H B Li ldquoExperimental determination of dynamictensile properties of a graniterdquo International Journal of RockMechanics and Mining Sciences vol 37 no 5 pp 861ndash8662000
[20] J R Klepaczko and A Brara ldquoAn experimental method fordynamic tensile testing of concrete by spallingrdquo InternationalJournal of Impact Engineering vol 25 no 4 pp 387ndash4092001
[21] S Kubota Y Ogata Y Wada G Simangunsong H Shimadaand K Matsui ldquoEstimation of dynamic tensile strength ofsandstonerdquo International Journal of Rock Mechanics andMining Sciences vol 45 no 3 pp 397ndash406 2008
[22] B Erzar and P Forquin ldquoAn experimental method to de-termine the tensile strength of concrete at high rates of strainrdquoExperimental Mechanics vol 50 no 7 pp 941ndash955 2010
[23] L Biolzi and J Labuz ldquoInstabilities in fracture of elastic-softening structuresrdquo Fracture of Engineering Materials andStructures vol 6 no 8 pp 821ndash826 1991
[24] Q ZWangW Li and H P Xie ldquoDynamic split tensile test offlattened Brazilian disc of rock with SHPB setuprdquo Mechanicsof Materials vol 41 no 3 pp 252ndash260 2009
[25] D Asprone E Cadoni A Prota and G Manfredi ldquoDynamicbehavior of a mediterranean natural stone under tensileloadingrdquo International Journal of Rock Mechanics and MiningSciences vol 46 no 3 pp 514ndash520 2009
[26] H Kolsky ldquoAn investigation of the mechanical properties ofmaterials at very high rates of loadingrdquo Proceedings of thePhysical Society Section B vol 62 no 11 pp 676ndash700 1949
[27] U S Lindholm ldquoSome experiments with the split Hopkinsonpressure barrdquo Journal of the Mechanics and Physics of Solidsvol 12 no 5 pp 317ndash335 1964
[28] G Subhash and G Ravichandran Split-Hopkinson PressureBar Testing of Ceramics pp 497ndash504 ASM InternationalMaterials Park OH USA 2000
[29] X Li T Zhou D Li and Z Wang ldquoExperimental and nu-merical investigations on feasibility and validity of prismaticrock specimen in SHPBrdquo Shock and Vibration vol 2016Article ID 7198980 13 pages 2016
[30] M R Ayatollahi and M Sistaninia ldquoMode __ fracture study ofrocks using Brazilian disk specimensrdquo International Journal ofRock Mechanics and Mining Sciences vol 48 no 5pp 819ndash826 2011
Shock and Vibration 13
[31] Q Z Wang X P Gou and H Fan ldquo+e minimum di-mensionless stress intensity factor and its upper bound forCCNBD fracture toughness specimen analyzed with straightthrough crack assumptionrdquo Engineering Fracture Mechanicsvol 82 pp 1ndash8 2012
[32] Q B Zhang and J Zhao ldquoQuasi-static and dynamic fracturebehaviour of rock materials phenomena and mechanismsrdquoInternational Journal of Fracture vol 189 no 1 pp 1ndash322014
[33] A Bertram and J F Kalthoff ldquoCrack propagation toughnessof rock for the range of low to very high crack speedsrdquo KeyEngineering Materials vol 251-252 pp 423ndash430 2003
[34] R Chen K Xia F Dai F Lu and S N Luo ldquoDeterminationof dynamic fracture parameters using a semi-circular bendtechnique in split Hopkinson pressure bar testingrdquo Engi-neering Fracture Mechanics vol 76 no 9 pp 1268ndash12762009
[35] P Forquin ldquoAn optical correlation technique for character-izing the crack velocity in concreterdquo e European PhysicalJournal Special Topics vol 206 no 1 pp 89ndash95 2012
[36] Y Zhao S Gong C Zhang Z Zhang and Y Jiang ldquoFractalcharacteristics of crack propagation in coal under impactloadingrdquo Fractals vol 26 no 2 article 1840014 2018
[37] J T Gomez A Shukla and A Sharma ldquoStatic and dynamicbehavior of concrete and granite in tension with damagerdquoeoretical and Applied Fracture Mechanics vol 36 no 1pp 37ndash49 2001
[38] Q B Zhang and J Zhao ldquoDetermination of mechanicalproperties and full-field strain measurements of rock materialunder dynamic loadsrdquo International Journal of Rock Me-chanics and Mining Sciences vol 60 pp 423ndash439 2013
[39] W Yao Y Xu H-W Liu and K Xia ldquoQuantification ofthermally induced damage and its effect on dynamic fracturetoughness of two mortarsrdquo Engineering Fracture Mechanicsvol 169 pp 74ndash88 2017
[40] T S Yun Y J Jeong K Y Kim and K-B Min ldquoEvaluation ofrock anisotropy using 3D X-ray computed tomographyrdquoEngineering Geology vol 163 pp 11ndash19 2013
[41] T Yin X Li K Xia and S Huang ldquoEffect of thermaltreatment on the dynamic fracture toughness of Laurentiangraniterdquo Rock Mechanics and Rock Engineering vol 45 no 6pp 1087ndash1094 2012
[42] S Huang K Xia F Yan and X Feng ldquoAn experimental studyof the rate dependence of tensile strength softening ofLongyou sandstonerdquo Rock Mechanics and Rock Engineeringvol 43 no 6 pp 677ndash683 2010
[43] S N Luo B J Jensen D E Hooks et al ldquoGas gun shockexperiments with single-pulse X-ray phase contrast imagingand diffraction at the advanced photon sourcerdquo Review ofScientific Instruments vol 83 no 7 article 073903 2012
[44] M Hudspeth B Claus S Dubelman et al ldquoHigh speedsynchrotron X-ray phase contrast imaging of dynamic ma-terial response to split Hopkinson bar loadingrdquo Review ofScientific Instruments vol 84 no 2 article 025102 2013
[45] Y Li and K T Ramesh ldquoAn optical technique for mea-surement of material properties in the tension Kolsky barrdquoInternational Journal of Impact Engineering vol 34 no 4pp 784ndash798 2007
[46] G Gao S Huang K Xia and Z Li ldquoApplication of digitalimage correlation (DIC) in dynamic notched semi-circularbend (NSCB) testsrdquo Experimental Mechanics vol 55 no 1pp 95ndash104 2015
[47] B Pan K Qian H Xie and A Asundi ldquoTwo-dimensionaldigital image correlation for in-plane displacement and strain
measurement a reviewrdquo Measurement Science and Technol-ogy vol 20 no 6 article 062001 2009
[48] F Amiot M Bornert P Doumalin et al ldquoAssessment ofdigital image correlation measurement accuracy in the ulti-mate error regime main results of a collaborative bench-markrdquo Strain vol 49 no 6 pp 483ndash496 2013
[49] W Shi Y Wu and L Wu ldquoQuantitative analysis of theprojectile impact on rock using infrared thermographyrdquoInternational Journal of Impact Engineering vol 34 no 5pp 990ndash1002 2007
[50] D K Iakovidis T Goudas C V Smailis and I MaglogiannisldquoRatsnake a versatile image annotation tool with applicationto computer-aided diagnosisrdquo e Scientific World Journalvol 2014 Article ID 286856 12 pages 2014
[51] B A Han H Y Xiang Z Li and J J Huang ldquoDefects de-tection of sheet metal parts based on HALCON and regionmorphologyrdquo Applied Mechanics and Materials vol 365-366pp 729ndash732 2013
[52] D Ai Y Zhao Q Wang and C Li ldquoExperimental andnumerical investigation of crack propagation and dynamicproperties of rock in SHPB indirect tension testrdquo In-ternational Journal of Impact Engineering vol 126 pp 135ndash146 2019
[53] H Xie and D J Sanderson ldquoFractal effects of crack propa-gation on dynamic stress intensity factors and crack veloci-tiesrdquo International Journal of Fracture vol 74 no 1pp 29ndash42 1996
[54] F Dai R Chen and K Xia ldquoA semi-circular bend techniquefor determining dynamic fracture toughnessrdquo ExperimentalMechanics vol 50 no 6 pp 783ndash791 2010
[55] D Chakerian and B B Mandelbrot ldquo+e fractal geometry ofnaturerdquo College Mathematics Journal vol 15 no 2pp 175ndash177 1984
[56] K Falconer ldquoFractal geometry mathematical foundationsand applicationsrdquo Biometrics vol 46 no 3 pp 886-887 1990
[57] T-B Yin K Peng L Wang P Wang X-Y Yin andY-L Zhang ldquoStudy on impact damage and energy dissipationof coal rock exposed to high temperaturesrdquo Shock and Vi-bration vol 2016 Article ID 5121932 10 pages 2016
14 Shock and Vibration
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Advances in
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Submit your manuscripts atwwwhindawicom
ISO light sensitivity of 10000 monochrome and 4000colors When the frame rate is set to 1000000 FPS theresolution of the captured image is only 16 times 64 pixels onthe other hand when the resolution is set to 1024 times1024the maximum frame rate is only 7000 FPS which cannotcapture the fracture process of a rock specimen underSHPB impact loading erefore the camera is set to272 times 512 pixels resolution at a frame rate of 50000 FPS inthe experiment
e rock samples utilized in the experiment aremanufactured by sandstone selected from a quarry in theFangshan area of Beijing China According to the ISRMsuggestion for BD specimens preparation the rock
specimens were cut from the same rock block withoutobvious bedding and manufactured to a cylinder with adimension of 50mm in diameter and 25mm in lengthMoreover two ends of the rock specimen were nelyground to be at within an accuracy of plusmn005mm andperpendicular to the longitudinal axis no morethan plusmn025deg At last the surface of the rock samples issmooth by Vaseline lubricant
22 SHPB Test SHPB is an ideal apparatus for testing thedynamic response of materials and its principle is basedon the one-dimensional (1D) stress wave propagation Toaccurately calculate the dynamic properties of rock ma-terial under SHPB loading the following three assump-tions also require to be satised [1] (1) propagation ofelastic waves in the bars satised 1D stress wave theorywhich determined by the bar dimensions (2) neglectingthe friction and inertia eects on the rock specimen whichcan be fullled approximately with the suggested testingprocedures (3) specimen reaches stress equilibrium For aclassic SHPB test when the bullet impacts the incidentbar a compressive pulse is generated and propagatestowards the rock sample With the above recorded in-cident εi(t) reected εr(t) and transmitted εt(t) strainsignals the stress σ(t) strain ε(t) and strain rate _ε(t) ofrock material under dierent impact velocities can beexpressed as
Laser beams
εi
εr
εt
Nitrogen
Bullet
Damper
Strain gauge
Light source
Specimen
Incident bar
TTL out
High frame rate camera
Transmission barAbsorption bar
Waveform record system
Strain amplifier
Speed test system
TTL in
Incident waveReflected waveTransmitted wave
εiεrεt
Figure 1 Schematic map of the SHPB experimental system
Figure 2 Physical map of the SHPB experimental system
Shock and Vibration 3
σ(t) AE
2ASεi(t) + εr(t) + εt(t)1113858 1113859 (1)
ε(t) C
LS1113946
t
0εi(t)minus εr(t)minus εt(t)1113858 1113859dt (2)
_ε(t) C
LSεi(t)minus εr(t)minus εt(t)1113858 1113859 (3)
where A and AS are the cross-sectional area of the bar androck specimen respectively E is Youngrsquos modulus of the barC is the longitudinal stress wave speed of the bar and LSdenotes the length of rock specimen
Also the dynamic forces on the incident and transmittedends P1 and P2 can be computed as
P1 AE εi + εr( 1113857
P2 AEεt(4)
3 Methodology
Figure 3 shows the framework of our proposed methodwhich mainly consists of two parts ie crack feature ex-traction and dynamic mechanical properties calculationFirstly the video of the fracture process of rock specimens issplit into several images which will be postprocessed by thecrack extraction module To achieve the accurate extractionof cracks a novel and efficient image annotation softwaretool Ratsnake [50] is adopted to identify and extract crackson rock surface accurately According to the principles ofconnected domain approach used in semantic image seg-mentation application images of extracted cracks of rockspecimens under SHPB impact loading are obtained +enby Halcon [51] machine vision software a number of novelcrack features have been proposed and calculated to describethe fracture process of rock under different loading rates Atthe same time dynamic mechanical properties also havebeen computed based on the above formulas Finally acorrelation matrix was constructed based on Pearsonrsquoscorrelation coefficient
As illustrated in Figure 4 the correlation matrix heat-map has been calculated based on the experimental data tovisualize the relationship between loading condition crackpropagation process and dynamic mechanical properties ofrocks under different SHPB impact velocities
Given paired data (x1 y1) (xn yn)1113864 1113865 consisting ofn pairs Pearsonrsquos correlation coefficient rxy is defined as
rxy 1113936
ni1 xi minusx( 1113857 yi minusy( 1113857
1113936ni1 xi minus x( 1113857
21113969
1113936ni1 yi minusy( 1113857
21113969 (5)
where n is the sample size xi yi are the individual pointsindexed with i and x y are the sample mean values of x andy points
In the correlation matrix heat-map larger positivevalues were represented by dark red colors denoting astrong positive correlation between two variables whilelarger negative values were represented by dark blue colors
which indicate a strong negative correlation between twovariables
4 Results and Discussion
41 Crack Propagation Process
411 Crack Propagation Velocity Over the past few de-cades there have been some investigations for crackpropagation velocities of rock materials under dynamicloading which provide a promising way to explore thefracture mechanisms of rock materials [1 18] Howeverrelatively few crack extraction approaches based on imageprocessing have been conducted on rock specimens to de-scribe the failure process and explore the fracture mecha-nism due to the technical difficulties associated with crackfeature extraction and computation
In this study the crack propagation velocity V and VAPwere calculated according to the crack length and crack area(the number of crack pixels) [52] as shown in Figures 5 and 6
To visualize the relationship between these two crackvelocity variables Figure 7 plots VAP
as a function of V aswell as the fitting curve It can be seen that VAP
increasesalmost linearly with the increased of V under SHPBloading
412 Crack Fractal Characteristic Since cracks on rocksurface are an important index to measure the state of rockmaterial and fractals exhibit the ability for measuring thecomplex topological pattern many significant endeavorshave been made to investigate the fractality of cracks to themechanics of fracture [53 54]
In mathematics a fractal dimension is used to evaluatethe fractal patterns by quantifying their complexity as a ratioof the change in detail to the change in scale [55] Unliketopological dimensions the fractal dimension can takenoninteger values Particularly there are many formalmathematical definitions for fractal dimension eg box-counting dimension information dimension and correla-tion dimension Among them the box-counting dimensionis calculated by counting how this number changes as itmakes the grid finer by applying a box-counting algorithmIn more detail by the box-counting dimension computationmethod the fractal dimension of an object can be computedas [56]
N C middot SD
(6)
where D is fractal dimension S the scale of the object(cracks) N the number of boxes of scale S required to coverthe object (cracks) and C a constant number Taking thelogarithm it can be rewritten
lnN lnC + D middot ln S (7)
+erefore the box-counting dimensionD can be definedas
D minuslimsrarr0
lnN
ln S (8)
4 Shock and Vibration
Figure 8 presents an illustration for crack coverageusing dierent scale boxes (S 8 16 32 64) whileFigure 9(a) plots the linear tting results of lnN and ln Swhich shows the fractal dimension is 114 for current crackson rock surface Based on the plots of lnN and ln S the
fractal dimension of the crack can be accumulated byformula (8)
In general the higher fractal dimension indicates a morecurved and intricate crack propagation path ereforeaccording to the above method the fractal dimension of
ρXY
= cov(x y)σxσy
3167ms3246ms3577ms3511ms3869ms4307ms4385ms4443ms4687ms5150ms5502ms
Set gridsCrack
annotation
Export mask binary image
Set connection domain
Input image
Output cracks
helliphellip
helliphellip
Crack central coordinate
Crack area and crack number
Crack fractal dimension
Crack statistical information
Crack morphological features
Crack extraction
Time
Time
Y
X
X
Y
Impact velocity
Absorbed energy
Max strain
Max stress
Mean strain rate
Crack fracture video
Images of extracted cracks
Dynamic fractureprocess investigation
(a)
(b)
(c)
(f) (g)
(d) (e)
(h)
6
5
4
Stre
ss (M
Pa)
3
2
1
0
00 25 50 75Strain (times10ndash3)
100 125 150 175
100
100
100
100
100
100
100
100
100
100
062
062
068
068
044
044
ndash078
ndash078
ndash029
ndash029
050
050
ndash062
067
ndash062
ndash049
ndash049
ndash02608
04
00
ndash04
ndash08ndash026 ndash065 ndash060 ndash019 010 ndash005 ndash063 ndash025
ndash074 ndash062 ndash022 018 004 ndash026
ndash010 ndash014 ndash021 053 ndash004 ndash027 ndash029 ndash025
023 035 014 ndash051 ndash016 ndash026ndash027 ndash063
005 ndash029 ndash023 039 004ndash004ndash016 ndash005
039ndash038ndash014 ndash040 018053ndash051 010
ndash040 ndash023072037
083
ndash022ndash021014 ndash019
072 ndash038 ndash029 ndash062ndash014035 ndash060
083 037 ndash014 005 ndash074ndash010023 ndash065
ndash029
067
Figure 3 An overview of the proposed approach for the investigation of dynamic fracture process of rock materials under SHPB impactloading (a) an input video of rock fracture process (b) an algorithm for multicracks extraction (c) crack extraction results for a fractureprocess video (d) dynamic strain-stress response of rock specimens (e) the formula of Pearsonrsquos correlation coeiexclcient (f ) matrix of crackevolution features (g) matrix of dynamic mechanical properties (h) a correlation matrix heat-map of relationship between crack evolutionfeatures and dynamic mechanical properties
Loadingcondition
Crackpropagation
process
Dynamicmechanicalproperties
Impact velocity v
v
V
V
VAP
VAP
VAnis
VAnis
VComp
VComp
WS
WS
σmax
σmax
εmax
εmax
VD
VD
Crack propagation velocity
Crack fractals characteristic
Crack morphological features
Dynamic fracture energy
Strain-stress parameters
ε
100
100
100
100
100
100
100
100
100
100
062
062
068
068
044
044
ndash078
ndash078
ndash029
ndash029
050
050
ndash062
067
ndash062
ndash049
ndash049
ndash026
ndash026 ndash065 ndash060 ndash019 010 ndash005 ndash063 ndash025
ndash074 ndash062 ndash022 018 004 ndash026
ndash010 ndash014 ndash021 053 ndash004 ndash027 ndash029 ndash025
023 035 014 ndash051 ndash016 ndash026ndash027 ndash063
005 ndash029 ndash023 039 004ndash004ndash016 ndash005
039ndash038ndash014 ndash040 018053ndash051 010
ndash040 ndash023072037
083
ndash022ndash021014 ndash019
072 ndash038 ndash029 ndash062ndash014035 ndash060
083 037 ndash014 005 ndash074ndash010023 ndash065
ndash029
067ε
08
04
00
ndash04
ndash08
Figure 4 An illustration of the correlation matrix heat-map with loading condition crack propagation process and dynamic mechanicalproperties
Shock and Vibration 5
cracks in each frame of the rock fracture process has beenincreasing Figure 9(b) gives a quantitative description of thecrack propagation process of rock specimens under dierentimpact velocities It can be observed from it that the fractaldimension of cracks increases gradually during the fractureprocess of rocks and the value of the fractal dimension ofcracks on rock surface ranges from 08 to 12
Figure 10 shows the relationship between crack prop-agation velocity and fractal dimension velocity It has beenfound that both crack propagation velocities V and VAPincrease with increasingVD for rocks under dierent impactvelocities
413 Crack Morphological Features In addition toadopting the crack area AP and fractal dimension D toquantitatively describe the crack characteristics twomorphological features that can further analyze the crackevolution path and failure process are also proposed basedon image processing technique Figure 11 demonstrates acrack morphological process for crack initiation propa-gation and coalescence In order to present a quantitativedescription of the distribution and shape factor of cracksAnisometry and Compactness which derived from imagemorphology are proposed In specic Anisometry isderived from the geometric moments for each crack anddened as
Anisometry Ra
Rb (9)
where Ra denotes the main radius of maximum ellipse of thecrack and Rb represents the secondary radius of the ellipseSimilarly Compactness is also a shape factor which valueranges from 0 to 1 and can be expressed as
Compactness max 1 Cprime( )
Cprime L2
4 middot F middot π
(10)
where L is the total length of the contour and F is the area ofthe region
As shown in Figure 12(a) VComp is decreasing withthe increase of VD as a whole It can also be seen fromFigure 12(b) that the values of VAnis decrease almostlinearly with the increase of impact velocity which in-dicates that longitudinal crack length produced bythe rock is less than transversersquos under higher impactvelocity
414 Distribution of Cracks It has been generally rec-ognized that for a valid and typical dynamic Brazilian
5mm
0μs
(a)
75μs
a = 175mm
(b)
Figure 5 An illustration of crack propagation velocity computation using crack length
6000
A P (p
ixel
s) 4000
2000
0
0 100Time (micros)
200
Crack initiation
Crack coalescence
Crack propagi
nation
300
APFitting curve of AP
Figure 6 An illustration of crack propagation velocity compu-tation using crack area
Fitting curve of V and VAP
3 times 107
2 times 107
1 times 107
0
V AP (p
ixel
ss)
100V (ms)
200 300 400 500 600 700
Figure 7 Relationship between V and VAPof rock specimens
under SHPB loading
6 Shock and Vibration
test crack should be first appeared along the impactdirection somewhere near the center of the specimen andthen propagates bilaterally to the loading endsAccording to the row and column index of the crackcenter Figure 13 shows the coordinate distribution ofcrack center in the process of rock failure It can beobserved from Figure 13 that most of the rock disc cracksnear the center of the specimen and the fracture prop-agation direction are bilateral to the loading ends and
some cracks also appeared at the contact side of rock andbars +e result indicates that the failure patterns ofdynamic Brazil test under SHPB loading approximatelyinclude tensile failure and shear failure Accordingly thecracks near the center of rocks are mainly caused by thetensile failure which is the main axial crack parallel to theloading direction and other cracks are caused by theshear failure that is a result of secondary fractures due tothe further compression
ndash1
Fitting curve
D = 114 R2 = 099
ndash2
InS ndash3
ndash4
ndash5
2 3InN
4 5
(a)
12
10
D08
06
04
02
00200 300 400 500
BXY1 (4687ms)BXY2 (5150ms)BXY3 (4443ms)BXY4 (4385ms)BXY5 (3377ms)BXY6 (3167ms)
BXY7 (3511ms)BXY8 (3246ms)BXY9 (3689ms)BXY10 (4307ms)BXY11 (5502ms)
600 7001000Time (micros)
(b)
Figure 9 (a) Number of covered boxes versus box size (b) fractal characteristics of crack for rock material under different velocities
200
Scale = 64
100
00 100 200 300 400 500
(a)
Scale = 32
200
100
00 100 200 300 400 500
(b)
Scale = 16
200
100
00 100 200 300 400 500
(c)
Scale = 8
200
100
00 100 200 300 400 500
(d)
Figure 8 An illustration of different box scales to fully cover cracks
Shock and Vibration 7
42 Dynamic Mechanical Properties Figure 14 illustratesthe incident εi(t) reected εr(t) and transmitted εt(t)strain signals of rock specimens under dierent impactvelocities during SHPB dynamic loading test According
to the three-wave analysis method the mechanicalproperties of rocks under SHPB loading are determinedIn this study the absorbed energy and stress-strain pa-rameters are calculated and further compared with crack
100V
(ms
)
200
300
400
500
600
700
000 001VD (Dframe)
002 003 004 005 006 007
Fitting curve of VD and VAP
VAP
Fitting curve of VD and VV
4 times 107
3 times 107
2 times 107
1 times 107
0
V AP (p
ixel
ss)
Figure 10 Relationship between V VAP and VD in the SHPB experiment
Crack initiation
(a) (b)
Crack propagination
(c) (d)
Crack coalescence
(e)
F
LRb
Ra
(f )
Figure 11 An illustration of crack morphological features (a) (c) and (e) are original images represent crack initiation propagation andcoalescence respectively (b) (d) and (f) are extracted cracks from corresponded images
8 Shock and Vibration
propagation features to explore the relationship betweenthem
421 Dynamic Fracture Energy It has been generally rec-ognized that the fracture of rock under loading rates is theprocess of accumulation and dissipation of energy [57] Inspecific the consumed energy under SHPB dynamic loadingcan be well quantified based on the first law of thermody-namics [34] During the SHPB dynamic loading test theenergy of the incident wave WI the energy of the reflectedwave WR and the energy of the transmitted wave WT can becomputed as
WI A middot C
E1113946 εi(t)
2dt
WR A middot C
E1113946 εr(t)
2dt
WT A middot C
E1113946 εt(t)
2dt
(11)
where A is the cross-sectional area C is the longitudinalwave speed and E is Youngrsquos modulus of the bars
Assuming that all the energy loss at the specimen and barinterfaces can be negligible the energy absorbed by the rockspecimen WS can be expressed as
Fitting curve of VD and VComp
10
12
14
16
18
20
22
24
26
28V C
omp (
com
pfr
ame)
001 002 003 004 005 006 007000VD (Dframe)
(a)
Fitting curve of v and VAnis
35 40 45 50 5530v (ms)
8
10
12
14
16
18
20
22
24
V Ani
s (an
isfr
ame)
(b)
Figure 12 (a) Relationship between VComp and VD (b) relationship between VAnis and V
Impact velocity
Incident bar Transmission bar
Rock specimen250
200
Imag
e hei
ght (
pixe
ls)
150
100
50
0
BXY1BXY2BXY3
BXY4BXY5BXY6
BXY7BXY8BXY9
BXY10BXY11
200 300 400 5001000Image width (pixels)
Figure 13 Crack distribution for rocks under different impact velocities
Shock and Vibration 9
WS WI minusWR minusWT (12)
Figure 15 shows the total energy absorbed versus theimpact velocity for the rock specimens It indicates that the
energy absorbed by the rock specimen increases with in-creasing impact velocity
Moreover substantial efforts have been devoted to per-forming quantitative measurements on fracture surface and it
εi-4687msεi-5150msεi-4443msεi-4385msεi-3377msεi-3167msεi-3511msεi-3246msεi-3869msεi-4307msεi-5502ms
εt-4687msεt-5150msεt-4443msεt-4385msεt-3377msεt-3167msεt-3511msεt-3246msεt-3869msεt-4307msεt-5502ms
εr-4687msεr-5150msεr-4443msεr-4385msεr-3377msεr-3167msεr-3511msεr-3246msεr-3869msεr-4307msεr-5502ms
140 160 180 200 220 240 260 280120100
3
2
1
0
ndash1V
olta
ge (V
)ndash2
ndash3
Time (μs)
Figure 14 Incident reflected and transmitted signals of rocks under different impact velocities
18
WS (
J)
16
14
12
10
8
6
4
2
030 35 40 45 50 55
v (ms)
Fitting curve of v and WS
Figure 15 Relationship between v and WS
10 Shock and Vibration
has been well recognized that surface roughness in rock-likematerials exhibits self-similarity properties at least over a givenrange of length scales In other words the fracture surfacetopography of rock-like materials reveals inherent details as-sociated with energy dissipation mechanisms that govern thefracturing process +erefore the relationship between fractaldimension and absorbed energy was first calculated and theresult is shown in Figure 16(a) However it can be found thatthere is no obvious relationship between the two variables
On the other hand Figure 16(b) presents the total energyabsorbed WS versus the crack feature VAnis for the rockspecimens It can be seen that there is a linearly negativecorrelation between the two variables the greater the WSthe smaller the VAnis
422 Strain-Stress Parameters According to the incidentεi(t) reflected εr(t) and transmitted εt(t) strain signalsillustrated in Figure 14 and formulas (1)ndash(3) the max stressmax strain and mean strain rate of rocks under differentimpact velocities were calculated Combining with the crackcharacteristic parameters in the above section the re-lationship between the crack propagation process and dy-namic mechanical properties was analyzed
Figure 17 shows the max strain and mean strain rateversus the crack propagation velocity V while Figure 18shows the max strain and mean strain rate versus the crackpropagation velocity VAP
It can be seen that with theincrease of the V both the max strain and mean strain rateare gradually decreased and mean strain rate basically
000
001
002
003
004
005
006
007V D
(Dfr
ame)
2 4 6 8 10 12 14 16 180WS (J)
(a)
Fitting curve of WS and VAnis
2 4 6 8 10 12 14 16 180WS (J)
8
10
12
14
16
18
20
22
24
V Ani
s (an
isfr
ame)
(b)
Figure 16 (a) Relationship between WS and VD (b) relationship between WS and VAnis
Fitting curve of V and ε
66
68
70
72
74
76
78
εmiddot (sndash1
)
200 300 400 500
600 700100V (ms)
(a)
Fitting curve of V and εmax
200 300 400 500 600 700100V (ms)
25
30
35
40
45
50
55
60
65
70
ε max
(10ndash3
)
(b)
Figure 17 Curves of strain parameters with crack propagation velocity V and associated results after linear fitting (a) _ε as a function of V(b) εmax as a function of V
Shock and Vibration 11
remains the same when V ranges from 350ms to 650msSimilarly the max strain and mean strain rate also linearlydecrease with the increase of crack propagation velocityVAP
5 Conclusion
In this study the Brazil test of rock specimens was per-formed under different impact velocities using the SHPBsystem to explore fracture characterizations of rocks underdynamic loads Based on image processing technique crackpropagation process was quantitatively described from threeperspectives the crack propagation velocity crack fractalcharacteristic and crack morphological features Accordingto the recorded strain wave signals the dynamic mechanicalproperties of rocks were also calculated and the relationshipbetween impact velocity and crack propagation process wasexplored and analyzed +e main conclusions are listed asfollows
(1) Crack propagation velocities V and VAPboth in-
crease with increase of the crack fractals velocity VD
(2) +e proposed two crack features Compactness andAnisometery have a capacity of describing thefracture process of rock In specific VAnis linearlydecreases with the increase of impact velocity v whileVComp exhibits a negative relationship with crackfractals velocity VD
(3) +e energy absorbed by the rocks increases with theincrease of impact velocity v but shows a linearnegative trend with VAnis
(4) +e mean strain rate and max strain both decreasewith increase of crack propagation velocity whichshows that there is a certain relationship between thecrack propagation process and dynamic mechanicalproperties of rocks under dynamic loading
In the future work we will conduct the static tensile testsusing the BD specimen on the same rock material andcompare the static and dynamic results in terms of me-chanical properties and crack propagation process
Nomenclature
_ε Mean strain rate (sminus1)σmax Max stress (MPa)εmax Max strain (10minus3)A Cross-sectional area of the bar (mm2)A Crack length (mm)Ap Crack quantification area (pixels)AS Cross-sectional area of the specimen (mm2)Anis Crack feature descriptormdashanisometryC Longitudinal stress wave speed of the bar (ms)Comp Crack feature descriptormdashcompactnessD Fractal dimensionE Youngrsquos modulus of the bar (GPa)LS Length of rock specimen (mm)P1 P2 Dynamic forces on incident and transmitted ends
(N)rxy Pearsonrsquos correlation coefficientV Crack propagation velocity (ms)v Impact velocity (ms)VD Fractal dimension velocity (Dframe)VAP
Crack propagation velocity (pixelss)VAnis Anisometry velocity (anisframe)VComp Compactness velocity (compframe)WS Absorbed energy (J)
Data Availability
+e data utilized in this study are available from the cor-responding author upon request
00 50 times 106 10 times 107 15 times 107
Fitting curve of VAP and ε
20 times 107 25 times 107 30 times 107 35 times 107
VAP (pixelss)
66
68
70
72
74
76
78ε (
sndash1)
(a)
70
65
60
55
50
44
40
30
25
35
ε max
(10ndash3
)
Fitting curve of VAP and εmax
00 50 times 106 10 times 107 15 times 107 20 times 107 25 times 107 30 times 107 35 times 107
VAP (pixelss)
(b)
Figure 18 Curves of strain parameters with crack propagation velocity VAPand associated results after linear fitting (a) _ε as a function of
VAP (b) εmax as a function of VAP
12 Shock and Vibration
Conflicts of Interest
+e authors declare that they have no conflicts of interest
Acknowledgments
+is research was financially supported by the NationalNatural Science Foundation of China (nos 51274206 and51404277) +is support is greatly acknowledged andappreciated
References
[1] K Xia and W Yao ldquoDynamic rock tests using split Hop-kinson (Kolsky) bar systemmdasha reviewrdquo Journal of RockMechanics and Geotechnical Engineering vol 7 no 1pp 27ndash59 2015
[2] F Gong H Ye and Y Luo ldquo+e effect of high loading rate onthe behaviour and mechanical properties of coal-rock com-bined bodyrdquo Shock and Vibration vol 2018 Article ID4374530 9 pages 2018
[3] Y X Zhou K Xia X B Li et al ldquoSuggested methods fordetermining the dynamic strength parameters and mode-ifracture toughness of rock materialsrdquo International Journal ofRock Mechanics and Mining Sciences vol 49 no 1pp 105ndash112 2012
[4] Y Zhao G-F Zhao Y Jiang D Elsworth and Y HuangldquoEffects of bedding on the dynamic indirect tensile strength ofcoal Laboratory experiments and numerical simulationrdquoInternational Journal of Coal Geology vol 132 pp 81ndash932014
[5] F Dai K Xia and S N Luo ldquoSemicircular bend testing withsplit Hopkinson pressure bar for measuring dynamic tensilestrength of brittle solidsrdquo Review of Scientific Instrumentsvol 79 no 12 article 123903 2008
[6] F Dai K Xia and L Tang ldquoRate dependence of the flexuraltensile strength of Laurentian graniterdquo International Journalof Rock Mechanics and Mining Sciences vol 47 no 3pp 469ndash475 2010
[7] Y Wang ldquoRock dynamic fracture characteristics based onNSCB impact methodrdquo Shock and Vibration vol 2018 Ar-ticle ID 3105384 13 pages 2018
[8] Q B Zhang and J Zhao ldquoEffect of loading rate on fracturetoughness and failure micromechanisms in marblerdquo Engi-neering Fracture Mechanics vol 102 pp 288ndash309 2013
[9] M D Kuruppu Y Obara M R Ayatollahi K P Chong andT Funatsu ldquoISRM-suggested method for determining themode i static fracture toughness using semi-circular bendspecimenrdquo Rock Mechanics and Rock Engineering vol 47no 1 pp 267ndash274 2014
[10] M RM Aliha andM R Ayatollahi ldquoRock fracture toughnessstudy using cracked chevron notched Brazilian disc specimenunder pure modes I and II loadingmdasha statistical approachrdquoeoretical and Applied Fracture Mechanics vol 69 no 2pp 17ndash25 2014
[11] F Dai K Xia H Zheng and Y X Wang ldquoDetermination ofdynamic rock mode-i fracture parameters using crackedchevron notched semi-circular bend specimenrdquo EngineeringFracture Mechanics vol 78 no 15 pp 2633ndash2644 2011
[12] T Tang Z P Bazant S Yang and D Zollinger ldquoVariable-notch one-size test method for fracture energy and processzone lengthrdquo Engineering Fracture Mechanics vol 55 no 3pp 383ndash404 1996
[13] Q Z Wang S Zhang and H P Xie ldquoRock dynamic fracturetoughness tested with holed-cracked flattened Brazilian discsdiametrically impacted by SHPB and its size effectrdquo Experi-mental Mechanics vol 50 no 7 pp 877ndash885 2010
[14] B Lundberg ldquoA split Hopkinson bar study of energy ab-sorption in dynamic rock fragmentationrdquo InternationalJournal of Rock Mechanics and Mining Sciences amp Geo-mechanics Abstracts vol 13 no 6 pp 187ndash197 1976
[15] V Isheyskiy and M Marinin ldquoDetermination of rock massweakening coefficient after blasting in various fracture zonesrdquoEngineering Solid Mechanics vol 5 no 3 pp 199ndash204 2017
[16] G Gary and P Bailly ldquoBehaviour of quasi-brittle material athigh strain rate Experiment and modellingrdquo EuropeanJournal of Mechanics-ASolids vol 17 no 3 pp 403ndash4201998
[17] J Zhao H B Li and Y H ZhaoDynamic Strength Tests of theBukit Timah Granite Nanyang Technological UniversitySingapore 1998
[18] Q B Zhang and J Zhao ldquoA review of dynamic experimentaltechniques andmechanical behaviour of rockmaterialsrdquo RockMechanics and Rock Engineering vol 47 no 4 pp 1411ndash14782014
[19] J Zhao and H B Li ldquoExperimental determination of dynamictensile properties of a graniterdquo International Journal of RockMechanics and Mining Sciences vol 37 no 5 pp 861ndash8662000
[20] J R Klepaczko and A Brara ldquoAn experimental method fordynamic tensile testing of concrete by spallingrdquo InternationalJournal of Impact Engineering vol 25 no 4 pp 387ndash4092001
[21] S Kubota Y Ogata Y Wada G Simangunsong H Shimadaand K Matsui ldquoEstimation of dynamic tensile strength ofsandstonerdquo International Journal of Rock Mechanics andMining Sciences vol 45 no 3 pp 397ndash406 2008
[22] B Erzar and P Forquin ldquoAn experimental method to de-termine the tensile strength of concrete at high rates of strainrdquoExperimental Mechanics vol 50 no 7 pp 941ndash955 2010
[23] L Biolzi and J Labuz ldquoInstabilities in fracture of elastic-softening structuresrdquo Fracture of Engineering Materials andStructures vol 6 no 8 pp 821ndash826 1991
[24] Q ZWangW Li and H P Xie ldquoDynamic split tensile test offlattened Brazilian disc of rock with SHPB setuprdquo Mechanicsof Materials vol 41 no 3 pp 252ndash260 2009
[25] D Asprone E Cadoni A Prota and G Manfredi ldquoDynamicbehavior of a mediterranean natural stone under tensileloadingrdquo International Journal of Rock Mechanics and MiningSciences vol 46 no 3 pp 514ndash520 2009
[26] H Kolsky ldquoAn investigation of the mechanical properties ofmaterials at very high rates of loadingrdquo Proceedings of thePhysical Society Section B vol 62 no 11 pp 676ndash700 1949
[27] U S Lindholm ldquoSome experiments with the split Hopkinsonpressure barrdquo Journal of the Mechanics and Physics of Solidsvol 12 no 5 pp 317ndash335 1964
[28] G Subhash and G Ravichandran Split-Hopkinson PressureBar Testing of Ceramics pp 497ndash504 ASM InternationalMaterials Park OH USA 2000
[29] X Li T Zhou D Li and Z Wang ldquoExperimental and nu-merical investigations on feasibility and validity of prismaticrock specimen in SHPBrdquo Shock and Vibration vol 2016Article ID 7198980 13 pages 2016
[30] M R Ayatollahi and M Sistaninia ldquoMode __ fracture study ofrocks using Brazilian disk specimensrdquo International Journal ofRock Mechanics and Mining Sciences vol 48 no 5pp 819ndash826 2011
Shock and Vibration 13
[31] Q Z Wang X P Gou and H Fan ldquo+e minimum di-mensionless stress intensity factor and its upper bound forCCNBD fracture toughness specimen analyzed with straightthrough crack assumptionrdquo Engineering Fracture Mechanicsvol 82 pp 1ndash8 2012
[32] Q B Zhang and J Zhao ldquoQuasi-static and dynamic fracturebehaviour of rock materials phenomena and mechanismsrdquoInternational Journal of Fracture vol 189 no 1 pp 1ndash322014
[33] A Bertram and J F Kalthoff ldquoCrack propagation toughnessof rock for the range of low to very high crack speedsrdquo KeyEngineering Materials vol 251-252 pp 423ndash430 2003
[34] R Chen K Xia F Dai F Lu and S N Luo ldquoDeterminationof dynamic fracture parameters using a semi-circular bendtechnique in split Hopkinson pressure bar testingrdquo Engi-neering Fracture Mechanics vol 76 no 9 pp 1268ndash12762009
[35] P Forquin ldquoAn optical correlation technique for character-izing the crack velocity in concreterdquo e European PhysicalJournal Special Topics vol 206 no 1 pp 89ndash95 2012
[36] Y Zhao S Gong C Zhang Z Zhang and Y Jiang ldquoFractalcharacteristics of crack propagation in coal under impactloadingrdquo Fractals vol 26 no 2 article 1840014 2018
[37] J T Gomez A Shukla and A Sharma ldquoStatic and dynamicbehavior of concrete and granite in tension with damagerdquoeoretical and Applied Fracture Mechanics vol 36 no 1pp 37ndash49 2001
[38] Q B Zhang and J Zhao ldquoDetermination of mechanicalproperties and full-field strain measurements of rock materialunder dynamic loadsrdquo International Journal of Rock Me-chanics and Mining Sciences vol 60 pp 423ndash439 2013
[39] W Yao Y Xu H-W Liu and K Xia ldquoQuantification ofthermally induced damage and its effect on dynamic fracturetoughness of two mortarsrdquo Engineering Fracture Mechanicsvol 169 pp 74ndash88 2017
[40] T S Yun Y J Jeong K Y Kim and K-B Min ldquoEvaluation ofrock anisotropy using 3D X-ray computed tomographyrdquoEngineering Geology vol 163 pp 11ndash19 2013
[41] T Yin X Li K Xia and S Huang ldquoEffect of thermaltreatment on the dynamic fracture toughness of Laurentiangraniterdquo Rock Mechanics and Rock Engineering vol 45 no 6pp 1087ndash1094 2012
[42] S Huang K Xia F Yan and X Feng ldquoAn experimental studyof the rate dependence of tensile strength softening ofLongyou sandstonerdquo Rock Mechanics and Rock Engineeringvol 43 no 6 pp 677ndash683 2010
[43] S N Luo B J Jensen D E Hooks et al ldquoGas gun shockexperiments with single-pulse X-ray phase contrast imagingand diffraction at the advanced photon sourcerdquo Review ofScientific Instruments vol 83 no 7 article 073903 2012
[44] M Hudspeth B Claus S Dubelman et al ldquoHigh speedsynchrotron X-ray phase contrast imaging of dynamic ma-terial response to split Hopkinson bar loadingrdquo Review ofScientific Instruments vol 84 no 2 article 025102 2013
[45] Y Li and K T Ramesh ldquoAn optical technique for mea-surement of material properties in the tension Kolsky barrdquoInternational Journal of Impact Engineering vol 34 no 4pp 784ndash798 2007
[46] G Gao S Huang K Xia and Z Li ldquoApplication of digitalimage correlation (DIC) in dynamic notched semi-circularbend (NSCB) testsrdquo Experimental Mechanics vol 55 no 1pp 95ndash104 2015
[47] B Pan K Qian H Xie and A Asundi ldquoTwo-dimensionaldigital image correlation for in-plane displacement and strain
measurement a reviewrdquo Measurement Science and Technol-ogy vol 20 no 6 article 062001 2009
[48] F Amiot M Bornert P Doumalin et al ldquoAssessment ofdigital image correlation measurement accuracy in the ulti-mate error regime main results of a collaborative bench-markrdquo Strain vol 49 no 6 pp 483ndash496 2013
[49] W Shi Y Wu and L Wu ldquoQuantitative analysis of theprojectile impact on rock using infrared thermographyrdquoInternational Journal of Impact Engineering vol 34 no 5pp 990ndash1002 2007
[50] D K Iakovidis T Goudas C V Smailis and I MaglogiannisldquoRatsnake a versatile image annotation tool with applicationto computer-aided diagnosisrdquo e Scientific World Journalvol 2014 Article ID 286856 12 pages 2014
[51] B A Han H Y Xiang Z Li and J J Huang ldquoDefects de-tection of sheet metal parts based on HALCON and regionmorphologyrdquo Applied Mechanics and Materials vol 365-366pp 729ndash732 2013
[52] D Ai Y Zhao Q Wang and C Li ldquoExperimental andnumerical investigation of crack propagation and dynamicproperties of rock in SHPB indirect tension testrdquo In-ternational Journal of Impact Engineering vol 126 pp 135ndash146 2019
[53] H Xie and D J Sanderson ldquoFractal effects of crack propa-gation on dynamic stress intensity factors and crack veloci-tiesrdquo International Journal of Fracture vol 74 no 1pp 29ndash42 1996
[54] F Dai R Chen and K Xia ldquoA semi-circular bend techniquefor determining dynamic fracture toughnessrdquo ExperimentalMechanics vol 50 no 6 pp 783ndash791 2010
[55] D Chakerian and B B Mandelbrot ldquo+e fractal geometry ofnaturerdquo College Mathematics Journal vol 15 no 2pp 175ndash177 1984
[56] K Falconer ldquoFractal geometry mathematical foundationsand applicationsrdquo Biometrics vol 46 no 3 pp 886-887 1990
[57] T-B Yin K Peng L Wang P Wang X-Y Yin andY-L Zhang ldquoStudy on impact damage and energy dissipationof coal rock exposed to high temperaturesrdquo Shock and Vi-bration vol 2016 Article ID 5121932 10 pages 2016
14 Shock and Vibration
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σ(t) AE
2ASεi(t) + εr(t) + εt(t)1113858 1113859 (1)
ε(t) C
LS1113946
t
0εi(t)minus εr(t)minus εt(t)1113858 1113859dt (2)
_ε(t) C
LSεi(t)minus εr(t)minus εt(t)1113858 1113859 (3)
where A and AS are the cross-sectional area of the bar androck specimen respectively E is Youngrsquos modulus of the barC is the longitudinal stress wave speed of the bar and LSdenotes the length of rock specimen
Also the dynamic forces on the incident and transmittedends P1 and P2 can be computed as
P1 AE εi + εr( 1113857
P2 AEεt(4)
3 Methodology
Figure 3 shows the framework of our proposed methodwhich mainly consists of two parts ie crack feature ex-traction and dynamic mechanical properties calculationFirstly the video of the fracture process of rock specimens issplit into several images which will be postprocessed by thecrack extraction module To achieve the accurate extractionof cracks a novel and efficient image annotation softwaretool Ratsnake [50] is adopted to identify and extract crackson rock surface accurately According to the principles ofconnected domain approach used in semantic image seg-mentation application images of extracted cracks of rockspecimens under SHPB impact loading are obtained +enby Halcon [51] machine vision software a number of novelcrack features have been proposed and calculated to describethe fracture process of rock under different loading rates Atthe same time dynamic mechanical properties also havebeen computed based on the above formulas Finally acorrelation matrix was constructed based on Pearsonrsquoscorrelation coefficient
As illustrated in Figure 4 the correlation matrix heat-map has been calculated based on the experimental data tovisualize the relationship between loading condition crackpropagation process and dynamic mechanical properties ofrocks under different SHPB impact velocities
Given paired data (x1 y1) (xn yn)1113864 1113865 consisting ofn pairs Pearsonrsquos correlation coefficient rxy is defined as
rxy 1113936
ni1 xi minusx( 1113857 yi minusy( 1113857
1113936ni1 xi minus x( 1113857
21113969
1113936ni1 yi minusy( 1113857
21113969 (5)
where n is the sample size xi yi are the individual pointsindexed with i and x y are the sample mean values of x andy points
In the correlation matrix heat-map larger positivevalues were represented by dark red colors denoting astrong positive correlation between two variables whilelarger negative values were represented by dark blue colors
which indicate a strong negative correlation between twovariables
4 Results and Discussion
41 Crack Propagation Process
411 Crack Propagation Velocity Over the past few de-cades there have been some investigations for crackpropagation velocities of rock materials under dynamicloading which provide a promising way to explore thefracture mechanisms of rock materials [1 18] Howeverrelatively few crack extraction approaches based on imageprocessing have been conducted on rock specimens to de-scribe the failure process and explore the fracture mecha-nism due to the technical difficulties associated with crackfeature extraction and computation
In this study the crack propagation velocity V and VAPwere calculated according to the crack length and crack area(the number of crack pixels) [52] as shown in Figures 5 and 6
To visualize the relationship between these two crackvelocity variables Figure 7 plots VAP
as a function of V aswell as the fitting curve It can be seen that VAP
increasesalmost linearly with the increased of V under SHPBloading
412 Crack Fractal Characteristic Since cracks on rocksurface are an important index to measure the state of rockmaterial and fractals exhibit the ability for measuring thecomplex topological pattern many significant endeavorshave been made to investigate the fractality of cracks to themechanics of fracture [53 54]
In mathematics a fractal dimension is used to evaluatethe fractal patterns by quantifying their complexity as a ratioof the change in detail to the change in scale [55] Unliketopological dimensions the fractal dimension can takenoninteger values Particularly there are many formalmathematical definitions for fractal dimension eg box-counting dimension information dimension and correla-tion dimension Among them the box-counting dimensionis calculated by counting how this number changes as itmakes the grid finer by applying a box-counting algorithmIn more detail by the box-counting dimension computationmethod the fractal dimension of an object can be computedas [56]
N C middot SD
(6)
where D is fractal dimension S the scale of the object(cracks) N the number of boxes of scale S required to coverthe object (cracks) and C a constant number Taking thelogarithm it can be rewritten
lnN lnC + D middot ln S (7)
+erefore the box-counting dimensionD can be definedas
D minuslimsrarr0
lnN
ln S (8)
4 Shock and Vibration
Figure 8 presents an illustration for crack coverageusing dierent scale boxes (S 8 16 32 64) whileFigure 9(a) plots the linear tting results of lnN and ln Swhich shows the fractal dimension is 114 for current crackson rock surface Based on the plots of lnN and ln S the
fractal dimension of the crack can be accumulated byformula (8)
In general the higher fractal dimension indicates a morecurved and intricate crack propagation path ereforeaccording to the above method the fractal dimension of
ρXY
= cov(x y)σxσy
3167ms3246ms3577ms3511ms3869ms4307ms4385ms4443ms4687ms5150ms5502ms
Set gridsCrack
annotation
Export mask binary image
Set connection domain
Input image
Output cracks
helliphellip
helliphellip
Crack central coordinate
Crack area and crack number
Crack fractal dimension
Crack statistical information
Crack morphological features
Crack extraction
Time
Time
Y
X
X
Y
Impact velocity
Absorbed energy
Max strain
Max stress
Mean strain rate
Crack fracture video
Images of extracted cracks
Dynamic fractureprocess investigation
(a)
(b)
(c)
(f) (g)
(d) (e)
(h)
6
5
4
Stre
ss (M
Pa)
3
2
1
0
00 25 50 75Strain (times10ndash3)
100 125 150 175
100
100
100
100
100
100
100
100
100
100
062
062
068
068
044
044
ndash078
ndash078
ndash029
ndash029
050
050
ndash062
067
ndash062
ndash049
ndash049
ndash02608
04
00
ndash04
ndash08ndash026 ndash065 ndash060 ndash019 010 ndash005 ndash063 ndash025
ndash074 ndash062 ndash022 018 004 ndash026
ndash010 ndash014 ndash021 053 ndash004 ndash027 ndash029 ndash025
023 035 014 ndash051 ndash016 ndash026ndash027 ndash063
005 ndash029 ndash023 039 004ndash004ndash016 ndash005
039ndash038ndash014 ndash040 018053ndash051 010
ndash040 ndash023072037
083
ndash022ndash021014 ndash019
072 ndash038 ndash029 ndash062ndash014035 ndash060
083 037 ndash014 005 ndash074ndash010023 ndash065
ndash029
067
Figure 3 An overview of the proposed approach for the investigation of dynamic fracture process of rock materials under SHPB impactloading (a) an input video of rock fracture process (b) an algorithm for multicracks extraction (c) crack extraction results for a fractureprocess video (d) dynamic strain-stress response of rock specimens (e) the formula of Pearsonrsquos correlation coeiexclcient (f ) matrix of crackevolution features (g) matrix of dynamic mechanical properties (h) a correlation matrix heat-map of relationship between crack evolutionfeatures and dynamic mechanical properties
Loadingcondition
Crackpropagation
process
Dynamicmechanicalproperties
Impact velocity v
v
V
V
VAP
VAP
VAnis
VAnis
VComp
VComp
WS
WS
σmax
σmax
εmax
εmax
VD
VD
Crack propagation velocity
Crack fractals characteristic
Crack morphological features
Dynamic fracture energy
Strain-stress parameters
ε
100
100
100
100
100
100
100
100
100
100
062
062
068
068
044
044
ndash078
ndash078
ndash029
ndash029
050
050
ndash062
067
ndash062
ndash049
ndash049
ndash026
ndash026 ndash065 ndash060 ndash019 010 ndash005 ndash063 ndash025
ndash074 ndash062 ndash022 018 004 ndash026
ndash010 ndash014 ndash021 053 ndash004 ndash027 ndash029 ndash025
023 035 014 ndash051 ndash016 ndash026ndash027 ndash063
005 ndash029 ndash023 039 004ndash004ndash016 ndash005
039ndash038ndash014 ndash040 018053ndash051 010
ndash040 ndash023072037
083
ndash022ndash021014 ndash019
072 ndash038 ndash029 ndash062ndash014035 ndash060
083 037 ndash014 005 ndash074ndash010023 ndash065
ndash029
067ε
08
04
00
ndash04
ndash08
Figure 4 An illustration of the correlation matrix heat-map with loading condition crack propagation process and dynamic mechanicalproperties
Shock and Vibration 5
cracks in each frame of the rock fracture process has beenincreasing Figure 9(b) gives a quantitative description of thecrack propagation process of rock specimens under dierentimpact velocities It can be observed from it that the fractaldimension of cracks increases gradually during the fractureprocess of rocks and the value of the fractal dimension ofcracks on rock surface ranges from 08 to 12
Figure 10 shows the relationship between crack prop-agation velocity and fractal dimension velocity It has beenfound that both crack propagation velocities V and VAPincrease with increasingVD for rocks under dierent impactvelocities
413 Crack Morphological Features In addition toadopting the crack area AP and fractal dimension D toquantitatively describe the crack characteristics twomorphological features that can further analyze the crackevolution path and failure process are also proposed basedon image processing technique Figure 11 demonstrates acrack morphological process for crack initiation propa-gation and coalescence In order to present a quantitativedescription of the distribution and shape factor of cracksAnisometry and Compactness which derived from imagemorphology are proposed In specic Anisometry isderived from the geometric moments for each crack anddened as
Anisometry Ra
Rb (9)
where Ra denotes the main radius of maximum ellipse of thecrack and Rb represents the secondary radius of the ellipseSimilarly Compactness is also a shape factor which valueranges from 0 to 1 and can be expressed as
Compactness max 1 Cprime( )
Cprime L2
4 middot F middot π
(10)
where L is the total length of the contour and F is the area ofthe region
As shown in Figure 12(a) VComp is decreasing withthe increase of VD as a whole It can also be seen fromFigure 12(b) that the values of VAnis decrease almostlinearly with the increase of impact velocity which in-dicates that longitudinal crack length produced bythe rock is less than transversersquos under higher impactvelocity
414 Distribution of Cracks It has been generally rec-ognized that for a valid and typical dynamic Brazilian
5mm
0μs
(a)
75μs
a = 175mm
(b)
Figure 5 An illustration of crack propagation velocity computation using crack length
6000
A P (p
ixel
s) 4000
2000
0
0 100Time (micros)
200
Crack initiation
Crack coalescence
Crack propagi
nation
300
APFitting curve of AP
Figure 6 An illustration of crack propagation velocity compu-tation using crack area
Fitting curve of V and VAP
3 times 107
2 times 107
1 times 107
0
V AP (p
ixel
ss)
100V (ms)
200 300 400 500 600 700
Figure 7 Relationship between V and VAPof rock specimens
under SHPB loading
6 Shock and Vibration
test crack should be first appeared along the impactdirection somewhere near the center of the specimen andthen propagates bilaterally to the loading endsAccording to the row and column index of the crackcenter Figure 13 shows the coordinate distribution ofcrack center in the process of rock failure It can beobserved from Figure 13 that most of the rock disc cracksnear the center of the specimen and the fracture prop-agation direction are bilateral to the loading ends and
some cracks also appeared at the contact side of rock andbars +e result indicates that the failure patterns ofdynamic Brazil test under SHPB loading approximatelyinclude tensile failure and shear failure Accordingly thecracks near the center of rocks are mainly caused by thetensile failure which is the main axial crack parallel to theloading direction and other cracks are caused by theshear failure that is a result of secondary fractures due tothe further compression
ndash1
Fitting curve
D = 114 R2 = 099
ndash2
InS ndash3
ndash4
ndash5
2 3InN
4 5
(a)
12
10
D08
06
04
02
00200 300 400 500
BXY1 (4687ms)BXY2 (5150ms)BXY3 (4443ms)BXY4 (4385ms)BXY5 (3377ms)BXY6 (3167ms)
BXY7 (3511ms)BXY8 (3246ms)BXY9 (3689ms)BXY10 (4307ms)BXY11 (5502ms)
600 7001000Time (micros)
(b)
Figure 9 (a) Number of covered boxes versus box size (b) fractal characteristics of crack for rock material under different velocities
200
Scale = 64
100
00 100 200 300 400 500
(a)
Scale = 32
200
100
00 100 200 300 400 500
(b)
Scale = 16
200
100
00 100 200 300 400 500
(c)
Scale = 8
200
100
00 100 200 300 400 500
(d)
Figure 8 An illustration of different box scales to fully cover cracks
Shock and Vibration 7
42 Dynamic Mechanical Properties Figure 14 illustratesthe incident εi(t) reected εr(t) and transmitted εt(t)strain signals of rock specimens under dierent impactvelocities during SHPB dynamic loading test According
to the three-wave analysis method the mechanicalproperties of rocks under SHPB loading are determinedIn this study the absorbed energy and stress-strain pa-rameters are calculated and further compared with crack
100V
(ms
)
200
300
400
500
600
700
000 001VD (Dframe)
002 003 004 005 006 007
Fitting curve of VD and VAP
VAP
Fitting curve of VD and VV
4 times 107
3 times 107
2 times 107
1 times 107
0
V AP (p
ixel
ss)
Figure 10 Relationship between V VAP and VD in the SHPB experiment
Crack initiation
(a) (b)
Crack propagination
(c) (d)
Crack coalescence
(e)
F
LRb
Ra
(f )
Figure 11 An illustration of crack morphological features (a) (c) and (e) are original images represent crack initiation propagation andcoalescence respectively (b) (d) and (f) are extracted cracks from corresponded images
8 Shock and Vibration
propagation features to explore the relationship betweenthem
421 Dynamic Fracture Energy It has been generally rec-ognized that the fracture of rock under loading rates is theprocess of accumulation and dissipation of energy [57] Inspecific the consumed energy under SHPB dynamic loadingcan be well quantified based on the first law of thermody-namics [34] During the SHPB dynamic loading test theenergy of the incident wave WI the energy of the reflectedwave WR and the energy of the transmitted wave WT can becomputed as
WI A middot C
E1113946 εi(t)
2dt
WR A middot C
E1113946 εr(t)
2dt
WT A middot C
E1113946 εt(t)
2dt
(11)
where A is the cross-sectional area C is the longitudinalwave speed and E is Youngrsquos modulus of the bars
Assuming that all the energy loss at the specimen and barinterfaces can be negligible the energy absorbed by the rockspecimen WS can be expressed as
Fitting curve of VD and VComp
10
12
14
16
18
20
22
24
26
28V C
omp (
com
pfr
ame)
001 002 003 004 005 006 007000VD (Dframe)
(a)
Fitting curve of v and VAnis
35 40 45 50 5530v (ms)
8
10
12
14
16
18
20
22
24
V Ani
s (an
isfr
ame)
(b)
Figure 12 (a) Relationship between VComp and VD (b) relationship between VAnis and V
Impact velocity
Incident bar Transmission bar
Rock specimen250
200
Imag
e hei
ght (
pixe
ls)
150
100
50
0
BXY1BXY2BXY3
BXY4BXY5BXY6
BXY7BXY8BXY9
BXY10BXY11
200 300 400 5001000Image width (pixels)
Figure 13 Crack distribution for rocks under different impact velocities
Shock and Vibration 9
WS WI minusWR minusWT (12)
Figure 15 shows the total energy absorbed versus theimpact velocity for the rock specimens It indicates that the
energy absorbed by the rock specimen increases with in-creasing impact velocity
Moreover substantial efforts have been devoted to per-forming quantitative measurements on fracture surface and it
εi-4687msεi-5150msεi-4443msεi-4385msεi-3377msεi-3167msεi-3511msεi-3246msεi-3869msεi-4307msεi-5502ms
εt-4687msεt-5150msεt-4443msεt-4385msεt-3377msεt-3167msεt-3511msεt-3246msεt-3869msεt-4307msεt-5502ms
εr-4687msεr-5150msεr-4443msεr-4385msεr-3377msεr-3167msεr-3511msεr-3246msεr-3869msεr-4307msεr-5502ms
140 160 180 200 220 240 260 280120100
3
2
1
0
ndash1V
olta
ge (V
)ndash2
ndash3
Time (μs)
Figure 14 Incident reflected and transmitted signals of rocks under different impact velocities
18
WS (
J)
16
14
12
10
8
6
4
2
030 35 40 45 50 55
v (ms)
Fitting curve of v and WS
Figure 15 Relationship between v and WS
10 Shock and Vibration
has been well recognized that surface roughness in rock-likematerials exhibits self-similarity properties at least over a givenrange of length scales In other words the fracture surfacetopography of rock-like materials reveals inherent details as-sociated with energy dissipation mechanisms that govern thefracturing process +erefore the relationship between fractaldimension and absorbed energy was first calculated and theresult is shown in Figure 16(a) However it can be found thatthere is no obvious relationship between the two variables
On the other hand Figure 16(b) presents the total energyabsorbed WS versus the crack feature VAnis for the rockspecimens It can be seen that there is a linearly negativecorrelation between the two variables the greater the WSthe smaller the VAnis
422 Strain-Stress Parameters According to the incidentεi(t) reflected εr(t) and transmitted εt(t) strain signalsillustrated in Figure 14 and formulas (1)ndash(3) the max stressmax strain and mean strain rate of rocks under differentimpact velocities were calculated Combining with the crackcharacteristic parameters in the above section the re-lationship between the crack propagation process and dy-namic mechanical properties was analyzed
Figure 17 shows the max strain and mean strain rateversus the crack propagation velocity V while Figure 18shows the max strain and mean strain rate versus the crackpropagation velocity VAP
It can be seen that with theincrease of the V both the max strain and mean strain rateare gradually decreased and mean strain rate basically
000
001
002
003
004
005
006
007V D
(Dfr
ame)
2 4 6 8 10 12 14 16 180WS (J)
(a)
Fitting curve of WS and VAnis
2 4 6 8 10 12 14 16 180WS (J)
8
10
12
14
16
18
20
22
24
V Ani
s (an
isfr
ame)
(b)
Figure 16 (a) Relationship between WS and VD (b) relationship between WS and VAnis
Fitting curve of V and ε
66
68
70
72
74
76
78
εmiddot (sndash1
)
200 300 400 500
600 700100V (ms)
(a)
Fitting curve of V and εmax
200 300 400 500 600 700100V (ms)
25
30
35
40
45
50
55
60
65
70
ε max
(10ndash3
)
(b)
Figure 17 Curves of strain parameters with crack propagation velocity V and associated results after linear fitting (a) _ε as a function of V(b) εmax as a function of V
Shock and Vibration 11
remains the same when V ranges from 350ms to 650msSimilarly the max strain and mean strain rate also linearlydecrease with the increase of crack propagation velocityVAP
5 Conclusion
In this study the Brazil test of rock specimens was per-formed under different impact velocities using the SHPBsystem to explore fracture characterizations of rocks underdynamic loads Based on image processing technique crackpropagation process was quantitatively described from threeperspectives the crack propagation velocity crack fractalcharacteristic and crack morphological features Accordingto the recorded strain wave signals the dynamic mechanicalproperties of rocks were also calculated and the relationshipbetween impact velocity and crack propagation process wasexplored and analyzed +e main conclusions are listed asfollows
(1) Crack propagation velocities V and VAPboth in-
crease with increase of the crack fractals velocity VD
(2) +e proposed two crack features Compactness andAnisometery have a capacity of describing thefracture process of rock In specific VAnis linearlydecreases with the increase of impact velocity v whileVComp exhibits a negative relationship with crackfractals velocity VD
(3) +e energy absorbed by the rocks increases with theincrease of impact velocity v but shows a linearnegative trend with VAnis
(4) +e mean strain rate and max strain both decreasewith increase of crack propagation velocity whichshows that there is a certain relationship between thecrack propagation process and dynamic mechanicalproperties of rocks under dynamic loading
In the future work we will conduct the static tensile testsusing the BD specimen on the same rock material andcompare the static and dynamic results in terms of me-chanical properties and crack propagation process
Nomenclature
_ε Mean strain rate (sminus1)σmax Max stress (MPa)εmax Max strain (10minus3)A Cross-sectional area of the bar (mm2)A Crack length (mm)Ap Crack quantification area (pixels)AS Cross-sectional area of the specimen (mm2)Anis Crack feature descriptormdashanisometryC Longitudinal stress wave speed of the bar (ms)Comp Crack feature descriptormdashcompactnessD Fractal dimensionE Youngrsquos modulus of the bar (GPa)LS Length of rock specimen (mm)P1 P2 Dynamic forces on incident and transmitted ends
(N)rxy Pearsonrsquos correlation coefficientV Crack propagation velocity (ms)v Impact velocity (ms)VD Fractal dimension velocity (Dframe)VAP
Crack propagation velocity (pixelss)VAnis Anisometry velocity (anisframe)VComp Compactness velocity (compframe)WS Absorbed energy (J)
Data Availability
+e data utilized in this study are available from the cor-responding author upon request
00 50 times 106 10 times 107 15 times 107
Fitting curve of VAP and ε
20 times 107 25 times 107 30 times 107 35 times 107
VAP (pixelss)
66
68
70
72
74
76
78ε (
sndash1)
(a)
70
65
60
55
50
44
40
30
25
35
ε max
(10ndash3
)
Fitting curve of VAP and εmax
00 50 times 106 10 times 107 15 times 107 20 times 107 25 times 107 30 times 107 35 times 107
VAP (pixelss)
(b)
Figure 18 Curves of strain parameters with crack propagation velocity VAPand associated results after linear fitting (a) _ε as a function of
VAP (b) εmax as a function of VAP
12 Shock and Vibration
Conflicts of Interest
+e authors declare that they have no conflicts of interest
Acknowledgments
+is research was financially supported by the NationalNatural Science Foundation of China (nos 51274206 and51404277) +is support is greatly acknowledged andappreciated
References
[1] K Xia and W Yao ldquoDynamic rock tests using split Hop-kinson (Kolsky) bar systemmdasha reviewrdquo Journal of RockMechanics and Geotechnical Engineering vol 7 no 1pp 27ndash59 2015
[2] F Gong H Ye and Y Luo ldquo+e effect of high loading rate onthe behaviour and mechanical properties of coal-rock com-bined bodyrdquo Shock and Vibration vol 2018 Article ID4374530 9 pages 2018
[3] Y X Zhou K Xia X B Li et al ldquoSuggested methods fordetermining the dynamic strength parameters and mode-ifracture toughness of rock materialsrdquo International Journal ofRock Mechanics and Mining Sciences vol 49 no 1pp 105ndash112 2012
[4] Y Zhao G-F Zhao Y Jiang D Elsworth and Y HuangldquoEffects of bedding on the dynamic indirect tensile strength ofcoal Laboratory experiments and numerical simulationrdquoInternational Journal of Coal Geology vol 132 pp 81ndash932014
[5] F Dai K Xia and S N Luo ldquoSemicircular bend testing withsplit Hopkinson pressure bar for measuring dynamic tensilestrength of brittle solidsrdquo Review of Scientific Instrumentsvol 79 no 12 article 123903 2008
[6] F Dai K Xia and L Tang ldquoRate dependence of the flexuraltensile strength of Laurentian graniterdquo International Journalof Rock Mechanics and Mining Sciences vol 47 no 3pp 469ndash475 2010
[7] Y Wang ldquoRock dynamic fracture characteristics based onNSCB impact methodrdquo Shock and Vibration vol 2018 Ar-ticle ID 3105384 13 pages 2018
[8] Q B Zhang and J Zhao ldquoEffect of loading rate on fracturetoughness and failure micromechanisms in marblerdquo Engi-neering Fracture Mechanics vol 102 pp 288ndash309 2013
[9] M D Kuruppu Y Obara M R Ayatollahi K P Chong andT Funatsu ldquoISRM-suggested method for determining themode i static fracture toughness using semi-circular bendspecimenrdquo Rock Mechanics and Rock Engineering vol 47no 1 pp 267ndash274 2014
[10] M RM Aliha andM R Ayatollahi ldquoRock fracture toughnessstudy using cracked chevron notched Brazilian disc specimenunder pure modes I and II loadingmdasha statistical approachrdquoeoretical and Applied Fracture Mechanics vol 69 no 2pp 17ndash25 2014
[11] F Dai K Xia H Zheng and Y X Wang ldquoDetermination ofdynamic rock mode-i fracture parameters using crackedchevron notched semi-circular bend specimenrdquo EngineeringFracture Mechanics vol 78 no 15 pp 2633ndash2644 2011
[12] T Tang Z P Bazant S Yang and D Zollinger ldquoVariable-notch one-size test method for fracture energy and processzone lengthrdquo Engineering Fracture Mechanics vol 55 no 3pp 383ndash404 1996
[13] Q Z Wang S Zhang and H P Xie ldquoRock dynamic fracturetoughness tested with holed-cracked flattened Brazilian discsdiametrically impacted by SHPB and its size effectrdquo Experi-mental Mechanics vol 50 no 7 pp 877ndash885 2010
[14] B Lundberg ldquoA split Hopkinson bar study of energy ab-sorption in dynamic rock fragmentationrdquo InternationalJournal of Rock Mechanics and Mining Sciences amp Geo-mechanics Abstracts vol 13 no 6 pp 187ndash197 1976
[15] V Isheyskiy and M Marinin ldquoDetermination of rock massweakening coefficient after blasting in various fracture zonesrdquoEngineering Solid Mechanics vol 5 no 3 pp 199ndash204 2017
[16] G Gary and P Bailly ldquoBehaviour of quasi-brittle material athigh strain rate Experiment and modellingrdquo EuropeanJournal of Mechanics-ASolids vol 17 no 3 pp 403ndash4201998
[17] J Zhao H B Li and Y H ZhaoDynamic Strength Tests of theBukit Timah Granite Nanyang Technological UniversitySingapore 1998
[18] Q B Zhang and J Zhao ldquoA review of dynamic experimentaltechniques andmechanical behaviour of rockmaterialsrdquo RockMechanics and Rock Engineering vol 47 no 4 pp 1411ndash14782014
[19] J Zhao and H B Li ldquoExperimental determination of dynamictensile properties of a graniterdquo International Journal of RockMechanics and Mining Sciences vol 37 no 5 pp 861ndash8662000
[20] J R Klepaczko and A Brara ldquoAn experimental method fordynamic tensile testing of concrete by spallingrdquo InternationalJournal of Impact Engineering vol 25 no 4 pp 387ndash4092001
[21] S Kubota Y Ogata Y Wada G Simangunsong H Shimadaand K Matsui ldquoEstimation of dynamic tensile strength ofsandstonerdquo International Journal of Rock Mechanics andMining Sciences vol 45 no 3 pp 397ndash406 2008
[22] B Erzar and P Forquin ldquoAn experimental method to de-termine the tensile strength of concrete at high rates of strainrdquoExperimental Mechanics vol 50 no 7 pp 941ndash955 2010
[23] L Biolzi and J Labuz ldquoInstabilities in fracture of elastic-softening structuresrdquo Fracture of Engineering Materials andStructures vol 6 no 8 pp 821ndash826 1991
[24] Q ZWangW Li and H P Xie ldquoDynamic split tensile test offlattened Brazilian disc of rock with SHPB setuprdquo Mechanicsof Materials vol 41 no 3 pp 252ndash260 2009
[25] D Asprone E Cadoni A Prota and G Manfredi ldquoDynamicbehavior of a mediterranean natural stone under tensileloadingrdquo International Journal of Rock Mechanics and MiningSciences vol 46 no 3 pp 514ndash520 2009
[26] H Kolsky ldquoAn investigation of the mechanical properties ofmaterials at very high rates of loadingrdquo Proceedings of thePhysical Society Section B vol 62 no 11 pp 676ndash700 1949
[27] U S Lindholm ldquoSome experiments with the split Hopkinsonpressure barrdquo Journal of the Mechanics and Physics of Solidsvol 12 no 5 pp 317ndash335 1964
[28] G Subhash and G Ravichandran Split-Hopkinson PressureBar Testing of Ceramics pp 497ndash504 ASM InternationalMaterials Park OH USA 2000
[29] X Li T Zhou D Li and Z Wang ldquoExperimental and nu-merical investigations on feasibility and validity of prismaticrock specimen in SHPBrdquo Shock and Vibration vol 2016Article ID 7198980 13 pages 2016
[30] M R Ayatollahi and M Sistaninia ldquoMode __ fracture study ofrocks using Brazilian disk specimensrdquo International Journal ofRock Mechanics and Mining Sciences vol 48 no 5pp 819ndash826 2011
Shock and Vibration 13
[31] Q Z Wang X P Gou and H Fan ldquo+e minimum di-mensionless stress intensity factor and its upper bound forCCNBD fracture toughness specimen analyzed with straightthrough crack assumptionrdquo Engineering Fracture Mechanicsvol 82 pp 1ndash8 2012
[32] Q B Zhang and J Zhao ldquoQuasi-static and dynamic fracturebehaviour of rock materials phenomena and mechanismsrdquoInternational Journal of Fracture vol 189 no 1 pp 1ndash322014
[33] A Bertram and J F Kalthoff ldquoCrack propagation toughnessof rock for the range of low to very high crack speedsrdquo KeyEngineering Materials vol 251-252 pp 423ndash430 2003
[34] R Chen K Xia F Dai F Lu and S N Luo ldquoDeterminationof dynamic fracture parameters using a semi-circular bendtechnique in split Hopkinson pressure bar testingrdquo Engi-neering Fracture Mechanics vol 76 no 9 pp 1268ndash12762009
[35] P Forquin ldquoAn optical correlation technique for character-izing the crack velocity in concreterdquo e European PhysicalJournal Special Topics vol 206 no 1 pp 89ndash95 2012
[36] Y Zhao S Gong C Zhang Z Zhang and Y Jiang ldquoFractalcharacteristics of crack propagation in coal under impactloadingrdquo Fractals vol 26 no 2 article 1840014 2018
[37] J T Gomez A Shukla and A Sharma ldquoStatic and dynamicbehavior of concrete and granite in tension with damagerdquoeoretical and Applied Fracture Mechanics vol 36 no 1pp 37ndash49 2001
[38] Q B Zhang and J Zhao ldquoDetermination of mechanicalproperties and full-field strain measurements of rock materialunder dynamic loadsrdquo International Journal of Rock Me-chanics and Mining Sciences vol 60 pp 423ndash439 2013
[39] W Yao Y Xu H-W Liu and K Xia ldquoQuantification ofthermally induced damage and its effect on dynamic fracturetoughness of two mortarsrdquo Engineering Fracture Mechanicsvol 169 pp 74ndash88 2017
[40] T S Yun Y J Jeong K Y Kim and K-B Min ldquoEvaluation ofrock anisotropy using 3D X-ray computed tomographyrdquoEngineering Geology vol 163 pp 11ndash19 2013
[41] T Yin X Li K Xia and S Huang ldquoEffect of thermaltreatment on the dynamic fracture toughness of Laurentiangraniterdquo Rock Mechanics and Rock Engineering vol 45 no 6pp 1087ndash1094 2012
[42] S Huang K Xia F Yan and X Feng ldquoAn experimental studyof the rate dependence of tensile strength softening ofLongyou sandstonerdquo Rock Mechanics and Rock Engineeringvol 43 no 6 pp 677ndash683 2010
[43] S N Luo B J Jensen D E Hooks et al ldquoGas gun shockexperiments with single-pulse X-ray phase contrast imagingand diffraction at the advanced photon sourcerdquo Review ofScientific Instruments vol 83 no 7 article 073903 2012
[44] M Hudspeth B Claus S Dubelman et al ldquoHigh speedsynchrotron X-ray phase contrast imaging of dynamic ma-terial response to split Hopkinson bar loadingrdquo Review ofScientific Instruments vol 84 no 2 article 025102 2013
[45] Y Li and K T Ramesh ldquoAn optical technique for mea-surement of material properties in the tension Kolsky barrdquoInternational Journal of Impact Engineering vol 34 no 4pp 784ndash798 2007
[46] G Gao S Huang K Xia and Z Li ldquoApplication of digitalimage correlation (DIC) in dynamic notched semi-circularbend (NSCB) testsrdquo Experimental Mechanics vol 55 no 1pp 95ndash104 2015
[47] B Pan K Qian H Xie and A Asundi ldquoTwo-dimensionaldigital image correlation for in-plane displacement and strain
measurement a reviewrdquo Measurement Science and Technol-ogy vol 20 no 6 article 062001 2009
[48] F Amiot M Bornert P Doumalin et al ldquoAssessment ofdigital image correlation measurement accuracy in the ulti-mate error regime main results of a collaborative bench-markrdquo Strain vol 49 no 6 pp 483ndash496 2013
[49] W Shi Y Wu and L Wu ldquoQuantitative analysis of theprojectile impact on rock using infrared thermographyrdquoInternational Journal of Impact Engineering vol 34 no 5pp 990ndash1002 2007
[50] D K Iakovidis T Goudas C V Smailis and I MaglogiannisldquoRatsnake a versatile image annotation tool with applicationto computer-aided diagnosisrdquo e Scientific World Journalvol 2014 Article ID 286856 12 pages 2014
[51] B A Han H Y Xiang Z Li and J J Huang ldquoDefects de-tection of sheet metal parts based on HALCON and regionmorphologyrdquo Applied Mechanics and Materials vol 365-366pp 729ndash732 2013
[52] D Ai Y Zhao Q Wang and C Li ldquoExperimental andnumerical investigation of crack propagation and dynamicproperties of rock in SHPB indirect tension testrdquo In-ternational Journal of Impact Engineering vol 126 pp 135ndash146 2019
[53] H Xie and D J Sanderson ldquoFractal effects of crack propa-gation on dynamic stress intensity factors and crack veloci-tiesrdquo International Journal of Fracture vol 74 no 1pp 29ndash42 1996
[54] F Dai R Chen and K Xia ldquoA semi-circular bend techniquefor determining dynamic fracture toughnessrdquo ExperimentalMechanics vol 50 no 6 pp 783ndash791 2010
[55] D Chakerian and B B Mandelbrot ldquo+e fractal geometry ofnaturerdquo College Mathematics Journal vol 15 no 2pp 175ndash177 1984
[56] K Falconer ldquoFractal geometry mathematical foundationsand applicationsrdquo Biometrics vol 46 no 3 pp 886-887 1990
[57] T-B Yin K Peng L Wang P Wang X-Y Yin andY-L Zhang ldquoStudy on impact damage and energy dissipationof coal rock exposed to high temperaturesrdquo Shock and Vi-bration vol 2016 Article ID 5121932 10 pages 2016
14 Shock and Vibration
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Figure 8 presents an illustration for crack coverageusing dierent scale boxes (S 8 16 32 64) whileFigure 9(a) plots the linear tting results of lnN and ln Swhich shows the fractal dimension is 114 for current crackson rock surface Based on the plots of lnN and ln S the
fractal dimension of the crack can be accumulated byformula (8)
In general the higher fractal dimension indicates a morecurved and intricate crack propagation path ereforeaccording to the above method the fractal dimension of
ρXY
= cov(x y)σxσy
3167ms3246ms3577ms3511ms3869ms4307ms4385ms4443ms4687ms5150ms5502ms
Set gridsCrack
annotation
Export mask binary image
Set connection domain
Input image
Output cracks
helliphellip
helliphellip
Crack central coordinate
Crack area and crack number
Crack fractal dimension
Crack statistical information
Crack morphological features
Crack extraction
Time
Time
Y
X
X
Y
Impact velocity
Absorbed energy
Max strain
Max stress
Mean strain rate
Crack fracture video
Images of extracted cracks
Dynamic fractureprocess investigation
(a)
(b)
(c)
(f) (g)
(d) (e)
(h)
6
5
4
Stre
ss (M
Pa)
3
2
1
0
00 25 50 75Strain (times10ndash3)
100 125 150 175
100
100
100
100
100
100
100
100
100
100
062
062
068
068
044
044
ndash078
ndash078
ndash029
ndash029
050
050
ndash062
067
ndash062
ndash049
ndash049
ndash02608
04
00
ndash04
ndash08ndash026 ndash065 ndash060 ndash019 010 ndash005 ndash063 ndash025
ndash074 ndash062 ndash022 018 004 ndash026
ndash010 ndash014 ndash021 053 ndash004 ndash027 ndash029 ndash025
023 035 014 ndash051 ndash016 ndash026ndash027 ndash063
005 ndash029 ndash023 039 004ndash004ndash016 ndash005
039ndash038ndash014 ndash040 018053ndash051 010
ndash040 ndash023072037
083
ndash022ndash021014 ndash019
072 ndash038 ndash029 ndash062ndash014035 ndash060
083 037 ndash014 005 ndash074ndash010023 ndash065
ndash029
067
Figure 3 An overview of the proposed approach for the investigation of dynamic fracture process of rock materials under SHPB impactloading (a) an input video of rock fracture process (b) an algorithm for multicracks extraction (c) crack extraction results for a fractureprocess video (d) dynamic strain-stress response of rock specimens (e) the formula of Pearsonrsquos correlation coeiexclcient (f ) matrix of crackevolution features (g) matrix of dynamic mechanical properties (h) a correlation matrix heat-map of relationship between crack evolutionfeatures and dynamic mechanical properties
Loadingcondition
Crackpropagation
process
Dynamicmechanicalproperties
Impact velocity v
v
V
V
VAP
VAP
VAnis
VAnis
VComp
VComp
WS
WS
σmax
σmax
εmax
εmax
VD
VD
Crack propagation velocity
Crack fractals characteristic
Crack morphological features
Dynamic fracture energy
Strain-stress parameters
ε
100
100
100
100
100
100
100
100
100
100
062
062
068
068
044
044
ndash078
ndash078
ndash029
ndash029
050
050
ndash062
067
ndash062
ndash049
ndash049
ndash026
ndash026 ndash065 ndash060 ndash019 010 ndash005 ndash063 ndash025
ndash074 ndash062 ndash022 018 004 ndash026
ndash010 ndash014 ndash021 053 ndash004 ndash027 ndash029 ndash025
023 035 014 ndash051 ndash016 ndash026ndash027 ndash063
005 ndash029 ndash023 039 004ndash004ndash016 ndash005
039ndash038ndash014 ndash040 018053ndash051 010
ndash040 ndash023072037
083
ndash022ndash021014 ndash019
072 ndash038 ndash029 ndash062ndash014035 ndash060
083 037 ndash014 005 ndash074ndash010023 ndash065
ndash029
067ε
08
04
00
ndash04
ndash08
Figure 4 An illustration of the correlation matrix heat-map with loading condition crack propagation process and dynamic mechanicalproperties
Shock and Vibration 5
cracks in each frame of the rock fracture process has beenincreasing Figure 9(b) gives a quantitative description of thecrack propagation process of rock specimens under dierentimpact velocities It can be observed from it that the fractaldimension of cracks increases gradually during the fractureprocess of rocks and the value of the fractal dimension ofcracks on rock surface ranges from 08 to 12
Figure 10 shows the relationship between crack prop-agation velocity and fractal dimension velocity It has beenfound that both crack propagation velocities V and VAPincrease with increasingVD for rocks under dierent impactvelocities
413 Crack Morphological Features In addition toadopting the crack area AP and fractal dimension D toquantitatively describe the crack characteristics twomorphological features that can further analyze the crackevolution path and failure process are also proposed basedon image processing technique Figure 11 demonstrates acrack morphological process for crack initiation propa-gation and coalescence In order to present a quantitativedescription of the distribution and shape factor of cracksAnisometry and Compactness which derived from imagemorphology are proposed In specic Anisometry isderived from the geometric moments for each crack anddened as
Anisometry Ra
Rb (9)
where Ra denotes the main radius of maximum ellipse of thecrack and Rb represents the secondary radius of the ellipseSimilarly Compactness is also a shape factor which valueranges from 0 to 1 and can be expressed as
Compactness max 1 Cprime( )
Cprime L2
4 middot F middot π
(10)
where L is the total length of the contour and F is the area ofthe region
As shown in Figure 12(a) VComp is decreasing withthe increase of VD as a whole It can also be seen fromFigure 12(b) that the values of VAnis decrease almostlinearly with the increase of impact velocity which in-dicates that longitudinal crack length produced bythe rock is less than transversersquos under higher impactvelocity
414 Distribution of Cracks It has been generally rec-ognized that for a valid and typical dynamic Brazilian
5mm
0μs
(a)
75μs
a = 175mm
(b)
Figure 5 An illustration of crack propagation velocity computation using crack length
6000
A P (p
ixel
s) 4000
2000
0
0 100Time (micros)
200
Crack initiation
Crack coalescence
Crack propagi
nation
300
APFitting curve of AP
Figure 6 An illustration of crack propagation velocity compu-tation using crack area
Fitting curve of V and VAP
3 times 107
2 times 107
1 times 107
0
V AP (p
ixel
ss)
100V (ms)
200 300 400 500 600 700
Figure 7 Relationship between V and VAPof rock specimens
under SHPB loading
6 Shock and Vibration
test crack should be first appeared along the impactdirection somewhere near the center of the specimen andthen propagates bilaterally to the loading endsAccording to the row and column index of the crackcenter Figure 13 shows the coordinate distribution ofcrack center in the process of rock failure It can beobserved from Figure 13 that most of the rock disc cracksnear the center of the specimen and the fracture prop-agation direction are bilateral to the loading ends and
some cracks also appeared at the contact side of rock andbars +e result indicates that the failure patterns ofdynamic Brazil test under SHPB loading approximatelyinclude tensile failure and shear failure Accordingly thecracks near the center of rocks are mainly caused by thetensile failure which is the main axial crack parallel to theloading direction and other cracks are caused by theshear failure that is a result of secondary fractures due tothe further compression
ndash1
Fitting curve
D = 114 R2 = 099
ndash2
InS ndash3
ndash4
ndash5
2 3InN
4 5
(a)
12
10
D08
06
04
02
00200 300 400 500
BXY1 (4687ms)BXY2 (5150ms)BXY3 (4443ms)BXY4 (4385ms)BXY5 (3377ms)BXY6 (3167ms)
BXY7 (3511ms)BXY8 (3246ms)BXY9 (3689ms)BXY10 (4307ms)BXY11 (5502ms)
600 7001000Time (micros)
(b)
Figure 9 (a) Number of covered boxes versus box size (b) fractal characteristics of crack for rock material under different velocities
200
Scale = 64
100
00 100 200 300 400 500
(a)
Scale = 32
200
100
00 100 200 300 400 500
(b)
Scale = 16
200
100
00 100 200 300 400 500
(c)
Scale = 8
200
100
00 100 200 300 400 500
(d)
Figure 8 An illustration of different box scales to fully cover cracks
Shock and Vibration 7
42 Dynamic Mechanical Properties Figure 14 illustratesthe incident εi(t) reected εr(t) and transmitted εt(t)strain signals of rock specimens under dierent impactvelocities during SHPB dynamic loading test According
to the three-wave analysis method the mechanicalproperties of rocks under SHPB loading are determinedIn this study the absorbed energy and stress-strain pa-rameters are calculated and further compared with crack
100V
(ms
)
200
300
400
500
600
700
000 001VD (Dframe)
002 003 004 005 006 007
Fitting curve of VD and VAP
VAP
Fitting curve of VD and VV
4 times 107
3 times 107
2 times 107
1 times 107
0
V AP (p
ixel
ss)
Figure 10 Relationship between V VAP and VD in the SHPB experiment
Crack initiation
(a) (b)
Crack propagination
(c) (d)
Crack coalescence
(e)
F
LRb
Ra
(f )
Figure 11 An illustration of crack morphological features (a) (c) and (e) are original images represent crack initiation propagation andcoalescence respectively (b) (d) and (f) are extracted cracks from corresponded images
8 Shock and Vibration
propagation features to explore the relationship betweenthem
421 Dynamic Fracture Energy It has been generally rec-ognized that the fracture of rock under loading rates is theprocess of accumulation and dissipation of energy [57] Inspecific the consumed energy under SHPB dynamic loadingcan be well quantified based on the first law of thermody-namics [34] During the SHPB dynamic loading test theenergy of the incident wave WI the energy of the reflectedwave WR and the energy of the transmitted wave WT can becomputed as
WI A middot C
E1113946 εi(t)
2dt
WR A middot C
E1113946 εr(t)
2dt
WT A middot C
E1113946 εt(t)
2dt
(11)
where A is the cross-sectional area C is the longitudinalwave speed and E is Youngrsquos modulus of the bars
Assuming that all the energy loss at the specimen and barinterfaces can be negligible the energy absorbed by the rockspecimen WS can be expressed as
Fitting curve of VD and VComp
10
12
14
16
18
20
22
24
26
28V C
omp (
com
pfr
ame)
001 002 003 004 005 006 007000VD (Dframe)
(a)
Fitting curve of v and VAnis
35 40 45 50 5530v (ms)
8
10
12
14
16
18
20
22
24
V Ani
s (an
isfr
ame)
(b)
Figure 12 (a) Relationship between VComp and VD (b) relationship between VAnis and V
Impact velocity
Incident bar Transmission bar
Rock specimen250
200
Imag
e hei
ght (
pixe
ls)
150
100
50
0
BXY1BXY2BXY3
BXY4BXY5BXY6
BXY7BXY8BXY9
BXY10BXY11
200 300 400 5001000Image width (pixels)
Figure 13 Crack distribution for rocks under different impact velocities
Shock and Vibration 9
WS WI minusWR minusWT (12)
Figure 15 shows the total energy absorbed versus theimpact velocity for the rock specimens It indicates that the
energy absorbed by the rock specimen increases with in-creasing impact velocity
Moreover substantial efforts have been devoted to per-forming quantitative measurements on fracture surface and it
εi-4687msεi-5150msεi-4443msεi-4385msεi-3377msεi-3167msεi-3511msεi-3246msεi-3869msεi-4307msεi-5502ms
εt-4687msεt-5150msεt-4443msεt-4385msεt-3377msεt-3167msεt-3511msεt-3246msεt-3869msεt-4307msεt-5502ms
εr-4687msεr-5150msεr-4443msεr-4385msεr-3377msεr-3167msεr-3511msεr-3246msεr-3869msεr-4307msεr-5502ms
140 160 180 200 220 240 260 280120100
3
2
1
0
ndash1V
olta
ge (V
)ndash2
ndash3
Time (μs)
Figure 14 Incident reflected and transmitted signals of rocks under different impact velocities
18
WS (
J)
16
14
12
10
8
6
4
2
030 35 40 45 50 55
v (ms)
Fitting curve of v and WS
Figure 15 Relationship between v and WS
10 Shock and Vibration
has been well recognized that surface roughness in rock-likematerials exhibits self-similarity properties at least over a givenrange of length scales In other words the fracture surfacetopography of rock-like materials reveals inherent details as-sociated with energy dissipation mechanisms that govern thefracturing process +erefore the relationship between fractaldimension and absorbed energy was first calculated and theresult is shown in Figure 16(a) However it can be found thatthere is no obvious relationship between the two variables
On the other hand Figure 16(b) presents the total energyabsorbed WS versus the crack feature VAnis for the rockspecimens It can be seen that there is a linearly negativecorrelation between the two variables the greater the WSthe smaller the VAnis
422 Strain-Stress Parameters According to the incidentεi(t) reflected εr(t) and transmitted εt(t) strain signalsillustrated in Figure 14 and formulas (1)ndash(3) the max stressmax strain and mean strain rate of rocks under differentimpact velocities were calculated Combining with the crackcharacteristic parameters in the above section the re-lationship between the crack propagation process and dy-namic mechanical properties was analyzed
Figure 17 shows the max strain and mean strain rateversus the crack propagation velocity V while Figure 18shows the max strain and mean strain rate versus the crackpropagation velocity VAP
It can be seen that with theincrease of the V both the max strain and mean strain rateare gradually decreased and mean strain rate basically
000
001
002
003
004
005
006
007V D
(Dfr
ame)
2 4 6 8 10 12 14 16 180WS (J)
(a)
Fitting curve of WS and VAnis
2 4 6 8 10 12 14 16 180WS (J)
8
10
12
14
16
18
20
22
24
V Ani
s (an
isfr
ame)
(b)
Figure 16 (a) Relationship between WS and VD (b) relationship between WS and VAnis
Fitting curve of V and ε
66
68
70
72
74
76
78
εmiddot (sndash1
)
200 300 400 500
600 700100V (ms)
(a)
Fitting curve of V and εmax
200 300 400 500 600 700100V (ms)
25
30
35
40
45
50
55
60
65
70
ε max
(10ndash3
)
(b)
Figure 17 Curves of strain parameters with crack propagation velocity V and associated results after linear fitting (a) _ε as a function of V(b) εmax as a function of V
Shock and Vibration 11
remains the same when V ranges from 350ms to 650msSimilarly the max strain and mean strain rate also linearlydecrease with the increase of crack propagation velocityVAP
5 Conclusion
In this study the Brazil test of rock specimens was per-formed under different impact velocities using the SHPBsystem to explore fracture characterizations of rocks underdynamic loads Based on image processing technique crackpropagation process was quantitatively described from threeperspectives the crack propagation velocity crack fractalcharacteristic and crack morphological features Accordingto the recorded strain wave signals the dynamic mechanicalproperties of rocks were also calculated and the relationshipbetween impact velocity and crack propagation process wasexplored and analyzed +e main conclusions are listed asfollows
(1) Crack propagation velocities V and VAPboth in-
crease with increase of the crack fractals velocity VD
(2) +e proposed two crack features Compactness andAnisometery have a capacity of describing thefracture process of rock In specific VAnis linearlydecreases with the increase of impact velocity v whileVComp exhibits a negative relationship with crackfractals velocity VD
(3) +e energy absorbed by the rocks increases with theincrease of impact velocity v but shows a linearnegative trend with VAnis
(4) +e mean strain rate and max strain both decreasewith increase of crack propagation velocity whichshows that there is a certain relationship between thecrack propagation process and dynamic mechanicalproperties of rocks under dynamic loading
In the future work we will conduct the static tensile testsusing the BD specimen on the same rock material andcompare the static and dynamic results in terms of me-chanical properties and crack propagation process
Nomenclature
_ε Mean strain rate (sminus1)σmax Max stress (MPa)εmax Max strain (10minus3)A Cross-sectional area of the bar (mm2)A Crack length (mm)Ap Crack quantification area (pixels)AS Cross-sectional area of the specimen (mm2)Anis Crack feature descriptormdashanisometryC Longitudinal stress wave speed of the bar (ms)Comp Crack feature descriptormdashcompactnessD Fractal dimensionE Youngrsquos modulus of the bar (GPa)LS Length of rock specimen (mm)P1 P2 Dynamic forces on incident and transmitted ends
(N)rxy Pearsonrsquos correlation coefficientV Crack propagation velocity (ms)v Impact velocity (ms)VD Fractal dimension velocity (Dframe)VAP
Crack propagation velocity (pixelss)VAnis Anisometry velocity (anisframe)VComp Compactness velocity (compframe)WS Absorbed energy (J)
Data Availability
+e data utilized in this study are available from the cor-responding author upon request
00 50 times 106 10 times 107 15 times 107
Fitting curve of VAP and ε
20 times 107 25 times 107 30 times 107 35 times 107
VAP (pixelss)
66
68
70
72
74
76
78ε (
sndash1)
(a)
70
65
60
55
50
44
40
30
25
35
ε max
(10ndash3
)
Fitting curve of VAP and εmax
00 50 times 106 10 times 107 15 times 107 20 times 107 25 times 107 30 times 107 35 times 107
VAP (pixelss)
(b)
Figure 18 Curves of strain parameters with crack propagation velocity VAPand associated results after linear fitting (a) _ε as a function of
VAP (b) εmax as a function of VAP
12 Shock and Vibration
Conflicts of Interest
+e authors declare that they have no conflicts of interest
Acknowledgments
+is research was financially supported by the NationalNatural Science Foundation of China (nos 51274206 and51404277) +is support is greatly acknowledged andappreciated
References
[1] K Xia and W Yao ldquoDynamic rock tests using split Hop-kinson (Kolsky) bar systemmdasha reviewrdquo Journal of RockMechanics and Geotechnical Engineering vol 7 no 1pp 27ndash59 2015
[2] F Gong H Ye and Y Luo ldquo+e effect of high loading rate onthe behaviour and mechanical properties of coal-rock com-bined bodyrdquo Shock and Vibration vol 2018 Article ID4374530 9 pages 2018
[3] Y X Zhou K Xia X B Li et al ldquoSuggested methods fordetermining the dynamic strength parameters and mode-ifracture toughness of rock materialsrdquo International Journal ofRock Mechanics and Mining Sciences vol 49 no 1pp 105ndash112 2012
[4] Y Zhao G-F Zhao Y Jiang D Elsworth and Y HuangldquoEffects of bedding on the dynamic indirect tensile strength ofcoal Laboratory experiments and numerical simulationrdquoInternational Journal of Coal Geology vol 132 pp 81ndash932014
[5] F Dai K Xia and S N Luo ldquoSemicircular bend testing withsplit Hopkinson pressure bar for measuring dynamic tensilestrength of brittle solidsrdquo Review of Scientific Instrumentsvol 79 no 12 article 123903 2008
[6] F Dai K Xia and L Tang ldquoRate dependence of the flexuraltensile strength of Laurentian graniterdquo International Journalof Rock Mechanics and Mining Sciences vol 47 no 3pp 469ndash475 2010
[7] Y Wang ldquoRock dynamic fracture characteristics based onNSCB impact methodrdquo Shock and Vibration vol 2018 Ar-ticle ID 3105384 13 pages 2018
[8] Q B Zhang and J Zhao ldquoEffect of loading rate on fracturetoughness and failure micromechanisms in marblerdquo Engi-neering Fracture Mechanics vol 102 pp 288ndash309 2013
[9] M D Kuruppu Y Obara M R Ayatollahi K P Chong andT Funatsu ldquoISRM-suggested method for determining themode i static fracture toughness using semi-circular bendspecimenrdquo Rock Mechanics and Rock Engineering vol 47no 1 pp 267ndash274 2014
[10] M RM Aliha andM R Ayatollahi ldquoRock fracture toughnessstudy using cracked chevron notched Brazilian disc specimenunder pure modes I and II loadingmdasha statistical approachrdquoeoretical and Applied Fracture Mechanics vol 69 no 2pp 17ndash25 2014
[11] F Dai K Xia H Zheng and Y X Wang ldquoDetermination ofdynamic rock mode-i fracture parameters using crackedchevron notched semi-circular bend specimenrdquo EngineeringFracture Mechanics vol 78 no 15 pp 2633ndash2644 2011
[12] T Tang Z P Bazant S Yang and D Zollinger ldquoVariable-notch one-size test method for fracture energy and processzone lengthrdquo Engineering Fracture Mechanics vol 55 no 3pp 383ndash404 1996
[13] Q Z Wang S Zhang and H P Xie ldquoRock dynamic fracturetoughness tested with holed-cracked flattened Brazilian discsdiametrically impacted by SHPB and its size effectrdquo Experi-mental Mechanics vol 50 no 7 pp 877ndash885 2010
[14] B Lundberg ldquoA split Hopkinson bar study of energy ab-sorption in dynamic rock fragmentationrdquo InternationalJournal of Rock Mechanics and Mining Sciences amp Geo-mechanics Abstracts vol 13 no 6 pp 187ndash197 1976
[15] V Isheyskiy and M Marinin ldquoDetermination of rock massweakening coefficient after blasting in various fracture zonesrdquoEngineering Solid Mechanics vol 5 no 3 pp 199ndash204 2017
[16] G Gary and P Bailly ldquoBehaviour of quasi-brittle material athigh strain rate Experiment and modellingrdquo EuropeanJournal of Mechanics-ASolids vol 17 no 3 pp 403ndash4201998
[17] J Zhao H B Li and Y H ZhaoDynamic Strength Tests of theBukit Timah Granite Nanyang Technological UniversitySingapore 1998
[18] Q B Zhang and J Zhao ldquoA review of dynamic experimentaltechniques andmechanical behaviour of rockmaterialsrdquo RockMechanics and Rock Engineering vol 47 no 4 pp 1411ndash14782014
[19] J Zhao and H B Li ldquoExperimental determination of dynamictensile properties of a graniterdquo International Journal of RockMechanics and Mining Sciences vol 37 no 5 pp 861ndash8662000
[20] J R Klepaczko and A Brara ldquoAn experimental method fordynamic tensile testing of concrete by spallingrdquo InternationalJournal of Impact Engineering vol 25 no 4 pp 387ndash4092001
[21] S Kubota Y Ogata Y Wada G Simangunsong H Shimadaand K Matsui ldquoEstimation of dynamic tensile strength ofsandstonerdquo International Journal of Rock Mechanics andMining Sciences vol 45 no 3 pp 397ndash406 2008
[22] B Erzar and P Forquin ldquoAn experimental method to de-termine the tensile strength of concrete at high rates of strainrdquoExperimental Mechanics vol 50 no 7 pp 941ndash955 2010
[23] L Biolzi and J Labuz ldquoInstabilities in fracture of elastic-softening structuresrdquo Fracture of Engineering Materials andStructures vol 6 no 8 pp 821ndash826 1991
[24] Q ZWangW Li and H P Xie ldquoDynamic split tensile test offlattened Brazilian disc of rock with SHPB setuprdquo Mechanicsof Materials vol 41 no 3 pp 252ndash260 2009
[25] D Asprone E Cadoni A Prota and G Manfredi ldquoDynamicbehavior of a mediterranean natural stone under tensileloadingrdquo International Journal of Rock Mechanics and MiningSciences vol 46 no 3 pp 514ndash520 2009
[26] H Kolsky ldquoAn investigation of the mechanical properties ofmaterials at very high rates of loadingrdquo Proceedings of thePhysical Society Section B vol 62 no 11 pp 676ndash700 1949
[27] U S Lindholm ldquoSome experiments with the split Hopkinsonpressure barrdquo Journal of the Mechanics and Physics of Solidsvol 12 no 5 pp 317ndash335 1964
[28] G Subhash and G Ravichandran Split-Hopkinson PressureBar Testing of Ceramics pp 497ndash504 ASM InternationalMaterials Park OH USA 2000
[29] X Li T Zhou D Li and Z Wang ldquoExperimental and nu-merical investigations on feasibility and validity of prismaticrock specimen in SHPBrdquo Shock and Vibration vol 2016Article ID 7198980 13 pages 2016
[30] M R Ayatollahi and M Sistaninia ldquoMode __ fracture study ofrocks using Brazilian disk specimensrdquo International Journal ofRock Mechanics and Mining Sciences vol 48 no 5pp 819ndash826 2011
Shock and Vibration 13
[31] Q Z Wang X P Gou and H Fan ldquo+e minimum di-mensionless stress intensity factor and its upper bound forCCNBD fracture toughness specimen analyzed with straightthrough crack assumptionrdquo Engineering Fracture Mechanicsvol 82 pp 1ndash8 2012
[32] Q B Zhang and J Zhao ldquoQuasi-static and dynamic fracturebehaviour of rock materials phenomena and mechanismsrdquoInternational Journal of Fracture vol 189 no 1 pp 1ndash322014
[33] A Bertram and J F Kalthoff ldquoCrack propagation toughnessof rock for the range of low to very high crack speedsrdquo KeyEngineering Materials vol 251-252 pp 423ndash430 2003
[34] R Chen K Xia F Dai F Lu and S N Luo ldquoDeterminationof dynamic fracture parameters using a semi-circular bendtechnique in split Hopkinson pressure bar testingrdquo Engi-neering Fracture Mechanics vol 76 no 9 pp 1268ndash12762009
[35] P Forquin ldquoAn optical correlation technique for character-izing the crack velocity in concreterdquo e European PhysicalJournal Special Topics vol 206 no 1 pp 89ndash95 2012
[36] Y Zhao S Gong C Zhang Z Zhang and Y Jiang ldquoFractalcharacteristics of crack propagation in coal under impactloadingrdquo Fractals vol 26 no 2 article 1840014 2018
[37] J T Gomez A Shukla and A Sharma ldquoStatic and dynamicbehavior of concrete and granite in tension with damagerdquoeoretical and Applied Fracture Mechanics vol 36 no 1pp 37ndash49 2001
[38] Q B Zhang and J Zhao ldquoDetermination of mechanicalproperties and full-field strain measurements of rock materialunder dynamic loadsrdquo International Journal of Rock Me-chanics and Mining Sciences vol 60 pp 423ndash439 2013
[39] W Yao Y Xu H-W Liu and K Xia ldquoQuantification ofthermally induced damage and its effect on dynamic fracturetoughness of two mortarsrdquo Engineering Fracture Mechanicsvol 169 pp 74ndash88 2017
[40] T S Yun Y J Jeong K Y Kim and K-B Min ldquoEvaluation ofrock anisotropy using 3D X-ray computed tomographyrdquoEngineering Geology vol 163 pp 11ndash19 2013
[41] T Yin X Li K Xia and S Huang ldquoEffect of thermaltreatment on the dynamic fracture toughness of Laurentiangraniterdquo Rock Mechanics and Rock Engineering vol 45 no 6pp 1087ndash1094 2012
[42] S Huang K Xia F Yan and X Feng ldquoAn experimental studyof the rate dependence of tensile strength softening ofLongyou sandstonerdquo Rock Mechanics and Rock Engineeringvol 43 no 6 pp 677ndash683 2010
[43] S N Luo B J Jensen D E Hooks et al ldquoGas gun shockexperiments with single-pulse X-ray phase contrast imagingand diffraction at the advanced photon sourcerdquo Review ofScientific Instruments vol 83 no 7 article 073903 2012
[44] M Hudspeth B Claus S Dubelman et al ldquoHigh speedsynchrotron X-ray phase contrast imaging of dynamic ma-terial response to split Hopkinson bar loadingrdquo Review ofScientific Instruments vol 84 no 2 article 025102 2013
[45] Y Li and K T Ramesh ldquoAn optical technique for mea-surement of material properties in the tension Kolsky barrdquoInternational Journal of Impact Engineering vol 34 no 4pp 784ndash798 2007
[46] G Gao S Huang K Xia and Z Li ldquoApplication of digitalimage correlation (DIC) in dynamic notched semi-circularbend (NSCB) testsrdquo Experimental Mechanics vol 55 no 1pp 95ndash104 2015
[47] B Pan K Qian H Xie and A Asundi ldquoTwo-dimensionaldigital image correlation for in-plane displacement and strain
measurement a reviewrdquo Measurement Science and Technol-ogy vol 20 no 6 article 062001 2009
[48] F Amiot M Bornert P Doumalin et al ldquoAssessment ofdigital image correlation measurement accuracy in the ulti-mate error regime main results of a collaborative bench-markrdquo Strain vol 49 no 6 pp 483ndash496 2013
[49] W Shi Y Wu and L Wu ldquoQuantitative analysis of theprojectile impact on rock using infrared thermographyrdquoInternational Journal of Impact Engineering vol 34 no 5pp 990ndash1002 2007
[50] D K Iakovidis T Goudas C V Smailis and I MaglogiannisldquoRatsnake a versatile image annotation tool with applicationto computer-aided diagnosisrdquo e Scientific World Journalvol 2014 Article ID 286856 12 pages 2014
[51] B A Han H Y Xiang Z Li and J J Huang ldquoDefects de-tection of sheet metal parts based on HALCON and regionmorphologyrdquo Applied Mechanics and Materials vol 365-366pp 729ndash732 2013
[52] D Ai Y Zhao Q Wang and C Li ldquoExperimental andnumerical investigation of crack propagation and dynamicproperties of rock in SHPB indirect tension testrdquo In-ternational Journal of Impact Engineering vol 126 pp 135ndash146 2019
[53] H Xie and D J Sanderson ldquoFractal effects of crack propa-gation on dynamic stress intensity factors and crack veloci-tiesrdquo International Journal of Fracture vol 74 no 1pp 29ndash42 1996
[54] F Dai R Chen and K Xia ldquoA semi-circular bend techniquefor determining dynamic fracture toughnessrdquo ExperimentalMechanics vol 50 no 6 pp 783ndash791 2010
[55] D Chakerian and B B Mandelbrot ldquo+e fractal geometry ofnaturerdquo College Mathematics Journal vol 15 no 2pp 175ndash177 1984
[56] K Falconer ldquoFractal geometry mathematical foundationsand applicationsrdquo Biometrics vol 46 no 3 pp 886-887 1990
[57] T-B Yin K Peng L Wang P Wang X-Y Yin andY-L Zhang ldquoStudy on impact damage and energy dissipationof coal rock exposed to high temperaturesrdquo Shock and Vi-bration vol 2016 Article ID 5121932 10 pages 2016
14 Shock and Vibration
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cracks in each frame of the rock fracture process has beenincreasing Figure 9(b) gives a quantitative description of thecrack propagation process of rock specimens under dierentimpact velocities It can be observed from it that the fractaldimension of cracks increases gradually during the fractureprocess of rocks and the value of the fractal dimension ofcracks on rock surface ranges from 08 to 12
Figure 10 shows the relationship between crack prop-agation velocity and fractal dimension velocity It has beenfound that both crack propagation velocities V and VAPincrease with increasingVD for rocks under dierent impactvelocities
413 Crack Morphological Features In addition toadopting the crack area AP and fractal dimension D toquantitatively describe the crack characteristics twomorphological features that can further analyze the crackevolution path and failure process are also proposed basedon image processing technique Figure 11 demonstrates acrack morphological process for crack initiation propa-gation and coalescence In order to present a quantitativedescription of the distribution and shape factor of cracksAnisometry and Compactness which derived from imagemorphology are proposed In specic Anisometry isderived from the geometric moments for each crack anddened as
Anisometry Ra
Rb (9)
where Ra denotes the main radius of maximum ellipse of thecrack and Rb represents the secondary radius of the ellipseSimilarly Compactness is also a shape factor which valueranges from 0 to 1 and can be expressed as
Compactness max 1 Cprime( )
Cprime L2
4 middot F middot π
(10)
where L is the total length of the contour and F is the area ofthe region
As shown in Figure 12(a) VComp is decreasing withthe increase of VD as a whole It can also be seen fromFigure 12(b) that the values of VAnis decrease almostlinearly with the increase of impact velocity which in-dicates that longitudinal crack length produced bythe rock is less than transversersquos under higher impactvelocity
414 Distribution of Cracks It has been generally rec-ognized that for a valid and typical dynamic Brazilian
5mm
0μs
(a)
75μs
a = 175mm
(b)
Figure 5 An illustration of crack propagation velocity computation using crack length
6000
A P (p
ixel
s) 4000
2000
0
0 100Time (micros)
200
Crack initiation
Crack coalescence
Crack propagi
nation
300
APFitting curve of AP
Figure 6 An illustration of crack propagation velocity compu-tation using crack area
Fitting curve of V and VAP
3 times 107
2 times 107
1 times 107
0
V AP (p
ixel
ss)
100V (ms)
200 300 400 500 600 700
Figure 7 Relationship between V and VAPof rock specimens
under SHPB loading
6 Shock and Vibration
test crack should be first appeared along the impactdirection somewhere near the center of the specimen andthen propagates bilaterally to the loading endsAccording to the row and column index of the crackcenter Figure 13 shows the coordinate distribution ofcrack center in the process of rock failure It can beobserved from Figure 13 that most of the rock disc cracksnear the center of the specimen and the fracture prop-agation direction are bilateral to the loading ends and
some cracks also appeared at the contact side of rock andbars +e result indicates that the failure patterns ofdynamic Brazil test under SHPB loading approximatelyinclude tensile failure and shear failure Accordingly thecracks near the center of rocks are mainly caused by thetensile failure which is the main axial crack parallel to theloading direction and other cracks are caused by theshear failure that is a result of secondary fractures due tothe further compression
ndash1
Fitting curve
D = 114 R2 = 099
ndash2
InS ndash3
ndash4
ndash5
2 3InN
4 5
(a)
12
10
D08
06
04
02
00200 300 400 500
BXY1 (4687ms)BXY2 (5150ms)BXY3 (4443ms)BXY4 (4385ms)BXY5 (3377ms)BXY6 (3167ms)
BXY7 (3511ms)BXY8 (3246ms)BXY9 (3689ms)BXY10 (4307ms)BXY11 (5502ms)
600 7001000Time (micros)
(b)
Figure 9 (a) Number of covered boxes versus box size (b) fractal characteristics of crack for rock material under different velocities
200
Scale = 64
100
00 100 200 300 400 500
(a)
Scale = 32
200
100
00 100 200 300 400 500
(b)
Scale = 16
200
100
00 100 200 300 400 500
(c)
Scale = 8
200
100
00 100 200 300 400 500
(d)
Figure 8 An illustration of different box scales to fully cover cracks
Shock and Vibration 7
42 Dynamic Mechanical Properties Figure 14 illustratesthe incident εi(t) reected εr(t) and transmitted εt(t)strain signals of rock specimens under dierent impactvelocities during SHPB dynamic loading test According
to the three-wave analysis method the mechanicalproperties of rocks under SHPB loading are determinedIn this study the absorbed energy and stress-strain pa-rameters are calculated and further compared with crack
100V
(ms
)
200
300
400
500
600
700
000 001VD (Dframe)
002 003 004 005 006 007
Fitting curve of VD and VAP
VAP
Fitting curve of VD and VV
4 times 107
3 times 107
2 times 107
1 times 107
0
V AP (p
ixel
ss)
Figure 10 Relationship between V VAP and VD in the SHPB experiment
Crack initiation
(a) (b)
Crack propagination
(c) (d)
Crack coalescence
(e)
F
LRb
Ra
(f )
Figure 11 An illustration of crack morphological features (a) (c) and (e) are original images represent crack initiation propagation andcoalescence respectively (b) (d) and (f) are extracted cracks from corresponded images
8 Shock and Vibration
propagation features to explore the relationship betweenthem
421 Dynamic Fracture Energy It has been generally rec-ognized that the fracture of rock under loading rates is theprocess of accumulation and dissipation of energy [57] Inspecific the consumed energy under SHPB dynamic loadingcan be well quantified based on the first law of thermody-namics [34] During the SHPB dynamic loading test theenergy of the incident wave WI the energy of the reflectedwave WR and the energy of the transmitted wave WT can becomputed as
WI A middot C
E1113946 εi(t)
2dt
WR A middot C
E1113946 εr(t)
2dt
WT A middot C
E1113946 εt(t)
2dt
(11)
where A is the cross-sectional area C is the longitudinalwave speed and E is Youngrsquos modulus of the bars
Assuming that all the energy loss at the specimen and barinterfaces can be negligible the energy absorbed by the rockspecimen WS can be expressed as
Fitting curve of VD and VComp
10
12
14
16
18
20
22
24
26
28V C
omp (
com
pfr
ame)
001 002 003 004 005 006 007000VD (Dframe)
(a)
Fitting curve of v and VAnis
35 40 45 50 5530v (ms)
8
10
12
14
16
18
20
22
24
V Ani
s (an
isfr
ame)
(b)
Figure 12 (a) Relationship between VComp and VD (b) relationship between VAnis and V
Impact velocity
Incident bar Transmission bar
Rock specimen250
200
Imag
e hei
ght (
pixe
ls)
150
100
50
0
BXY1BXY2BXY3
BXY4BXY5BXY6
BXY7BXY8BXY9
BXY10BXY11
200 300 400 5001000Image width (pixels)
Figure 13 Crack distribution for rocks under different impact velocities
Shock and Vibration 9
WS WI minusWR minusWT (12)
Figure 15 shows the total energy absorbed versus theimpact velocity for the rock specimens It indicates that the
energy absorbed by the rock specimen increases with in-creasing impact velocity
Moreover substantial efforts have been devoted to per-forming quantitative measurements on fracture surface and it
εi-4687msεi-5150msεi-4443msεi-4385msεi-3377msεi-3167msεi-3511msεi-3246msεi-3869msεi-4307msεi-5502ms
εt-4687msεt-5150msεt-4443msεt-4385msεt-3377msεt-3167msεt-3511msεt-3246msεt-3869msεt-4307msεt-5502ms
εr-4687msεr-5150msεr-4443msεr-4385msεr-3377msεr-3167msεr-3511msεr-3246msεr-3869msεr-4307msεr-5502ms
140 160 180 200 220 240 260 280120100
3
2
1
0
ndash1V
olta
ge (V
)ndash2
ndash3
Time (μs)
Figure 14 Incident reflected and transmitted signals of rocks under different impact velocities
18
WS (
J)
16
14
12
10
8
6
4
2
030 35 40 45 50 55
v (ms)
Fitting curve of v and WS
Figure 15 Relationship between v and WS
10 Shock and Vibration
has been well recognized that surface roughness in rock-likematerials exhibits self-similarity properties at least over a givenrange of length scales In other words the fracture surfacetopography of rock-like materials reveals inherent details as-sociated with energy dissipation mechanisms that govern thefracturing process +erefore the relationship between fractaldimension and absorbed energy was first calculated and theresult is shown in Figure 16(a) However it can be found thatthere is no obvious relationship between the two variables
On the other hand Figure 16(b) presents the total energyabsorbed WS versus the crack feature VAnis for the rockspecimens It can be seen that there is a linearly negativecorrelation between the two variables the greater the WSthe smaller the VAnis
422 Strain-Stress Parameters According to the incidentεi(t) reflected εr(t) and transmitted εt(t) strain signalsillustrated in Figure 14 and formulas (1)ndash(3) the max stressmax strain and mean strain rate of rocks under differentimpact velocities were calculated Combining with the crackcharacteristic parameters in the above section the re-lationship between the crack propagation process and dy-namic mechanical properties was analyzed
Figure 17 shows the max strain and mean strain rateversus the crack propagation velocity V while Figure 18shows the max strain and mean strain rate versus the crackpropagation velocity VAP
It can be seen that with theincrease of the V both the max strain and mean strain rateare gradually decreased and mean strain rate basically
000
001
002
003
004
005
006
007V D
(Dfr
ame)
2 4 6 8 10 12 14 16 180WS (J)
(a)
Fitting curve of WS and VAnis
2 4 6 8 10 12 14 16 180WS (J)
8
10
12
14
16
18
20
22
24
V Ani
s (an
isfr
ame)
(b)
Figure 16 (a) Relationship between WS and VD (b) relationship between WS and VAnis
Fitting curve of V and ε
66
68
70
72
74
76
78
εmiddot (sndash1
)
200 300 400 500
600 700100V (ms)
(a)
Fitting curve of V and εmax
200 300 400 500 600 700100V (ms)
25
30
35
40
45
50
55
60
65
70
ε max
(10ndash3
)
(b)
Figure 17 Curves of strain parameters with crack propagation velocity V and associated results after linear fitting (a) _ε as a function of V(b) εmax as a function of V
Shock and Vibration 11
remains the same when V ranges from 350ms to 650msSimilarly the max strain and mean strain rate also linearlydecrease with the increase of crack propagation velocityVAP
5 Conclusion
In this study the Brazil test of rock specimens was per-formed under different impact velocities using the SHPBsystem to explore fracture characterizations of rocks underdynamic loads Based on image processing technique crackpropagation process was quantitatively described from threeperspectives the crack propagation velocity crack fractalcharacteristic and crack morphological features Accordingto the recorded strain wave signals the dynamic mechanicalproperties of rocks were also calculated and the relationshipbetween impact velocity and crack propagation process wasexplored and analyzed +e main conclusions are listed asfollows
(1) Crack propagation velocities V and VAPboth in-
crease with increase of the crack fractals velocity VD
(2) +e proposed two crack features Compactness andAnisometery have a capacity of describing thefracture process of rock In specific VAnis linearlydecreases with the increase of impact velocity v whileVComp exhibits a negative relationship with crackfractals velocity VD
(3) +e energy absorbed by the rocks increases with theincrease of impact velocity v but shows a linearnegative trend with VAnis
(4) +e mean strain rate and max strain both decreasewith increase of crack propagation velocity whichshows that there is a certain relationship between thecrack propagation process and dynamic mechanicalproperties of rocks under dynamic loading
In the future work we will conduct the static tensile testsusing the BD specimen on the same rock material andcompare the static and dynamic results in terms of me-chanical properties and crack propagation process
Nomenclature
_ε Mean strain rate (sminus1)σmax Max stress (MPa)εmax Max strain (10minus3)A Cross-sectional area of the bar (mm2)A Crack length (mm)Ap Crack quantification area (pixels)AS Cross-sectional area of the specimen (mm2)Anis Crack feature descriptormdashanisometryC Longitudinal stress wave speed of the bar (ms)Comp Crack feature descriptormdashcompactnessD Fractal dimensionE Youngrsquos modulus of the bar (GPa)LS Length of rock specimen (mm)P1 P2 Dynamic forces on incident and transmitted ends
(N)rxy Pearsonrsquos correlation coefficientV Crack propagation velocity (ms)v Impact velocity (ms)VD Fractal dimension velocity (Dframe)VAP
Crack propagation velocity (pixelss)VAnis Anisometry velocity (anisframe)VComp Compactness velocity (compframe)WS Absorbed energy (J)
Data Availability
+e data utilized in this study are available from the cor-responding author upon request
00 50 times 106 10 times 107 15 times 107
Fitting curve of VAP and ε
20 times 107 25 times 107 30 times 107 35 times 107
VAP (pixelss)
66
68
70
72
74
76
78ε (
sndash1)
(a)
70
65
60
55
50
44
40
30
25
35
ε max
(10ndash3
)
Fitting curve of VAP and εmax
00 50 times 106 10 times 107 15 times 107 20 times 107 25 times 107 30 times 107 35 times 107
VAP (pixelss)
(b)
Figure 18 Curves of strain parameters with crack propagation velocity VAPand associated results after linear fitting (a) _ε as a function of
VAP (b) εmax as a function of VAP
12 Shock and Vibration
Conflicts of Interest
+e authors declare that they have no conflicts of interest
Acknowledgments
+is research was financially supported by the NationalNatural Science Foundation of China (nos 51274206 and51404277) +is support is greatly acknowledged andappreciated
References
[1] K Xia and W Yao ldquoDynamic rock tests using split Hop-kinson (Kolsky) bar systemmdasha reviewrdquo Journal of RockMechanics and Geotechnical Engineering vol 7 no 1pp 27ndash59 2015
[2] F Gong H Ye and Y Luo ldquo+e effect of high loading rate onthe behaviour and mechanical properties of coal-rock com-bined bodyrdquo Shock and Vibration vol 2018 Article ID4374530 9 pages 2018
[3] Y X Zhou K Xia X B Li et al ldquoSuggested methods fordetermining the dynamic strength parameters and mode-ifracture toughness of rock materialsrdquo International Journal ofRock Mechanics and Mining Sciences vol 49 no 1pp 105ndash112 2012
[4] Y Zhao G-F Zhao Y Jiang D Elsworth and Y HuangldquoEffects of bedding on the dynamic indirect tensile strength ofcoal Laboratory experiments and numerical simulationrdquoInternational Journal of Coal Geology vol 132 pp 81ndash932014
[5] F Dai K Xia and S N Luo ldquoSemicircular bend testing withsplit Hopkinson pressure bar for measuring dynamic tensilestrength of brittle solidsrdquo Review of Scientific Instrumentsvol 79 no 12 article 123903 2008
[6] F Dai K Xia and L Tang ldquoRate dependence of the flexuraltensile strength of Laurentian graniterdquo International Journalof Rock Mechanics and Mining Sciences vol 47 no 3pp 469ndash475 2010
[7] Y Wang ldquoRock dynamic fracture characteristics based onNSCB impact methodrdquo Shock and Vibration vol 2018 Ar-ticle ID 3105384 13 pages 2018
[8] Q B Zhang and J Zhao ldquoEffect of loading rate on fracturetoughness and failure micromechanisms in marblerdquo Engi-neering Fracture Mechanics vol 102 pp 288ndash309 2013
[9] M D Kuruppu Y Obara M R Ayatollahi K P Chong andT Funatsu ldquoISRM-suggested method for determining themode i static fracture toughness using semi-circular bendspecimenrdquo Rock Mechanics and Rock Engineering vol 47no 1 pp 267ndash274 2014
[10] M RM Aliha andM R Ayatollahi ldquoRock fracture toughnessstudy using cracked chevron notched Brazilian disc specimenunder pure modes I and II loadingmdasha statistical approachrdquoeoretical and Applied Fracture Mechanics vol 69 no 2pp 17ndash25 2014
[11] F Dai K Xia H Zheng and Y X Wang ldquoDetermination ofdynamic rock mode-i fracture parameters using crackedchevron notched semi-circular bend specimenrdquo EngineeringFracture Mechanics vol 78 no 15 pp 2633ndash2644 2011
[12] T Tang Z P Bazant S Yang and D Zollinger ldquoVariable-notch one-size test method for fracture energy and processzone lengthrdquo Engineering Fracture Mechanics vol 55 no 3pp 383ndash404 1996
[13] Q Z Wang S Zhang and H P Xie ldquoRock dynamic fracturetoughness tested with holed-cracked flattened Brazilian discsdiametrically impacted by SHPB and its size effectrdquo Experi-mental Mechanics vol 50 no 7 pp 877ndash885 2010
[14] B Lundberg ldquoA split Hopkinson bar study of energy ab-sorption in dynamic rock fragmentationrdquo InternationalJournal of Rock Mechanics and Mining Sciences amp Geo-mechanics Abstracts vol 13 no 6 pp 187ndash197 1976
[15] V Isheyskiy and M Marinin ldquoDetermination of rock massweakening coefficient after blasting in various fracture zonesrdquoEngineering Solid Mechanics vol 5 no 3 pp 199ndash204 2017
[16] G Gary and P Bailly ldquoBehaviour of quasi-brittle material athigh strain rate Experiment and modellingrdquo EuropeanJournal of Mechanics-ASolids vol 17 no 3 pp 403ndash4201998
[17] J Zhao H B Li and Y H ZhaoDynamic Strength Tests of theBukit Timah Granite Nanyang Technological UniversitySingapore 1998
[18] Q B Zhang and J Zhao ldquoA review of dynamic experimentaltechniques andmechanical behaviour of rockmaterialsrdquo RockMechanics and Rock Engineering vol 47 no 4 pp 1411ndash14782014
[19] J Zhao and H B Li ldquoExperimental determination of dynamictensile properties of a graniterdquo International Journal of RockMechanics and Mining Sciences vol 37 no 5 pp 861ndash8662000
[20] J R Klepaczko and A Brara ldquoAn experimental method fordynamic tensile testing of concrete by spallingrdquo InternationalJournal of Impact Engineering vol 25 no 4 pp 387ndash4092001
[21] S Kubota Y Ogata Y Wada G Simangunsong H Shimadaand K Matsui ldquoEstimation of dynamic tensile strength ofsandstonerdquo International Journal of Rock Mechanics andMining Sciences vol 45 no 3 pp 397ndash406 2008
[22] B Erzar and P Forquin ldquoAn experimental method to de-termine the tensile strength of concrete at high rates of strainrdquoExperimental Mechanics vol 50 no 7 pp 941ndash955 2010
[23] L Biolzi and J Labuz ldquoInstabilities in fracture of elastic-softening structuresrdquo Fracture of Engineering Materials andStructures vol 6 no 8 pp 821ndash826 1991
[24] Q ZWangW Li and H P Xie ldquoDynamic split tensile test offlattened Brazilian disc of rock with SHPB setuprdquo Mechanicsof Materials vol 41 no 3 pp 252ndash260 2009
[25] D Asprone E Cadoni A Prota and G Manfredi ldquoDynamicbehavior of a mediterranean natural stone under tensileloadingrdquo International Journal of Rock Mechanics and MiningSciences vol 46 no 3 pp 514ndash520 2009
[26] H Kolsky ldquoAn investigation of the mechanical properties ofmaterials at very high rates of loadingrdquo Proceedings of thePhysical Society Section B vol 62 no 11 pp 676ndash700 1949
[27] U S Lindholm ldquoSome experiments with the split Hopkinsonpressure barrdquo Journal of the Mechanics and Physics of Solidsvol 12 no 5 pp 317ndash335 1964
[28] G Subhash and G Ravichandran Split-Hopkinson PressureBar Testing of Ceramics pp 497ndash504 ASM InternationalMaterials Park OH USA 2000
[29] X Li T Zhou D Li and Z Wang ldquoExperimental and nu-merical investigations on feasibility and validity of prismaticrock specimen in SHPBrdquo Shock and Vibration vol 2016Article ID 7198980 13 pages 2016
[30] M R Ayatollahi and M Sistaninia ldquoMode __ fracture study ofrocks using Brazilian disk specimensrdquo International Journal ofRock Mechanics and Mining Sciences vol 48 no 5pp 819ndash826 2011
Shock and Vibration 13
[31] Q Z Wang X P Gou and H Fan ldquo+e minimum di-mensionless stress intensity factor and its upper bound forCCNBD fracture toughness specimen analyzed with straightthrough crack assumptionrdquo Engineering Fracture Mechanicsvol 82 pp 1ndash8 2012
[32] Q B Zhang and J Zhao ldquoQuasi-static and dynamic fracturebehaviour of rock materials phenomena and mechanismsrdquoInternational Journal of Fracture vol 189 no 1 pp 1ndash322014
[33] A Bertram and J F Kalthoff ldquoCrack propagation toughnessof rock for the range of low to very high crack speedsrdquo KeyEngineering Materials vol 251-252 pp 423ndash430 2003
[34] R Chen K Xia F Dai F Lu and S N Luo ldquoDeterminationof dynamic fracture parameters using a semi-circular bendtechnique in split Hopkinson pressure bar testingrdquo Engi-neering Fracture Mechanics vol 76 no 9 pp 1268ndash12762009
[35] P Forquin ldquoAn optical correlation technique for character-izing the crack velocity in concreterdquo e European PhysicalJournal Special Topics vol 206 no 1 pp 89ndash95 2012
[36] Y Zhao S Gong C Zhang Z Zhang and Y Jiang ldquoFractalcharacteristics of crack propagation in coal under impactloadingrdquo Fractals vol 26 no 2 article 1840014 2018
[37] J T Gomez A Shukla and A Sharma ldquoStatic and dynamicbehavior of concrete and granite in tension with damagerdquoeoretical and Applied Fracture Mechanics vol 36 no 1pp 37ndash49 2001
[38] Q B Zhang and J Zhao ldquoDetermination of mechanicalproperties and full-field strain measurements of rock materialunder dynamic loadsrdquo International Journal of Rock Me-chanics and Mining Sciences vol 60 pp 423ndash439 2013
[39] W Yao Y Xu H-W Liu and K Xia ldquoQuantification ofthermally induced damage and its effect on dynamic fracturetoughness of two mortarsrdquo Engineering Fracture Mechanicsvol 169 pp 74ndash88 2017
[40] T S Yun Y J Jeong K Y Kim and K-B Min ldquoEvaluation ofrock anisotropy using 3D X-ray computed tomographyrdquoEngineering Geology vol 163 pp 11ndash19 2013
[41] T Yin X Li K Xia and S Huang ldquoEffect of thermaltreatment on the dynamic fracture toughness of Laurentiangraniterdquo Rock Mechanics and Rock Engineering vol 45 no 6pp 1087ndash1094 2012
[42] S Huang K Xia F Yan and X Feng ldquoAn experimental studyof the rate dependence of tensile strength softening ofLongyou sandstonerdquo Rock Mechanics and Rock Engineeringvol 43 no 6 pp 677ndash683 2010
[43] S N Luo B J Jensen D E Hooks et al ldquoGas gun shockexperiments with single-pulse X-ray phase contrast imagingand diffraction at the advanced photon sourcerdquo Review ofScientific Instruments vol 83 no 7 article 073903 2012
[44] M Hudspeth B Claus S Dubelman et al ldquoHigh speedsynchrotron X-ray phase contrast imaging of dynamic ma-terial response to split Hopkinson bar loadingrdquo Review ofScientific Instruments vol 84 no 2 article 025102 2013
[45] Y Li and K T Ramesh ldquoAn optical technique for mea-surement of material properties in the tension Kolsky barrdquoInternational Journal of Impact Engineering vol 34 no 4pp 784ndash798 2007
[46] G Gao S Huang K Xia and Z Li ldquoApplication of digitalimage correlation (DIC) in dynamic notched semi-circularbend (NSCB) testsrdquo Experimental Mechanics vol 55 no 1pp 95ndash104 2015
[47] B Pan K Qian H Xie and A Asundi ldquoTwo-dimensionaldigital image correlation for in-plane displacement and strain
measurement a reviewrdquo Measurement Science and Technol-ogy vol 20 no 6 article 062001 2009
[48] F Amiot M Bornert P Doumalin et al ldquoAssessment ofdigital image correlation measurement accuracy in the ulti-mate error regime main results of a collaborative bench-markrdquo Strain vol 49 no 6 pp 483ndash496 2013
[49] W Shi Y Wu and L Wu ldquoQuantitative analysis of theprojectile impact on rock using infrared thermographyrdquoInternational Journal of Impact Engineering vol 34 no 5pp 990ndash1002 2007
[50] D K Iakovidis T Goudas C V Smailis and I MaglogiannisldquoRatsnake a versatile image annotation tool with applicationto computer-aided diagnosisrdquo e Scientific World Journalvol 2014 Article ID 286856 12 pages 2014
[51] B A Han H Y Xiang Z Li and J J Huang ldquoDefects de-tection of sheet metal parts based on HALCON and regionmorphologyrdquo Applied Mechanics and Materials vol 365-366pp 729ndash732 2013
[52] D Ai Y Zhao Q Wang and C Li ldquoExperimental andnumerical investigation of crack propagation and dynamicproperties of rock in SHPB indirect tension testrdquo In-ternational Journal of Impact Engineering vol 126 pp 135ndash146 2019
[53] H Xie and D J Sanderson ldquoFractal effects of crack propa-gation on dynamic stress intensity factors and crack veloci-tiesrdquo International Journal of Fracture vol 74 no 1pp 29ndash42 1996
[54] F Dai R Chen and K Xia ldquoA semi-circular bend techniquefor determining dynamic fracture toughnessrdquo ExperimentalMechanics vol 50 no 6 pp 783ndash791 2010
[55] D Chakerian and B B Mandelbrot ldquo+e fractal geometry ofnaturerdquo College Mathematics Journal vol 15 no 2pp 175ndash177 1984
[56] K Falconer ldquoFractal geometry mathematical foundationsand applicationsrdquo Biometrics vol 46 no 3 pp 886-887 1990
[57] T-B Yin K Peng L Wang P Wang X-Y Yin andY-L Zhang ldquoStudy on impact damage and energy dissipationof coal rock exposed to high temperaturesrdquo Shock and Vi-bration vol 2016 Article ID 5121932 10 pages 2016
14 Shock and Vibration
International Journal of
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test crack should be first appeared along the impactdirection somewhere near the center of the specimen andthen propagates bilaterally to the loading endsAccording to the row and column index of the crackcenter Figure 13 shows the coordinate distribution ofcrack center in the process of rock failure It can beobserved from Figure 13 that most of the rock disc cracksnear the center of the specimen and the fracture prop-agation direction are bilateral to the loading ends and
some cracks also appeared at the contact side of rock andbars +e result indicates that the failure patterns ofdynamic Brazil test under SHPB loading approximatelyinclude tensile failure and shear failure Accordingly thecracks near the center of rocks are mainly caused by thetensile failure which is the main axial crack parallel to theloading direction and other cracks are caused by theshear failure that is a result of secondary fractures due tothe further compression
ndash1
Fitting curve
D = 114 R2 = 099
ndash2
InS ndash3
ndash4
ndash5
2 3InN
4 5
(a)
12
10
D08
06
04
02
00200 300 400 500
BXY1 (4687ms)BXY2 (5150ms)BXY3 (4443ms)BXY4 (4385ms)BXY5 (3377ms)BXY6 (3167ms)
BXY7 (3511ms)BXY8 (3246ms)BXY9 (3689ms)BXY10 (4307ms)BXY11 (5502ms)
600 7001000Time (micros)
(b)
Figure 9 (a) Number of covered boxes versus box size (b) fractal characteristics of crack for rock material under different velocities
200
Scale = 64
100
00 100 200 300 400 500
(a)
Scale = 32
200
100
00 100 200 300 400 500
(b)
Scale = 16
200
100
00 100 200 300 400 500
(c)
Scale = 8
200
100
00 100 200 300 400 500
(d)
Figure 8 An illustration of different box scales to fully cover cracks
Shock and Vibration 7
42 Dynamic Mechanical Properties Figure 14 illustratesthe incident εi(t) reected εr(t) and transmitted εt(t)strain signals of rock specimens under dierent impactvelocities during SHPB dynamic loading test According
to the three-wave analysis method the mechanicalproperties of rocks under SHPB loading are determinedIn this study the absorbed energy and stress-strain pa-rameters are calculated and further compared with crack
100V
(ms
)
200
300
400
500
600
700
000 001VD (Dframe)
002 003 004 005 006 007
Fitting curve of VD and VAP
VAP
Fitting curve of VD and VV
4 times 107
3 times 107
2 times 107
1 times 107
0
V AP (p
ixel
ss)
Figure 10 Relationship between V VAP and VD in the SHPB experiment
Crack initiation
(a) (b)
Crack propagination
(c) (d)
Crack coalescence
(e)
F
LRb
Ra
(f )
Figure 11 An illustration of crack morphological features (a) (c) and (e) are original images represent crack initiation propagation andcoalescence respectively (b) (d) and (f) are extracted cracks from corresponded images
8 Shock and Vibration
propagation features to explore the relationship betweenthem
421 Dynamic Fracture Energy It has been generally rec-ognized that the fracture of rock under loading rates is theprocess of accumulation and dissipation of energy [57] Inspecific the consumed energy under SHPB dynamic loadingcan be well quantified based on the first law of thermody-namics [34] During the SHPB dynamic loading test theenergy of the incident wave WI the energy of the reflectedwave WR and the energy of the transmitted wave WT can becomputed as
WI A middot C
E1113946 εi(t)
2dt
WR A middot C
E1113946 εr(t)
2dt
WT A middot C
E1113946 εt(t)
2dt
(11)
where A is the cross-sectional area C is the longitudinalwave speed and E is Youngrsquos modulus of the bars
Assuming that all the energy loss at the specimen and barinterfaces can be negligible the energy absorbed by the rockspecimen WS can be expressed as
Fitting curve of VD and VComp
10
12
14
16
18
20
22
24
26
28V C
omp (
com
pfr
ame)
001 002 003 004 005 006 007000VD (Dframe)
(a)
Fitting curve of v and VAnis
35 40 45 50 5530v (ms)
8
10
12
14
16
18
20
22
24
V Ani
s (an
isfr
ame)
(b)
Figure 12 (a) Relationship between VComp and VD (b) relationship between VAnis and V
Impact velocity
Incident bar Transmission bar
Rock specimen250
200
Imag
e hei
ght (
pixe
ls)
150
100
50
0
BXY1BXY2BXY3
BXY4BXY5BXY6
BXY7BXY8BXY9
BXY10BXY11
200 300 400 5001000Image width (pixels)
Figure 13 Crack distribution for rocks under different impact velocities
Shock and Vibration 9
WS WI minusWR minusWT (12)
Figure 15 shows the total energy absorbed versus theimpact velocity for the rock specimens It indicates that the
energy absorbed by the rock specimen increases with in-creasing impact velocity
Moreover substantial efforts have been devoted to per-forming quantitative measurements on fracture surface and it
εi-4687msεi-5150msεi-4443msεi-4385msεi-3377msεi-3167msεi-3511msεi-3246msεi-3869msεi-4307msεi-5502ms
εt-4687msεt-5150msεt-4443msεt-4385msεt-3377msεt-3167msεt-3511msεt-3246msεt-3869msεt-4307msεt-5502ms
εr-4687msεr-5150msεr-4443msεr-4385msεr-3377msεr-3167msεr-3511msεr-3246msεr-3869msεr-4307msεr-5502ms
140 160 180 200 220 240 260 280120100
3
2
1
0
ndash1V
olta
ge (V
)ndash2
ndash3
Time (μs)
Figure 14 Incident reflected and transmitted signals of rocks under different impact velocities
18
WS (
J)
16
14
12
10
8
6
4
2
030 35 40 45 50 55
v (ms)
Fitting curve of v and WS
Figure 15 Relationship between v and WS
10 Shock and Vibration
has been well recognized that surface roughness in rock-likematerials exhibits self-similarity properties at least over a givenrange of length scales In other words the fracture surfacetopography of rock-like materials reveals inherent details as-sociated with energy dissipation mechanisms that govern thefracturing process +erefore the relationship between fractaldimension and absorbed energy was first calculated and theresult is shown in Figure 16(a) However it can be found thatthere is no obvious relationship between the two variables
On the other hand Figure 16(b) presents the total energyabsorbed WS versus the crack feature VAnis for the rockspecimens It can be seen that there is a linearly negativecorrelation between the two variables the greater the WSthe smaller the VAnis
422 Strain-Stress Parameters According to the incidentεi(t) reflected εr(t) and transmitted εt(t) strain signalsillustrated in Figure 14 and formulas (1)ndash(3) the max stressmax strain and mean strain rate of rocks under differentimpact velocities were calculated Combining with the crackcharacteristic parameters in the above section the re-lationship between the crack propagation process and dy-namic mechanical properties was analyzed
Figure 17 shows the max strain and mean strain rateversus the crack propagation velocity V while Figure 18shows the max strain and mean strain rate versus the crackpropagation velocity VAP
It can be seen that with theincrease of the V both the max strain and mean strain rateare gradually decreased and mean strain rate basically
000
001
002
003
004
005
006
007V D
(Dfr
ame)
2 4 6 8 10 12 14 16 180WS (J)
(a)
Fitting curve of WS and VAnis
2 4 6 8 10 12 14 16 180WS (J)
8
10
12
14
16
18
20
22
24
V Ani
s (an
isfr
ame)
(b)
Figure 16 (a) Relationship between WS and VD (b) relationship between WS and VAnis
Fitting curve of V and ε
66
68
70
72
74
76
78
εmiddot (sndash1
)
200 300 400 500
600 700100V (ms)
(a)
Fitting curve of V and εmax
200 300 400 500 600 700100V (ms)
25
30
35
40
45
50
55
60
65
70
ε max
(10ndash3
)
(b)
Figure 17 Curves of strain parameters with crack propagation velocity V and associated results after linear fitting (a) _ε as a function of V(b) εmax as a function of V
Shock and Vibration 11
remains the same when V ranges from 350ms to 650msSimilarly the max strain and mean strain rate also linearlydecrease with the increase of crack propagation velocityVAP
5 Conclusion
In this study the Brazil test of rock specimens was per-formed under different impact velocities using the SHPBsystem to explore fracture characterizations of rocks underdynamic loads Based on image processing technique crackpropagation process was quantitatively described from threeperspectives the crack propagation velocity crack fractalcharacteristic and crack morphological features Accordingto the recorded strain wave signals the dynamic mechanicalproperties of rocks were also calculated and the relationshipbetween impact velocity and crack propagation process wasexplored and analyzed +e main conclusions are listed asfollows
(1) Crack propagation velocities V and VAPboth in-
crease with increase of the crack fractals velocity VD
(2) +e proposed two crack features Compactness andAnisometery have a capacity of describing thefracture process of rock In specific VAnis linearlydecreases with the increase of impact velocity v whileVComp exhibits a negative relationship with crackfractals velocity VD
(3) +e energy absorbed by the rocks increases with theincrease of impact velocity v but shows a linearnegative trend with VAnis
(4) +e mean strain rate and max strain both decreasewith increase of crack propagation velocity whichshows that there is a certain relationship between thecrack propagation process and dynamic mechanicalproperties of rocks under dynamic loading
In the future work we will conduct the static tensile testsusing the BD specimen on the same rock material andcompare the static and dynamic results in terms of me-chanical properties and crack propagation process
Nomenclature
_ε Mean strain rate (sminus1)σmax Max stress (MPa)εmax Max strain (10minus3)A Cross-sectional area of the bar (mm2)A Crack length (mm)Ap Crack quantification area (pixels)AS Cross-sectional area of the specimen (mm2)Anis Crack feature descriptormdashanisometryC Longitudinal stress wave speed of the bar (ms)Comp Crack feature descriptormdashcompactnessD Fractal dimensionE Youngrsquos modulus of the bar (GPa)LS Length of rock specimen (mm)P1 P2 Dynamic forces on incident and transmitted ends
(N)rxy Pearsonrsquos correlation coefficientV Crack propagation velocity (ms)v Impact velocity (ms)VD Fractal dimension velocity (Dframe)VAP
Crack propagation velocity (pixelss)VAnis Anisometry velocity (anisframe)VComp Compactness velocity (compframe)WS Absorbed energy (J)
Data Availability
+e data utilized in this study are available from the cor-responding author upon request
00 50 times 106 10 times 107 15 times 107
Fitting curve of VAP and ε
20 times 107 25 times 107 30 times 107 35 times 107
VAP (pixelss)
66
68
70
72
74
76
78ε (
sndash1)
(a)
70
65
60
55
50
44
40
30
25
35
ε max
(10ndash3
)
Fitting curve of VAP and εmax
00 50 times 106 10 times 107 15 times 107 20 times 107 25 times 107 30 times 107 35 times 107
VAP (pixelss)
(b)
Figure 18 Curves of strain parameters with crack propagation velocity VAPand associated results after linear fitting (a) _ε as a function of
VAP (b) εmax as a function of VAP
12 Shock and Vibration
Conflicts of Interest
+e authors declare that they have no conflicts of interest
Acknowledgments
+is research was financially supported by the NationalNatural Science Foundation of China (nos 51274206 and51404277) +is support is greatly acknowledged andappreciated
References
[1] K Xia and W Yao ldquoDynamic rock tests using split Hop-kinson (Kolsky) bar systemmdasha reviewrdquo Journal of RockMechanics and Geotechnical Engineering vol 7 no 1pp 27ndash59 2015
[2] F Gong H Ye and Y Luo ldquo+e effect of high loading rate onthe behaviour and mechanical properties of coal-rock com-bined bodyrdquo Shock and Vibration vol 2018 Article ID4374530 9 pages 2018
[3] Y X Zhou K Xia X B Li et al ldquoSuggested methods fordetermining the dynamic strength parameters and mode-ifracture toughness of rock materialsrdquo International Journal ofRock Mechanics and Mining Sciences vol 49 no 1pp 105ndash112 2012
[4] Y Zhao G-F Zhao Y Jiang D Elsworth and Y HuangldquoEffects of bedding on the dynamic indirect tensile strength ofcoal Laboratory experiments and numerical simulationrdquoInternational Journal of Coal Geology vol 132 pp 81ndash932014
[5] F Dai K Xia and S N Luo ldquoSemicircular bend testing withsplit Hopkinson pressure bar for measuring dynamic tensilestrength of brittle solidsrdquo Review of Scientific Instrumentsvol 79 no 12 article 123903 2008
[6] F Dai K Xia and L Tang ldquoRate dependence of the flexuraltensile strength of Laurentian graniterdquo International Journalof Rock Mechanics and Mining Sciences vol 47 no 3pp 469ndash475 2010
[7] Y Wang ldquoRock dynamic fracture characteristics based onNSCB impact methodrdquo Shock and Vibration vol 2018 Ar-ticle ID 3105384 13 pages 2018
[8] Q B Zhang and J Zhao ldquoEffect of loading rate on fracturetoughness and failure micromechanisms in marblerdquo Engi-neering Fracture Mechanics vol 102 pp 288ndash309 2013
[9] M D Kuruppu Y Obara M R Ayatollahi K P Chong andT Funatsu ldquoISRM-suggested method for determining themode i static fracture toughness using semi-circular bendspecimenrdquo Rock Mechanics and Rock Engineering vol 47no 1 pp 267ndash274 2014
[10] M RM Aliha andM R Ayatollahi ldquoRock fracture toughnessstudy using cracked chevron notched Brazilian disc specimenunder pure modes I and II loadingmdasha statistical approachrdquoeoretical and Applied Fracture Mechanics vol 69 no 2pp 17ndash25 2014
[11] F Dai K Xia H Zheng and Y X Wang ldquoDetermination ofdynamic rock mode-i fracture parameters using crackedchevron notched semi-circular bend specimenrdquo EngineeringFracture Mechanics vol 78 no 15 pp 2633ndash2644 2011
[12] T Tang Z P Bazant S Yang and D Zollinger ldquoVariable-notch one-size test method for fracture energy and processzone lengthrdquo Engineering Fracture Mechanics vol 55 no 3pp 383ndash404 1996
[13] Q Z Wang S Zhang and H P Xie ldquoRock dynamic fracturetoughness tested with holed-cracked flattened Brazilian discsdiametrically impacted by SHPB and its size effectrdquo Experi-mental Mechanics vol 50 no 7 pp 877ndash885 2010
[14] B Lundberg ldquoA split Hopkinson bar study of energy ab-sorption in dynamic rock fragmentationrdquo InternationalJournal of Rock Mechanics and Mining Sciences amp Geo-mechanics Abstracts vol 13 no 6 pp 187ndash197 1976
[15] V Isheyskiy and M Marinin ldquoDetermination of rock massweakening coefficient after blasting in various fracture zonesrdquoEngineering Solid Mechanics vol 5 no 3 pp 199ndash204 2017
[16] G Gary and P Bailly ldquoBehaviour of quasi-brittle material athigh strain rate Experiment and modellingrdquo EuropeanJournal of Mechanics-ASolids vol 17 no 3 pp 403ndash4201998
[17] J Zhao H B Li and Y H ZhaoDynamic Strength Tests of theBukit Timah Granite Nanyang Technological UniversitySingapore 1998
[18] Q B Zhang and J Zhao ldquoA review of dynamic experimentaltechniques andmechanical behaviour of rockmaterialsrdquo RockMechanics and Rock Engineering vol 47 no 4 pp 1411ndash14782014
[19] J Zhao and H B Li ldquoExperimental determination of dynamictensile properties of a graniterdquo International Journal of RockMechanics and Mining Sciences vol 37 no 5 pp 861ndash8662000
[20] J R Klepaczko and A Brara ldquoAn experimental method fordynamic tensile testing of concrete by spallingrdquo InternationalJournal of Impact Engineering vol 25 no 4 pp 387ndash4092001
[21] S Kubota Y Ogata Y Wada G Simangunsong H Shimadaand K Matsui ldquoEstimation of dynamic tensile strength ofsandstonerdquo International Journal of Rock Mechanics andMining Sciences vol 45 no 3 pp 397ndash406 2008
[22] B Erzar and P Forquin ldquoAn experimental method to de-termine the tensile strength of concrete at high rates of strainrdquoExperimental Mechanics vol 50 no 7 pp 941ndash955 2010
[23] L Biolzi and J Labuz ldquoInstabilities in fracture of elastic-softening structuresrdquo Fracture of Engineering Materials andStructures vol 6 no 8 pp 821ndash826 1991
[24] Q ZWangW Li and H P Xie ldquoDynamic split tensile test offlattened Brazilian disc of rock with SHPB setuprdquo Mechanicsof Materials vol 41 no 3 pp 252ndash260 2009
[25] D Asprone E Cadoni A Prota and G Manfredi ldquoDynamicbehavior of a mediterranean natural stone under tensileloadingrdquo International Journal of Rock Mechanics and MiningSciences vol 46 no 3 pp 514ndash520 2009
[26] H Kolsky ldquoAn investigation of the mechanical properties ofmaterials at very high rates of loadingrdquo Proceedings of thePhysical Society Section B vol 62 no 11 pp 676ndash700 1949
[27] U S Lindholm ldquoSome experiments with the split Hopkinsonpressure barrdquo Journal of the Mechanics and Physics of Solidsvol 12 no 5 pp 317ndash335 1964
[28] G Subhash and G Ravichandran Split-Hopkinson PressureBar Testing of Ceramics pp 497ndash504 ASM InternationalMaterials Park OH USA 2000
[29] X Li T Zhou D Li and Z Wang ldquoExperimental and nu-merical investigations on feasibility and validity of prismaticrock specimen in SHPBrdquo Shock and Vibration vol 2016Article ID 7198980 13 pages 2016
[30] M R Ayatollahi and M Sistaninia ldquoMode __ fracture study ofrocks using Brazilian disk specimensrdquo International Journal ofRock Mechanics and Mining Sciences vol 48 no 5pp 819ndash826 2011
Shock and Vibration 13
[31] Q Z Wang X P Gou and H Fan ldquo+e minimum di-mensionless stress intensity factor and its upper bound forCCNBD fracture toughness specimen analyzed with straightthrough crack assumptionrdquo Engineering Fracture Mechanicsvol 82 pp 1ndash8 2012
[32] Q B Zhang and J Zhao ldquoQuasi-static and dynamic fracturebehaviour of rock materials phenomena and mechanismsrdquoInternational Journal of Fracture vol 189 no 1 pp 1ndash322014
[33] A Bertram and J F Kalthoff ldquoCrack propagation toughnessof rock for the range of low to very high crack speedsrdquo KeyEngineering Materials vol 251-252 pp 423ndash430 2003
[34] R Chen K Xia F Dai F Lu and S N Luo ldquoDeterminationof dynamic fracture parameters using a semi-circular bendtechnique in split Hopkinson pressure bar testingrdquo Engi-neering Fracture Mechanics vol 76 no 9 pp 1268ndash12762009
[35] P Forquin ldquoAn optical correlation technique for character-izing the crack velocity in concreterdquo e European PhysicalJournal Special Topics vol 206 no 1 pp 89ndash95 2012
[36] Y Zhao S Gong C Zhang Z Zhang and Y Jiang ldquoFractalcharacteristics of crack propagation in coal under impactloadingrdquo Fractals vol 26 no 2 article 1840014 2018
[37] J T Gomez A Shukla and A Sharma ldquoStatic and dynamicbehavior of concrete and granite in tension with damagerdquoeoretical and Applied Fracture Mechanics vol 36 no 1pp 37ndash49 2001
[38] Q B Zhang and J Zhao ldquoDetermination of mechanicalproperties and full-field strain measurements of rock materialunder dynamic loadsrdquo International Journal of Rock Me-chanics and Mining Sciences vol 60 pp 423ndash439 2013
[39] W Yao Y Xu H-W Liu and K Xia ldquoQuantification ofthermally induced damage and its effect on dynamic fracturetoughness of two mortarsrdquo Engineering Fracture Mechanicsvol 169 pp 74ndash88 2017
[40] T S Yun Y J Jeong K Y Kim and K-B Min ldquoEvaluation ofrock anisotropy using 3D X-ray computed tomographyrdquoEngineering Geology vol 163 pp 11ndash19 2013
[41] T Yin X Li K Xia and S Huang ldquoEffect of thermaltreatment on the dynamic fracture toughness of Laurentiangraniterdquo Rock Mechanics and Rock Engineering vol 45 no 6pp 1087ndash1094 2012
[42] S Huang K Xia F Yan and X Feng ldquoAn experimental studyof the rate dependence of tensile strength softening ofLongyou sandstonerdquo Rock Mechanics and Rock Engineeringvol 43 no 6 pp 677ndash683 2010
[43] S N Luo B J Jensen D E Hooks et al ldquoGas gun shockexperiments with single-pulse X-ray phase contrast imagingand diffraction at the advanced photon sourcerdquo Review ofScientific Instruments vol 83 no 7 article 073903 2012
[44] M Hudspeth B Claus S Dubelman et al ldquoHigh speedsynchrotron X-ray phase contrast imaging of dynamic ma-terial response to split Hopkinson bar loadingrdquo Review ofScientific Instruments vol 84 no 2 article 025102 2013
[45] Y Li and K T Ramesh ldquoAn optical technique for mea-surement of material properties in the tension Kolsky barrdquoInternational Journal of Impact Engineering vol 34 no 4pp 784ndash798 2007
[46] G Gao S Huang K Xia and Z Li ldquoApplication of digitalimage correlation (DIC) in dynamic notched semi-circularbend (NSCB) testsrdquo Experimental Mechanics vol 55 no 1pp 95ndash104 2015
[47] B Pan K Qian H Xie and A Asundi ldquoTwo-dimensionaldigital image correlation for in-plane displacement and strain
measurement a reviewrdquo Measurement Science and Technol-ogy vol 20 no 6 article 062001 2009
[48] F Amiot M Bornert P Doumalin et al ldquoAssessment ofdigital image correlation measurement accuracy in the ulti-mate error regime main results of a collaborative bench-markrdquo Strain vol 49 no 6 pp 483ndash496 2013
[49] W Shi Y Wu and L Wu ldquoQuantitative analysis of theprojectile impact on rock using infrared thermographyrdquoInternational Journal of Impact Engineering vol 34 no 5pp 990ndash1002 2007
[50] D K Iakovidis T Goudas C V Smailis and I MaglogiannisldquoRatsnake a versatile image annotation tool with applicationto computer-aided diagnosisrdquo e Scientific World Journalvol 2014 Article ID 286856 12 pages 2014
[51] B A Han H Y Xiang Z Li and J J Huang ldquoDefects de-tection of sheet metal parts based on HALCON and regionmorphologyrdquo Applied Mechanics and Materials vol 365-366pp 729ndash732 2013
[52] D Ai Y Zhao Q Wang and C Li ldquoExperimental andnumerical investigation of crack propagation and dynamicproperties of rock in SHPB indirect tension testrdquo In-ternational Journal of Impact Engineering vol 126 pp 135ndash146 2019
[53] H Xie and D J Sanderson ldquoFractal effects of crack propa-gation on dynamic stress intensity factors and crack veloci-tiesrdquo International Journal of Fracture vol 74 no 1pp 29ndash42 1996
[54] F Dai R Chen and K Xia ldquoA semi-circular bend techniquefor determining dynamic fracture toughnessrdquo ExperimentalMechanics vol 50 no 6 pp 783ndash791 2010
[55] D Chakerian and B B Mandelbrot ldquo+e fractal geometry ofnaturerdquo College Mathematics Journal vol 15 no 2pp 175ndash177 1984
[56] K Falconer ldquoFractal geometry mathematical foundationsand applicationsrdquo Biometrics vol 46 no 3 pp 886-887 1990
[57] T-B Yin K Peng L Wang P Wang X-Y Yin andY-L Zhang ldquoStudy on impact damage and energy dissipationof coal rock exposed to high temperaturesrdquo Shock and Vi-bration vol 2016 Article ID 5121932 10 pages 2016
14 Shock and Vibration
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Shock and Vibration
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42 Dynamic Mechanical Properties Figure 14 illustratesthe incident εi(t) reected εr(t) and transmitted εt(t)strain signals of rock specimens under dierent impactvelocities during SHPB dynamic loading test According
to the three-wave analysis method the mechanicalproperties of rocks under SHPB loading are determinedIn this study the absorbed energy and stress-strain pa-rameters are calculated and further compared with crack
100V
(ms
)
200
300
400
500
600
700
000 001VD (Dframe)
002 003 004 005 006 007
Fitting curve of VD and VAP
VAP
Fitting curve of VD and VV
4 times 107
3 times 107
2 times 107
1 times 107
0
V AP (p
ixel
ss)
Figure 10 Relationship between V VAP and VD in the SHPB experiment
Crack initiation
(a) (b)
Crack propagination
(c) (d)
Crack coalescence
(e)
F
LRb
Ra
(f )
Figure 11 An illustration of crack morphological features (a) (c) and (e) are original images represent crack initiation propagation andcoalescence respectively (b) (d) and (f) are extracted cracks from corresponded images
8 Shock and Vibration
propagation features to explore the relationship betweenthem
421 Dynamic Fracture Energy It has been generally rec-ognized that the fracture of rock under loading rates is theprocess of accumulation and dissipation of energy [57] Inspecific the consumed energy under SHPB dynamic loadingcan be well quantified based on the first law of thermody-namics [34] During the SHPB dynamic loading test theenergy of the incident wave WI the energy of the reflectedwave WR and the energy of the transmitted wave WT can becomputed as
WI A middot C
E1113946 εi(t)
2dt
WR A middot C
E1113946 εr(t)
2dt
WT A middot C
E1113946 εt(t)
2dt
(11)
where A is the cross-sectional area C is the longitudinalwave speed and E is Youngrsquos modulus of the bars
Assuming that all the energy loss at the specimen and barinterfaces can be negligible the energy absorbed by the rockspecimen WS can be expressed as
Fitting curve of VD and VComp
10
12
14
16
18
20
22
24
26
28V C
omp (
com
pfr
ame)
001 002 003 004 005 006 007000VD (Dframe)
(a)
Fitting curve of v and VAnis
35 40 45 50 5530v (ms)
8
10
12
14
16
18
20
22
24
V Ani
s (an
isfr
ame)
(b)
Figure 12 (a) Relationship between VComp and VD (b) relationship between VAnis and V
Impact velocity
Incident bar Transmission bar
Rock specimen250
200
Imag
e hei
ght (
pixe
ls)
150
100
50
0
BXY1BXY2BXY3
BXY4BXY5BXY6
BXY7BXY8BXY9
BXY10BXY11
200 300 400 5001000Image width (pixels)
Figure 13 Crack distribution for rocks under different impact velocities
Shock and Vibration 9
WS WI minusWR minusWT (12)
Figure 15 shows the total energy absorbed versus theimpact velocity for the rock specimens It indicates that the
energy absorbed by the rock specimen increases with in-creasing impact velocity
Moreover substantial efforts have been devoted to per-forming quantitative measurements on fracture surface and it
εi-4687msεi-5150msεi-4443msεi-4385msεi-3377msεi-3167msεi-3511msεi-3246msεi-3869msεi-4307msεi-5502ms
εt-4687msεt-5150msεt-4443msεt-4385msεt-3377msεt-3167msεt-3511msεt-3246msεt-3869msεt-4307msεt-5502ms
εr-4687msεr-5150msεr-4443msεr-4385msεr-3377msεr-3167msεr-3511msεr-3246msεr-3869msεr-4307msεr-5502ms
140 160 180 200 220 240 260 280120100
3
2
1
0
ndash1V
olta
ge (V
)ndash2
ndash3
Time (μs)
Figure 14 Incident reflected and transmitted signals of rocks under different impact velocities
18
WS (
J)
16
14
12
10
8
6
4
2
030 35 40 45 50 55
v (ms)
Fitting curve of v and WS
Figure 15 Relationship between v and WS
10 Shock and Vibration
has been well recognized that surface roughness in rock-likematerials exhibits self-similarity properties at least over a givenrange of length scales In other words the fracture surfacetopography of rock-like materials reveals inherent details as-sociated with energy dissipation mechanisms that govern thefracturing process +erefore the relationship between fractaldimension and absorbed energy was first calculated and theresult is shown in Figure 16(a) However it can be found thatthere is no obvious relationship between the two variables
On the other hand Figure 16(b) presents the total energyabsorbed WS versus the crack feature VAnis for the rockspecimens It can be seen that there is a linearly negativecorrelation between the two variables the greater the WSthe smaller the VAnis
422 Strain-Stress Parameters According to the incidentεi(t) reflected εr(t) and transmitted εt(t) strain signalsillustrated in Figure 14 and formulas (1)ndash(3) the max stressmax strain and mean strain rate of rocks under differentimpact velocities were calculated Combining with the crackcharacteristic parameters in the above section the re-lationship between the crack propagation process and dy-namic mechanical properties was analyzed
Figure 17 shows the max strain and mean strain rateversus the crack propagation velocity V while Figure 18shows the max strain and mean strain rate versus the crackpropagation velocity VAP
It can be seen that with theincrease of the V both the max strain and mean strain rateare gradually decreased and mean strain rate basically
000
001
002
003
004
005
006
007V D
(Dfr
ame)
2 4 6 8 10 12 14 16 180WS (J)
(a)
Fitting curve of WS and VAnis
2 4 6 8 10 12 14 16 180WS (J)
8
10
12
14
16
18
20
22
24
V Ani
s (an
isfr
ame)
(b)
Figure 16 (a) Relationship between WS and VD (b) relationship between WS and VAnis
Fitting curve of V and ε
66
68
70
72
74
76
78
εmiddot (sndash1
)
200 300 400 500
600 700100V (ms)
(a)
Fitting curve of V and εmax
200 300 400 500 600 700100V (ms)
25
30
35
40
45
50
55
60
65
70
ε max
(10ndash3
)
(b)
Figure 17 Curves of strain parameters with crack propagation velocity V and associated results after linear fitting (a) _ε as a function of V(b) εmax as a function of V
Shock and Vibration 11
remains the same when V ranges from 350ms to 650msSimilarly the max strain and mean strain rate also linearlydecrease with the increase of crack propagation velocityVAP
5 Conclusion
In this study the Brazil test of rock specimens was per-formed under different impact velocities using the SHPBsystem to explore fracture characterizations of rocks underdynamic loads Based on image processing technique crackpropagation process was quantitatively described from threeperspectives the crack propagation velocity crack fractalcharacteristic and crack morphological features Accordingto the recorded strain wave signals the dynamic mechanicalproperties of rocks were also calculated and the relationshipbetween impact velocity and crack propagation process wasexplored and analyzed +e main conclusions are listed asfollows
(1) Crack propagation velocities V and VAPboth in-
crease with increase of the crack fractals velocity VD
(2) +e proposed two crack features Compactness andAnisometery have a capacity of describing thefracture process of rock In specific VAnis linearlydecreases with the increase of impact velocity v whileVComp exhibits a negative relationship with crackfractals velocity VD
(3) +e energy absorbed by the rocks increases with theincrease of impact velocity v but shows a linearnegative trend with VAnis
(4) +e mean strain rate and max strain both decreasewith increase of crack propagation velocity whichshows that there is a certain relationship between thecrack propagation process and dynamic mechanicalproperties of rocks under dynamic loading
In the future work we will conduct the static tensile testsusing the BD specimen on the same rock material andcompare the static and dynamic results in terms of me-chanical properties and crack propagation process
Nomenclature
_ε Mean strain rate (sminus1)σmax Max stress (MPa)εmax Max strain (10minus3)A Cross-sectional area of the bar (mm2)A Crack length (mm)Ap Crack quantification area (pixels)AS Cross-sectional area of the specimen (mm2)Anis Crack feature descriptormdashanisometryC Longitudinal stress wave speed of the bar (ms)Comp Crack feature descriptormdashcompactnessD Fractal dimensionE Youngrsquos modulus of the bar (GPa)LS Length of rock specimen (mm)P1 P2 Dynamic forces on incident and transmitted ends
(N)rxy Pearsonrsquos correlation coefficientV Crack propagation velocity (ms)v Impact velocity (ms)VD Fractal dimension velocity (Dframe)VAP
Crack propagation velocity (pixelss)VAnis Anisometry velocity (anisframe)VComp Compactness velocity (compframe)WS Absorbed energy (J)
Data Availability
+e data utilized in this study are available from the cor-responding author upon request
00 50 times 106 10 times 107 15 times 107
Fitting curve of VAP and ε
20 times 107 25 times 107 30 times 107 35 times 107
VAP (pixelss)
66
68
70
72
74
76
78ε (
sndash1)
(a)
70
65
60
55
50
44
40
30
25
35
ε max
(10ndash3
)
Fitting curve of VAP and εmax
00 50 times 106 10 times 107 15 times 107 20 times 107 25 times 107 30 times 107 35 times 107
VAP (pixelss)
(b)
Figure 18 Curves of strain parameters with crack propagation velocity VAPand associated results after linear fitting (a) _ε as a function of
VAP (b) εmax as a function of VAP
12 Shock and Vibration
Conflicts of Interest
+e authors declare that they have no conflicts of interest
Acknowledgments
+is research was financially supported by the NationalNatural Science Foundation of China (nos 51274206 and51404277) +is support is greatly acknowledged andappreciated
References
[1] K Xia and W Yao ldquoDynamic rock tests using split Hop-kinson (Kolsky) bar systemmdasha reviewrdquo Journal of RockMechanics and Geotechnical Engineering vol 7 no 1pp 27ndash59 2015
[2] F Gong H Ye and Y Luo ldquo+e effect of high loading rate onthe behaviour and mechanical properties of coal-rock com-bined bodyrdquo Shock and Vibration vol 2018 Article ID4374530 9 pages 2018
[3] Y X Zhou K Xia X B Li et al ldquoSuggested methods fordetermining the dynamic strength parameters and mode-ifracture toughness of rock materialsrdquo International Journal ofRock Mechanics and Mining Sciences vol 49 no 1pp 105ndash112 2012
[4] Y Zhao G-F Zhao Y Jiang D Elsworth and Y HuangldquoEffects of bedding on the dynamic indirect tensile strength ofcoal Laboratory experiments and numerical simulationrdquoInternational Journal of Coal Geology vol 132 pp 81ndash932014
[5] F Dai K Xia and S N Luo ldquoSemicircular bend testing withsplit Hopkinson pressure bar for measuring dynamic tensilestrength of brittle solidsrdquo Review of Scientific Instrumentsvol 79 no 12 article 123903 2008
[6] F Dai K Xia and L Tang ldquoRate dependence of the flexuraltensile strength of Laurentian graniterdquo International Journalof Rock Mechanics and Mining Sciences vol 47 no 3pp 469ndash475 2010
[7] Y Wang ldquoRock dynamic fracture characteristics based onNSCB impact methodrdquo Shock and Vibration vol 2018 Ar-ticle ID 3105384 13 pages 2018
[8] Q B Zhang and J Zhao ldquoEffect of loading rate on fracturetoughness and failure micromechanisms in marblerdquo Engi-neering Fracture Mechanics vol 102 pp 288ndash309 2013
[9] M D Kuruppu Y Obara M R Ayatollahi K P Chong andT Funatsu ldquoISRM-suggested method for determining themode i static fracture toughness using semi-circular bendspecimenrdquo Rock Mechanics and Rock Engineering vol 47no 1 pp 267ndash274 2014
[10] M RM Aliha andM R Ayatollahi ldquoRock fracture toughnessstudy using cracked chevron notched Brazilian disc specimenunder pure modes I and II loadingmdasha statistical approachrdquoeoretical and Applied Fracture Mechanics vol 69 no 2pp 17ndash25 2014
[11] F Dai K Xia H Zheng and Y X Wang ldquoDetermination ofdynamic rock mode-i fracture parameters using crackedchevron notched semi-circular bend specimenrdquo EngineeringFracture Mechanics vol 78 no 15 pp 2633ndash2644 2011
[12] T Tang Z P Bazant S Yang and D Zollinger ldquoVariable-notch one-size test method for fracture energy and processzone lengthrdquo Engineering Fracture Mechanics vol 55 no 3pp 383ndash404 1996
[13] Q Z Wang S Zhang and H P Xie ldquoRock dynamic fracturetoughness tested with holed-cracked flattened Brazilian discsdiametrically impacted by SHPB and its size effectrdquo Experi-mental Mechanics vol 50 no 7 pp 877ndash885 2010
[14] B Lundberg ldquoA split Hopkinson bar study of energy ab-sorption in dynamic rock fragmentationrdquo InternationalJournal of Rock Mechanics and Mining Sciences amp Geo-mechanics Abstracts vol 13 no 6 pp 187ndash197 1976
[15] V Isheyskiy and M Marinin ldquoDetermination of rock massweakening coefficient after blasting in various fracture zonesrdquoEngineering Solid Mechanics vol 5 no 3 pp 199ndash204 2017
[16] G Gary and P Bailly ldquoBehaviour of quasi-brittle material athigh strain rate Experiment and modellingrdquo EuropeanJournal of Mechanics-ASolids vol 17 no 3 pp 403ndash4201998
[17] J Zhao H B Li and Y H ZhaoDynamic Strength Tests of theBukit Timah Granite Nanyang Technological UniversitySingapore 1998
[18] Q B Zhang and J Zhao ldquoA review of dynamic experimentaltechniques andmechanical behaviour of rockmaterialsrdquo RockMechanics and Rock Engineering vol 47 no 4 pp 1411ndash14782014
[19] J Zhao and H B Li ldquoExperimental determination of dynamictensile properties of a graniterdquo International Journal of RockMechanics and Mining Sciences vol 37 no 5 pp 861ndash8662000
[20] J R Klepaczko and A Brara ldquoAn experimental method fordynamic tensile testing of concrete by spallingrdquo InternationalJournal of Impact Engineering vol 25 no 4 pp 387ndash4092001
[21] S Kubota Y Ogata Y Wada G Simangunsong H Shimadaand K Matsui ldquoEstimation of dynamic tensile strength ofsandstonerdquo International Journal of Rock Mechanics andMining Sciences vol 45 no 3 pp 397ndash406 2008
[22] B Erzar and P Forquin ldquoAn experimental method to de-termine the tensile strength of concrete at high rates of strainrdquoExperimental Mechanics vol 50 no 7 pp 941ndash955 2010
[23] L Biolzi and J Labuz ldquoInstabilities in fracture of elastic-softening structuresrdquo Fracture of Engineering Materials andStructures vol 6 no 8 pp 821ndash826 1991
[24] Q ZWangW Li and H P Xie ldquoDynamic split tensile test offlattened Brazilian disc of rock with SHPB setuprdquo Mechanicsof Materials vol 41 no 3 pp 252ndash260 2009
[25] D Asprone E Cadoni A Prota and G Manfredi ldquoDynamicbehavior of a mediterranean natural stone under tensileloadingrdquo International Journal of Rock Mechanics and MiningSciences vol 46 no 3 pp 514ndash520 2009
[26] H Kolsky ldquoAn investigation of the mechanical properties ofmaterials at very high rates of loadingrdquo Proceedings of thePhysical Society Section B vol 62 no 11 pp 676ndash700 1949
[27] U S Lindholm ldquoSome experiments with the split Hopkinsonpressure barrdquo Journal of the Mechanics and Physics of Solidsvol 12 no 5 pp 317ndash335 1964
[28] G Subhash and G Ravichandran Split-Hopkinson PressureBar Testing of Ceramics pp 497ndash504 ASM InternationalMaterials Park OH USA 2000
[29] X Li T Zhou D Li and Z Wang ldquoExperimental and nu-merical investigations on feasibility and validity of prismaticrock specimen in SHPBrdquo Shock and Vibration vol 2016Article ID 7198980 13 pages 2016
[30] M R Ayatollahi and M Sistaninia ldquoMode __ fracture study ofrocks using Brazilian disk specimensrdquo International Journal ofRock Mechanics and Mining Sciences vol 48 no 5pp 819ndash826 2011
Shock and Vibration 13
[31] Q Z Wang X P Gou and H Fan ldquo+e minimum di-mensionless stress intensity factor and its upper bound forCCNBD fracture toughness specimen analyzed with straightthrough crack assumptionrdquo Engineering Fracture Mechanicsvol 82 pp 1ndash8 2012
[32] Q B Zhang and J Zhao ldquoQuasi-static and dynamic fracturebehaviour of rock materials phenomena and mechanismsrdquoInternational Journal of Fracture vol 189 no 1 pp 1ndash322014
[33] A Bertram and J F Kalthoff ldquoCrack propagation toughnessof rock for the range of low to very high crack speedsrdquo KeyEngineering Materials vol 251-252 pp 423ndash430 2003
[34] R Chen K Xia F Dai F Lu and S N Luo ldquoDeterminationof dynamic fracture parameters using a semi-circular bendtechnique in split Hopkinson pressure bar testingrdquo Engi-neering Fracture Mechanics vol 76 no 9 pp 1268ndash12762009
[35] P Forquin ldquoAn optical correlation technique for character-izing the crack velocity in concreterdquo e European PhysicalJournal Special Topics vol 206 no 1 pp 89ndash95 2012
[36] Y Zhao S Gong C Zhang Z Zhang and Y Jiang ldquoFractalcharacteristics of crack propagation in coal under impactloadingrdquo Fractals vol 26 no 2 article 1840014 2018
[37] J T Gomez A Shukla and A Sharma ldquoStatic and dynamicbehavior of concrete and granite in tension with damagerdquoeoretical and Applied Fracture Mechanics vol 36 no 1pp 37ndash49 2001
[38] Q B Zhang and J Zhao ldquoDetermination of mechanicalproperties and full-field strain measurements of rock materialunder dynamic loadsrdquo International Journal of Rock Me-chanics and Mining Sciences vol 60 pp 423ndash439 2013
[39] W Yao Y Xu H-W Liu and K Xia ldquoQuantification ofthermally induced damage and its effect on dynamic fracturetoughness of two mortarsrdquo Engineering Fracture Mechanicsvol 169 pp 74ndash88 2017
[40] T S Yun Y J Jeong K Y Kim and K-B Min ldquoEvaluation ofrock anisotropy using 3D X-ray computed tomographyrdquoEngineering Geology vol 163 pp 11ndash19 2013
[41] T Yin X Li K Xia and S Huang ldquoEffect of thermaltreatment on the dynamic fracture toughness of Laurentiangraniterdquo Rock Mechanics and Rock Engineering vol 45 no 6pp 1087ndash1094 2012
[42] S Huang K Xia F Yan and X Feng ldquoAn experimental studyof the rate dependence of tensile strength softening ofLongyou sandstonerdquo Rock Mechanics and Rock Engineeringvol 43 no 6 pp 677ndash683 2010
[43] S N Luo B J Jensen D E Hooks et al ldquoGas gun shockexperiments with single-pulse X-ray phase contrast imagingand diffraction at the advanced photon sourcerdquo Review ofScientific Instruments vol 83 no 7 article 073903 2012
[44] M Hudspeth B Claus S Dubelman et al ldquoHigh speedsynchrotron X-ray phase contrast imaging of dynamic ma-terial response to split Hopkinson bar loadingrdquo Review ofScientific Instruments vol 84 no 2 article 025102 2013
[45] Y Li and K T Ramesh ldquoAn optical technique for mea-surement of material properties in the tension Kolsky barrdquoInternational Journal of Impact Engineering vol 34 no 4pp 784ndash798 2007
[46] G Gao S Huang K Xia and Z Li ldquoApplication of digitalimage correlation (DIC) in dynamic notched semi-circularbend (NSCB) testsrdquo Experimental Mechanics vol 55 no 1pp 95ndash104 2015
[47] B Pan K Qian H Xie and A Asundi ldquoTwo-dimensionaldigital image correlation for in-plane displacement and strain
measurement a reviewrdquo Measurement Science and Technol-ogy vol 20 no 6 article 062001 2009
[48] F Amiot M Bornert P Doumalin et al ldquoAssessment ofdigital image correlation measurement accuracy in the ulti-mate error regime main results of a collaborative bench-markrdquo Strain vol 49 no 6 pp 483ndash496 2013
[49] W Shi Y Wu and L Wu ldquoQuantitative analysis of theprojectile impact on rock using infrared thermographyrdquoInternational Journal of Impact Engineering vol 34 no 5pp 990ndash1002 2007
[50] D K Iakovidis T Goudas C V Smailis and I MaglogiannisldquoRatsnake a versatile image annotation tool with applicationto computer-aided diagnosisrdquo e Scientific World Journalvol 2014 Article ID 286856 12 pages 2014
[51] B A Han H Y Xiang Z Li and J J Huang ldquoDefects de-tection of sheet metal parts based on HALCON and regionmorphologyrdquo Applied Mechanics and Materials vol 365-366pp 729ndash732 2013
[52] D Ai Y Zhao Q Wang and C Li ldquoExperimental andnumerical investigation of crack propagation and dynamicproperties of rock in SHPB indirect tension testrdquo In-ternational Journal of Impact Engineering vol 126 pp 135ndash146 2019
[53] H Xie and D J Sanderson ldquoFractal effects of crack propa-gation on dynamic stress intensity factors and crack veloci-tiesrdquo International Journal of Fracture vol 74 no 1pp 29ndash42 1996
[54] F Dai R Chen and K Xia ldquoA semi-circular bend techniquefor determining dynamic fracture toughnessrdquo ExperimentalMechanics vol 50 no 6 pp 783ndash791 2010
[55] D Chakerian and B B Mandelbrot ldquo+e fractal geometry ofnaturerdquo College Mathematics Journal vol 15 no 2pp 175ndash177 1984
[56] K Falconer ldquoFractal geometry mathematical foundationsand applicationsrdquo Biometrics vol 46 no 3 pp 886-887 1990
[57] T-B Yin K Peng L Wang P Wang X-Y Yin andY-L Zhang ldquoStudy on impact damage and energy dissipationof coal rock exposed to high temperaturesrdquo Shock and Vi-bration vol 2016 Article ID 5121932 10 pages 2016
14 Shock and Vibration
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
RoboticsJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
VLSI Design
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawiwwwhindawicom
Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Control Scienceand Engineering
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
SensorsJournal of
Hindawiwwwhindawicom Volume 2018
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
propagation features to explore the relationship betweenthem
421 Dynamic Fracture Energy It has been generally rec-ognized that the fracture of rock under loading rates is theprocess of accumulation and dissipation of energy [57] Inspecific the consumed energy under SHPB dynamic loadingcan be well quantified based on the first law of thermody-namics [34] During the SHPB dynamic loading test theenergy of the incident wave WI the energy of the reflectedwave WR and the energy of the transmitted wave WT can becomputed as
WI A middot C
E1113946 εi(t)
2dt
WR A middot C
E1113946 εr(t)
2dt
WT A middot C
E1113946 εt(t)
2dt
(11)
where A is the cross-sectional area C is the longitudinalwave speed and E is Youngrsquos modulus of the bars
Assuming that all the energy loss at the specimen and barinterfaces can be negligible the energy absorbed by the rockspecimen WS can be expressed as
Fitting curve of VD and VComp
10
12
14
16
18
20
22
24
26
28V C
omp (
com
pfr
ame)
001 002 003 004 005 006 007000VD (Dframe)
(a)
Fitting curve of v and VAnis
35 40 45 50 5530v (ms)
8
10
12
14
16
18
20
22
24
V Ani
s (an
isfr
ame)
(b)
Figure 12 (a) Relationship between VComp and VD (b) relationship between VAnis and V
Impact velocity
Incident bar Transmission bar
Rock specimen250
200
Imag
e hei
ght (
pixe
ls)
150
100
50
0
BXY1BXY2BXY3
BXY4BXY5BXY6
BXY7BXY8BXY9
BXY10BXY11
200 300 400 5001000Image width (pixels)
Figure 13 Crack distribution for rocks under different impact velocities
Shock and Vibration 9
WS WI minusWR minusWT (12)
Figure 15 shows the total energy absorbed versus theimpact velocity for the rock specimens It indicates that the
energy absorbed by the rock specimen increases with in-creasing impact velocity
Moreover substantial efforts have been devoted to per-forming quantitative measurements on fracture surface and it
εi-4687msεi-5150msεi-4443msεi-4385msεi-3377msεi-3167msεi-3511msεi-3246msεi-3869msεi-4307msεi-5502ms
εt-4687msεt-5150msεt-4443msεt-4385msεt-3377msεt-3167msεt-3511msεt-3246msεt-3869msεt-4307msεt-5502ms
εr-4687msεr-5150msεr-4443msεr-4385msεr-3377msεr-3167msεr-3511msεr-3246msεr-3869msεr-4307msεr-5502ms
140 160 180 200 220 240 260 280120100
3
2
1
0
ndash1V
olta
ge (V
)ndash2
ndash3
Time (μs)
Figure 14 Incident reflected and transmitted signals of rocks under different impact velocities
18
WS (
J)
16
14
12
10
8
6
4
2
030 35 40 45 50 55
v (ms)
Fitting curve of v and WS
Figure 15 Relationship between v and WS
10 Shock and Vibration
has been well recognized that surface roughness in rock-likematerials exhibits self-similarity properties at least over a givenrange of length scales In other words the fracture surfacetopography of rock-like materials reveals inherent details as-sociated with energy dissipation mechanisms that govern thefracturing process +erefore the relationship between fractaldimension and absorbed energy was first calculated and theresult is shown in Figure 16(a) However it can be found thatthere is no obvious relationship between the two variables
On the other hand Figure 16(b) presents the total energyabsorbed WS versus the crack feature VAnis for the rockspecimens It can be seen that there is a linearly negativecorrelation between the two variables the greater the WSthe smaller the VAnis
422 Strain-Stress Parameters According to the incidentεi(t) reflected εr(t) and transmitted εt(t) strain signalsillustrated in Figure 14 and formulas (1)ndash(3) the max stressmax strain and mean strain rate of rocks under differentimpact velocities were calculated Combining with the crackcharacteristic parameters in the above section the re-lationship between the crack propagation process and dy-namic mechanical properties was analyzed
Figure 17 shows the max strain and mean strain rateversus the crack propagation velocity V while Figure 18shows the max strain and mean strain rate versus the crackpropagation velocity VAP
It can be seen that with theincrease of the V both the max strain and mean strain rateare gradually decreased and mean strain rate basically
000
001
002
003
004
005
006
007V D
(Dfr
ame)
2 4 6 8 10 12 14 16 180WS (J)
(a)
Fitting curve of WS and VAnis
2 4 6 8 10 12 14 16 180WS (J)
8
10
12
14
16
18
20
22
24
V Ani
s (an
isfr
ame)
(b)
Figure 16 (a) Relationship between WS and VD (b) relationship between WS and VAnis
Fitting curve of V and ε
66
68
70
72
74
76
78
εmiddot (sndash1
)
200 300 400 500
600 700100V (ms)
(a)
Fitting curve of V and εmax
200 300 400 500 600 700100V (ms)
25
30
35
40
45
50
55
60
65
70
ε max
(10ndash3
)
(b)
Figure 17 Curves of strain parameters with crack propagation velocity V and associated results after linear fitting (a) _ε as a function of V(b) εmax as a function of V
Shock and Vibration 11
remains the same when V ranges from 350ms to 650msSimilarly the max strain and mean strain rate also linearlydecrease with the increase of crack propagation velocityVAP
5 Conclusion
In this study the Brazil test of rock specimens was per-formed under different impact velocities using the SHPBsystem to explore fracture characterizations of rocks underdynamic loads Based on image processing technique crackpropagation process was quantitatively described from threeperspectives the crack propagation velocity crack fractalcharacteristic and crack morphological features Accordingto the recorded strain wave signals the dynamic mechanicalproperties of rocks were also calculated and the relationshipbetween impact velocity and crack propagation process wasexplored and analyzed +e main conclusions are listed asfollows
(1) Crack propagation velocities V and VAPboth in-
crease with increase of the crack fractals velocity VD
(2) +e proposed two crack features Compactness andAnisometery have a capacity of describing thefracture process of rock In specific VAnis linearlydecreases with the increase of impact velocity v whileVComp exhibits a negative relationship with crackfractals velocity VD
(3) +e energy absorbed by the rocks increases with theincrease of impact velocity v but shows a linearnegative trend with VAnis
(4) +e mean strain rate and max strain both decreasewith increase of crack propagation velocity whichshows that there is a certain relationship between thecrack propagation process and dynamic mechanicalproperties of rocks under dynamic loading
In the future work we will conduct the static tensile testsusing the BD specimen on the same rock material andcompare the static and dynamic results in terms of me-chanical properties and crack propagation process
Nomenclature
_ε Mean strain rate (sminus1)σmax Max stress (MPa)εmax Max strain (10minus3)A Cross-sectional area of the bar (mm2)A Crack length (mm)Ap Crack quantification area (pixels)AS Cross-sectional area of the specimen (mm2)Anis Crack feature descriptormdashanisometryC Longitudinal stress wave speed of the bar (ms)Comp Crack feature descriptormdashcompactnessD Fractal dimensionE Youngrsquos modulus of the bar (GPa)LS Length of rock specimen (mm)P1 P2 Dynamic forces on incident and transmitted ends
(N)rxy Pearsonrsquos correlation coefficientV Crack propagation velocity (ms)v Impact velocity (ms)VD Fractal dimension velocity (Dframe)VAP
Crack propagation velocity (pixelss)VAnis Anisometry velocity (anisframe)VComp Compactness velocity (compframe)WS Absorbed energy (J)
Data Availability
+e data utilized in this study are available from the cor-responding author upon request
00 50 times 106 10 times 107 15 times 107
Fitting curve of VAP and ε
20 times 107 25 times 107 30 times 107 35 times 107
VAP (pixelss)
66
68
70
72
74
76
78ε (
sndash1)
(a)
70
65
60
55
50
44
40
30
25
35
ε max
(10ndash3
)
Fitting curve of VAP and εmax
00 50 times 106 10 times 107 15 times 107 20 times 107 25 times 107 30 times 107 35 times 107
VAP (pixelss)
(b)
Figure 18 Curves of strain parameters with crack propagation velocity VAPand associated results after linear fitting (a) _ε as a function of
VAP (b) εmax as a function of VAP
12 Shock and Vibration
Conflicts of Interest
+e authors declare that they have no conflicts of interest
Acknowledgments
+is research was financially supported by the NationalNatural Science Foundation of China (nos 51274206 and51404277) +is support is greatly acknowledged andappreciated
References
[1] K Xia and W Yao ldquoDynamic rock tests using split Hop-kinson (Kolsky) bar systemmdasha reviewrdquo Journal of RockMechanics and Geotechnical Engineering vol 7 no 1pp 27ndash59 2015
[2] F Gong H Ye and Y Luo ldquo+e effect of high loading rate onthe behaviour and mechanical properties of coal-rock com-bined bodyrdquo Shock and Vibration vol 2018 Article ID4374530 9 pages 2018
[3] Y X Zhou K Xia X B Li et al ldquoSuggested methods fordetermining the dynamic strength parameters and mode-ifracture toughness of rock materialsrdquo International Journal ofRock Mechanics and Mining Sciences vol 49 no 1pp 105ndash112 2012
[4] Y Zhao G-F Zhao Y Jiang D Elsworth and Y HuangldquoEffects of bedding on the dynamic indirect tensile strength ofcoal Laboratory experiments and numerical simulationrdquoInternational Journal of Coal Geology vol 132 pp 81ndash932014
[5] F Dai K Xia and S N Luo ldquoSemicircular bend testing withsplit Hopkinson pressure bar for measuring dynamic tensilestrength of brittle solidsrdquo Review of Scientific Instrumentsvol 79 no 12 article 123903 2008
[6] F Dai K Xia and L Tang ldquoRate dependence of the flexuraltensile strength of Laurentian graniterdquo International Journalof Rock Mechanics and Mining Sciences vol 47 no 3pp 469ndash475 2010
[7] Y Wang ldquoRock dynamic fracture characteristics based onNSCB impact methodrdquo Shock and Vibration vol 2018 Ar-ticle ID 3105384 13 pages 2018
[8] Q B Zhang and J Zhao ldquoEffect of loading rate on fracturetoughness and failure micromechanisms in marblerdquo Engi-neering Fracture Mechanics vol 102 pp 288ndash309 2013
[9] M D Kuruppu Y Obara M R Ayatollahi K P Chong andT Funatsu ldquoISRM-suggested method for determining themode i static fracture toughness using semi-circular bendspecimenrdquo Rock Mechanics and Rock Engineering vol 47no 1 pp 267ndash274 2014
[10] M RM Aliha andM R Ayatollahi ldquoRock fracture toughnessstudy using cracked chevron notched Brazilian disc specimenunder pure modes I and II loadingmdasha statistical approachrdquoeoretical and Applied Fracture Mechanics vol 69 no 2pp 17ndash25 2014
[11] F Dai K Xia H Zheng and Y X Wang ldquoDetermination ofdynamic rock mode-i fracture parameters using crackedchevron notched semi-circular bend specimenrdquo EngineeringFracture Mechanics vol 78 no 15 pp 2633ndash2644 2011
[12] T Tang Z P Bazant S Yang and D Zollinger ldquoVariable-notch one-size test method for fracture energy and processzone lengthrdquo Engineering Fracture Mechanics vol 55 no 3pp 383ndash404 1996
[13] Q Z Wang S Zhang and H P Xie ldquoRock dynamic fracturetoughness tested with holed-cracked flattened Brazilian discsdiametrically impacted by SHPB and its size effectrdquo Experi-mental Mechanics vol 50 no 7 pp 877ndash885 2010
[14] B Lundberg ldquoA split Hopkinson bar study of energy ab-sorption in dynamic rock fragmentationrdquo InternationalJournal of Rock Mechanics and Mining Sciences amp Geo-mechanics Abstracts vol 13 no 6 pp 187ndash197 1976
[15] V Isheyskiy and M Marinin ldquoDetermination of rock massweakening coefficient after blasting in various fracture zonesrdquoEngineering Solid Mechanics vol 5 no 3 pp 199ndash204 2017
[16] G Gary and P Bailly ldquoBehaviour of quasi-brittle material athigh strain rate Experiment and modellingrdquo EuropeanJournal of Mechanics-ASolids vol 17 no 3 pp 403ndash4201998
[17] J Zhao H B Li and Y H ZhaoDynamic Strength Tests of theBukit Timah Granite Nanyang Technological UniversitySingapore 1998
[18] Q B Zhang and J Zhao ldquoA review of dynamic experimentaltechniques andmechanical behaviour of rockmaterialsrdquo RockMechanics and Rock Engineering vol 47 no 4 pp 1411ndash14782014
[19] J Zhao and H B Li ldquoExperimental determination of dynamictensile properties of a graniterdquo International Journal of RockMechanics and Mining Sciences vol 37 no 5 pp 861ndash8662000
[20] J R Klepaczko and A Brara ldquoAn experimental method fordynamic tensile testing of concrete by spallingrdquo InternationalJournal of Impact Engineering vol 25 no 4 pp 387ndash4092001
[21] S Kubota Y Ogata Y Wada G Simangunsong H Shimadaand K Matsui ldquoEstimation of dynamic tensile strength ofsandstonerdquo International Journal of Rock Mechanics andMining Sciences vol 45 no 3 pp 397ndash406 2008
[22] B Erzar and P Forquin ldquoAn experimental method to de-termine the tensile strength of concrete at high rates of strainrdquoExperimental Mechanics vol 50 no 7 pp 941ndash955 2010
[23] L Biolzi and J Labuz ldquoInstabilities in fracture of elastic-softening structuresrdquo Fracture of Engineering Materials andStructures vol 6 no 8 pp 821ndash826 1991
[24] Q ZWangW Li and H P Xie ldquoDynamic split tensile test offlattened Brazilian disc of rock with SHPB setuprdquo Mechanicsof Materials vol 41 no 3 pp 252ndash260 2009
[25] D Asprone E Cadoni A Prota and G Manfredi ldquoDynamicbehavior of a mediterranean natural stone under tensileloadingrdquo International Journal of Rock Mechanics and MiningSciences vol 46 no 3 pp 514ndash520 2009
[26] H Kolsky ldquoAn investigation of the mechanical properties ofmaterials at very high rates of loadingrdquo Proceedings of thePhysical Society Section B vol 62 no 11 pp 676ndash700 1949
[27] U S Lindholm ldquoSome experiments with the split Hopkinsonpressure barrdquo Journal of the Mechanics and Physics of Solidsvol 12 no 5 pp 317ndash335 1964
[28] G Subhash and G Ravichandran Split-Hopkinson PressureBar Testing of Ceramics pp 497ndash504 ASM InternationalMaterials Park OH USA 2000
[29] X Li T Zhou D Li and Z Wang ldquoExperimental and nu-merical investigations on feasibility and validity of prismaticrock specimen in SHPBrdquo Shock and Vibration vol 2016Article ID 7198980 13 pages 2016
[30] M R Ayatollahi and M Sistaninia ldquoMode __ fracture study ofrocks using Brazilian disk specimensrdquo International Journal ofRock Mechanics and Mining Sciences vol 48 no 5pp 819ndash826 2011
Shock and Vibration 13
[31] Q Z Wang X P Gou and H Fan ldquo+e minimum di-mensionless stress intensity factor and its upper bound forCCNBD fracture toughness specimen analyzed with straightthrough crack assumptionrdquo Engineering Fracture Mechanicsvol 82 pp 1ndash8 2012
[32] Q B Zhang and J Zhao ldquoQuasi-static and dynamic fracturebehaviour of rock materials phenomena and mechanismsrdquoInternational Journal of Fracture vol 189 no 1 pp 1ndash322014
[33] A Bertram and J F Kalthoff ldquoCrack propagation toughnessof rock for the range of low to very high crack speedsrdquo KeyEngineering Materials vol 251-252 pp 423ndash430 2003
[34] R Chen K Xia F Dai F Lu and S N Luo ldquoDeterminationof dynamic fracture parameters using a semi-circular bendtechnique in split Hopkinson pressure bar testingrdquo Engi-neering Fracture Mechanics vol 76 no 9 pp 1268ndash12762009
[35] P Forquin ldquoAn optical correlation technique for character-izing the crack velocity in concreterdquo e European PhysicalJournal Special Topics vol 206 no 1 pp 89ndash95 2012
[36] Y Zhao S Gong C Zhang Z Zhang and Y Jiang ldquoFractalcharacteristics of crack propagation in coal under impactloadingrdquo Fractals vol 26 no 2 article 1840014 2018
[37] J T Gomez A Shukla and A Sharma ldquoStatic and dynamicbehavior of concrete and granite in tension with damagerdquoeoretical and Applied Fracture Mechanics vol 36 no 1pp 37ndash49 2001
[38] Q B Zhang and J Zhao ldquoDetermination of mechanicalproperties and full-field strain measurements of rock materialunder dynamic loadsrdquo International Journal of Rock Me-chanics and Mining Sciences vol 60 pp 423ndash439 2013
[39] W Yao Y Xu H-W Liu and K Xia ldquoQuantification ofthermally induced damage and its effect on dynamic fracturetoughness of two mortarsrdquo Engineering Fracture Mechanicsvol 169 pp 74ndash88 2017
[40] T S Yun Y J Jeong K Y Kim and K-B Min ldquoEvaluation ofrock anisotropy using 3D X-ray computed tomographyrdquoEngineering Geology vol 163 pp 11ndash19 2013
[41] T Yin X Li K Xia and S Huang ldquoEffect of thermaltreatment on the dynamic fracture toughness of Laurentiangraniterdquo Rock Mechanics and Rock Engineering vol 45 no 6pp 1087ndash1094 2012
[42] S Huang K Xia F Yan and X Feng ldquoAn experimental studyof the rate dependence of tensile strength softening ofLongyou sandstonerdquo Rock Mechanics and Rock Engineeringvol 43 no 6 pp 677ndash683 2010
[43] S N Luo B J Jensen D E Hooks et al ldquoGas gun shockexperiments with single-pulse X-ray phase contrast imagingand diffraction at the advanced photon sourcerdquo Review ofScientific Instruments vol 83 no 7 article 073903 2012
[44] M Hudspeth B Claus S Dubelman et al ldquoHigh speedsynchrotron X-ray phase contrast imaging of dynamic ma-terial response to split Hopkinson bar loadingrdquo Review ofScientific Instruments vol 84 no 2 article 025102 2013
[45] Y Li and K T Ramesh ldquoAn optical technique for mea-surement of material properties in the tension Kolsky barrdquoInternational Journal of Impact Engineering vol 34 no 4pp 784ndash798 2007
[46] G Gao S Huang K Xia and Z Li ldquoApplication of digitalimage correlation (DIC) in dynamic notched semi-circularbend (NSCB) testsrdquo Experimental Mechanics vol 55 no 1pp 95ndash104 2015
[47] B Pan K Qian H Xie and A Asundi ldquoTwo-dimensionaldigital image correlation for in-plane displacement and strain
measurement a reviewrdquo Measurement Science and Technol-ogy vol 20 no 6 article 062001 2009
[48] F Amiot M Bornert P Doumalin et al ldquoAssessment ofdigital image correlation measurement accuracy in the ulti-mate error regime main results of a collaborative bench-markrdquo Strain vol 49 no 6 pp 483ndash496 2013
[49] W Shi Y Wu and L Wu ldquoQuantitative analysis of theprojectile impact on rock using infrared thermographyrdquoInternational Journal of Impact Engineering vol 34 no 5pp 990ndash1002 2007
[50] D K Iakovidis T Goudas C V Smailis and I MaglogiannisldquoRatsnake a versatile image annotation tool with applicationto computer-aided diagnosisrdquo e Scientific World Journalvol 2014 Article ID 286856 12 pages 2014
[51] B A Han H Y Xiang Z Li and J J Huang ldquoDefects de-tection of sheet metal parts based on HALCON and regionmorphologyrdquo Applied Mechanics and Materials vol 365-366pp 729ndash732 2013
[52] D Ai Y Zhao Q Wang and C Li ldquoExperimental andnumerical investigation of crack propagation and dynamicproperties of rock in SHPB indirect tension testrdquo In-ternational Journal of Impact Engineering vol 126 pp 135ndash146 2019
[53] H Xie and D J Sanderson ldquoFractal effects of crack propa-gation on dynamic stress intensity factors and crack veloci-tiesrdquo International Journal of Fracture vol 74 no 1pp 29ndash42 1996
[54] F Dai R Chen and K Xia ldquoA semi-circular bend techniquefor determining dynamic fracture toughnessrdquo ExperimentalMechanics vol 50 no 6 pp 783ndash791 2010
[55] D Chakerian and B B Mandelbrot ldquo+e fractal geometry ofnaturerdquo College Mathematics Journal vol 15 no 2pp 175ndash177 1984
[56] K Falconer ldquoFractal geometry mathematical foundationsand applicationsrdquo Biometrics vol 46 no 3 pp 886-887 1990
[57] T-B Yin K Peng L Wang P Wang X-Y Yin andY-L Zhang ldquoStudy on impact damage and energy dissipationof coal rock exposed to high temperaturesrdquo Shock and Vi-bration vol 2016 Article ID 5121932 10 pages 2016
14 Shock and Vibration
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
RoboticsJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
VLSI Design
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawiwwwhindawicom
Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Control Scienceand Engineering
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
SensorsJournal of
Hindawiwwwhindawicom Volume 2018
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
WS WI minusWR minusWT (12)
Figure 15 shows the total energy absorbed versus theimpact velocity for the rock specimens It indicates that the
energy absorbed by the rock specimen increases with in-creasing impact velocity
Moreover substantial efforts have been devoted to per-forming quantitative measurements on fracture surface and it
εi-4687msεi-5150msεi-4443msεi-4385msεi-3377msεi-3167msεi-3511msεi-3246msεi-3869msεi-4307msεi-5502ms
εt-4687msεt-5150msεt-4443msεt-4385msεt-3377msεt-3167msεt-3511msεt-3246msεt-3869msεt-4307msεt-5502ms
εr-4687msεr-5150msεr-4443msεr-4385msεr-3377msεr-3167msεr-3511msεr-3246msεr-3869msεr-4307msεr-5502ms
140 160 180 200 220 240 260 280120100
3
2
1
0
ndash1V
olta
ge (V
)ndash2
ndash3
Time (μs)
Figure 14 Incident reflected and transmitted signals of rocks under different impact velocities
18
WS (
J)
16
14
12
10
8
6
4
2
030 35 40 45 50 55
v (ms)
Fitting curve of v and WS
Figure 15 Relationship between v and WS
10 Shock and Vibration
has been well recognized that surface roughness in rock-likematerials exhibits self-similarity properties at least over a givenrange of length scales In other words the fracture surfacetopography of rock-like materials reveals inherent details as-sociated with energy dissipation mechanisms that govern thefracturing process +erefore the relationship between fractaldimension and absorbed energy was first calculated and theresult is shown in Figure 16(a) However it can be found thatthere is no obvious relationship between the two variables
On the other hand Figure 16(b) presents the total energyabsorbed WS versus the crack feature VAnis for the rockspecimens It can be seen that there is a linearly negativecorrelation between the two variables the greater the WSthe smaller the VAnis
422 Strain-Stress Parameters According to the incidentεi(t) reflected εr(t) and transmitted εt(t) strain signalsillustrated in Figure 14 and formulas (1)ndash(3) the max stressmax strain and mean strain rate of rocks under differentimpact velocities were calculated Combining with the crackcharacteristic parameters in the above section the re-lationship between the crack propagation process and dy-namic mechanical properties was analyzed
Figure 17 shows the max strain and mean strain rateversus the crack propagation velocity V while Figure 18shows the max strain and mean strain rate versus the crackpropagation velocity VAP
It can be seen that with theincrease of the V both the max strain and mean strain rateare gradually decreased and mean strain rate basically
000
001
002
003
004
005
006
007V D
(Dfr
ame)
2 4 6 8 10 12 14 16 180WS (J)
(a)
Fitting curve of WS and VAnis
2 4 6 8 10 12 14 16 180WS (J)
8
10
12
14
16
18
20
22
24
V Ani
s (an
isfr
ame)
(b)
Figure 16 (a) Relationship between WS and VD (b) relationship between WS and VAnis
Fitting curve of V and ε
66
68
70
72
74
76
78
εmiddot (sndash1
)
200 300 400 500
600 700100V (ms)
(a)
Fitting curve of V and εmax
200 300 400 500 600 700100V (ms)
25
30
35
40
45
50
55
60
65
70
ε max
(10ndash3
)
(b)
Figure 17 Curves of strain parameters with crack propagation velocity V and associated results after linear fitting (a) _ε as a function of V(b) εmax as a function of V
Shock and Vibration 11
remains the same when V ranges from 350ms to 650msSimilarly the max strain and mean strain rate also linearlydecrease with the increase of crack propagation velocityVAP
5 Conclusion
In this study the Brazil test of rock specimens was per-formed under different impact velocities using the SHPBsystem to explore fracture characterizations of rocks underdynamic loads Based on image processing technique crackpropagation process was quantitatively described from threeperspectives the crack propagation velocity crack fractalcharacteristic and crack morphological features Accordingto the recorded strain wave signals the dynamic mechanicalproperties of rocks were also calculated and the relationshipbetween impact velocity and crack propagation process wasexplored and analyzed +e main conclusions are listed asfollows
(1) Crack propagation velocities V and VAPboth in-
crease with increase of the crack fractals velocity VD
(2) +e proposed two crack features Compactness andAnisometery have a capacity of describing thefracture process of rock In specific VAnis linearlydecreases with the increase of impact velocity v whileVComp exhibits a negative relationship with crackfractals velocity VD
(3) +e energy absorbed by the rocks increases with theincrease of impact velocity v but shows a linearnegative trend with VAnis
(4) +e mean strain rate and max strain both decreasewith increase of crack propagation velocity whichshows that there is a certain relationship between thecrack propagation process and dynamic mechanicalproperties of rocks under dynamic loading
In the future work we will conduct the static tensile testsusing the BD specimen on the same rock material andcompare the static and dynamic results in terms of me-chanical properties and crack propagation process
Nomenclature
_ε Mean strain rate (sminus1)σmax Max stress (MPa)εmax Max strain (10minus3)A Cross-sectional area of the bar (mm2)A Crack length (mm)Ap Crack quantification area (pixels)AS Cross-sectional area of the specimen (mm2)Anis Crack feature descriptormdashanisometryC Longitudinal stress wave speed of the bar (ms)Comp Crack feature descriptormdashcompactnessD Fractal dimensionE Youngrsquos modulus of the bar (GPa)LS Length of rock specimen (mm)P1 P2 Dynamic forces on incident and transmitted ends
(N)rxy Pearsonrsquos correlation coefficientV Crack propagation velocity (ms)v Impact velocity (ms)VD Fractal dimension velocity (Dframe)VAP
Crack propagation velocity (pixelss)VAnis Anisometry velocity (anisframe)VComp Compactness velocity (compframe)WS Absorbed energy (J)
Data Availability
+e data utilized in this study are available from the cor-responding author upon request
00 50 times 106 10 times 107 15 times 107
Fitting curve of VAP and ε
20 times 107 25 times 107 30 times 107 35 times 107
VAP (pixelss)
66
68
70
72
74
76
78ε (
sndash1)
(a)
70
65
60
55
50
44
40
30
25
35
ε max
(10ndash3
)
Fitting curve of VAP and εmax
00 50 times 106 10 times 107 15 times 107 20 times 107 25 times 107 30 times 107 35 times 107
VAP (pixelss)
(b)
Figure 18 Curves of strain parameters with crack propagation velocity VAPand associated results after linear fitting (a) _ε as a function of
VAP (b) εmax as a function of VAP
12 Shock and Vibration
Conflicts of Interest
+e authors declare that they have no conflicts of interest
Acknowledgments
+is research was financially supported by the NationalNatural Science Foundation of China (nos 51274206 and51404277) +is support is greatly acknowledged andappreciated
References
[1] K Xia and W Yao ldquoDynamic rock tests using split Hop-kinson (Kolsky) bar systemmdasha reviewrdquo Journal of RockMechanics and Geotechnical Engineering vol 7 no 1pp 27ndash59 2015
[2] F Gong H Ye and Y Luo ldquo+e effect of high loading rate onthe behaviour and mechanical properties of coal-rock com-bined bodyrdquo Shock and Vibration vol 2018 Article ID4374530 9 pages 2018
[3] Y X Zhou K Xia X B Li et al ldquoSuggested methods fordetermining the dynamic strength parameters and mode-ifracture toughness of rock materialsrdquo International Journal ofRock Mechanics and Mining Sciences vol 49 no 1pp 105ndash112 2012
[4] Y Zhao G-F Zhao Y Jiang D Elsworth and Y HuangldquoEffects of bedding on the dynamic indirect tensile strength ofcoal Laboratory experiments and numerical simulationrdquoInternational Journal of Coal Geology vol 132 pp 81ndash932014
[5] F Dai K Xia and S N Luo ldquoSemicircular bend testing withsplit Hopkinson pressure bar for measuring dynamic tensilestrength of brittle solidsrdquo Review of Scientific Instrumentsvol 79 no 12 article 123903 2008
[6] F Dai K Xia and L Tang ldquoRate dependence of the flexuraltensile strength of Laurentian graniterdquo International Journalof Rock Mechanics and Mining Sciences vol 47 no 3pp 469ndash475 2010
[7] Y Wang ldquoRock dynamic fracture characteristics based onNSCB impact methodrdquo Shock and Vibration vol 2018 Ar-ticle ID 3105384 13 pages 2018
[8] Q B Zhang and J Zhao ldquoEffect of loading rate on fracturetoughness and failure micromechanisms in marblerdquo Engi-neering Fracture Mechanics vol 102 pp 288ndash309 2013
[9] M D Kuruppu Y Obara M R Ayatollahi K P Chong andT Funatsu ldquoISRM-suggested method for determining themode i static fracture toughness using semi-circular bendspecimenrdquo Rock Mechanics and Rock Engineering vol 47no 1 pp 267ndash274 2014
[10] M RM Aliha andM R Ayatollahi ldquoRock fracture toughnessstudy using cracked chevron notched Brazilian disc specimenunder pure modes I and II loadingmdasha statistical approachrdquoeoretical and Applied Fracture Mechanics vol 69 no 2pp 17ndash25 2014
[11] F Dai K Xia H Zheng and Y X Wang ldquoDetermination ofdynamic rock mode-i fracture parameters using crackedchevron notched semi-circular bend specimenrdquo EngineeringFracture Mechanics vol 78 no 15 pp 2633ndash2644 2011
[12] T Tang Z P Bazant S Yang and D Zollinger ldquoVariable-notch one-size test method for fracture energy and processzone lengthrdquo Engineering Fracture Mechanics vol 55 no 3pp 383ndash404 1996
[13] Q Z Wang S Zhang and H P Xie ldquoRock dynamic fracturetoughness tested with holed-cracked flattened Brazilian discsdiametrically impacted by SHPB and its size effectrdquo Experi-mental Mechanics vol 50 no 7 pp 877ndash885 2010
[14] B Lundberg ldquoA split Hopkinson bar study of energy ab-sorption in dynamic rock fragmentationrdquo InternationalJournal of Rock Mechanics and Mining Sciences amp Geo-mechanics Abstracts vol 13 no 6 pp 187ndash197 1976
[15] V Isheyskiy and M Marinin ldquoDetermination of rock massweakening coefficient after blasting in various fracture zonesrdquoEngineering Solid Mechanics vol 5 no 3 pp 199ndash204 2017
[16] G Gary and P Bailly ldquoBehaviour of quasi-brittle material athigh strain rate Experiment and modellingrdquo EuropeanJournal of Mechanics-ASolids vol 17 no 3 pp 403ndash4201998
[17] J Zhao H B Li and Y H ZhaoDynamic Strength Tests of theBukit Timah Granite Nanyang Technological UniversitySingapore 1998
[18] Q B Zhang and J Zhao ldquoA review of dynamic experimentaltechniques andmechanical behaviour of rockmaterialsrdquo RockMechanics and Rock Engineering vol 47 no 4 pp 1411ndash14782014
[19] J Zhao and H B Li ldquoExperimental determination of dynamictensile properties of a graniterdquo International Journal of RockMechanics and Mining Sciences vol 37 no 5 pp 861ndash8662000
[20] J R Klepaczko and A Brara ldquoAn experimental method fordynamic tensile testing of concrete by spallingrdquo InternationalJournal of Impact Engineering vol 25 no 4 pp 387ndash4092001
[21] S Kubota Y Ogata Y Wada G Simangunsong H Shimadaand K Matsui ldquoEstimation of dynamic tensile strength ofsandstonerdquo International Journal of Rock Mechanics andMining Sciences vol 45 no 3 pp 397ndash406 2008
[22] B Erzar and P Forquin ldquoAn experimental method to de-termine the tensile strength of concrete at high rates of strainrdquoExperimental Mechanics vol 50 no 7 pp 941ndash955 2010
[23] L Biolzi and J Labuz ldquoInstabilities in fracture of elastic-softening structuresrdquo Fracture of Engineering Materials andStructures vol 6 no 8 pp 821ndash826 1991
[24] Q ZWangW Li and H P Xie ldquoDynamic split tensile test offlattened Brazilian disc of rock with SHPB setuprdquo Mechanicsof Materials vol 41 no 3 pp 252ndash260 2009
[25] D Asprone E Cadoni A Prota and G Manfredi ldquoDynamicbehavior of a mediterranean natural stone under tensileloadingrdquo International Journal of Rock Mechanics and MiningSciences vol 46 no 3 pp 514ndash520 2009
[26] H Kolsky ldquoAn investigation of the mechanical properties ofmaterials at very high rates of loadingrdquo Proceedings of thePhysical Society Section B vol 62 no 11 pp 676ndash700 1949
[27] U S Lindholm ldquoSome experiments with the split Hopkinsonpressure barrdquo Journal of the Mechanics and Physics of Solidsvol 12 no 5 pp 317ndash335 1964
[28] G Subhash and G Ravichandran Split-Hopkinson PressureBar Testing of Ceramics pp 497ndash504 ASM InternationalMaterials Park OH USA 2000
[29] X Li T Zhou D Li and Z Wang ldquoExperimental and nu-merical investigations on feasibility and validity of prismaticrock specimen in SHPBrdquo Shock and Vibration vol 2016Article ID 7198980 13 pages 2016
[30] M R Ayatollahi and M Sistaninia ldquoMode __ fracture study ofrocks using Brazilian disk specimensrdquo International Journal ofRock Mechanics and Mining Sciences vol 48 no 5pp 819ndash826 2011
Shock and Vibration 13
[31] Q Z Wang X P Gou and H Fan ldquo+e minimum di-mensionless stress intensity factor and its upper bound forCCNBD fracture toughness specimen analyzed with straightthrough crack assumptionrdquo Engineering Fracture Mechanicsvol 82 pp 1ndash8 2012
[32] Q B Zhang and J Zhao ldquoQuasi-static and dynamic fracturebehaviour of rock materials phenomena and mechanismsrdquoInternational Journal of Fracture vol 189 no 1 pp 1ndash322014
[33] A Bertram and J F Kalthoff ldquoCrack propagation toughnessof rock for the range of low to very high crack speedsrdquo KeyEngineering Materials vol 251-252 pp 423ndash430 2003
[34] R Chen K Xia F Dai F Lu and S N Luo ldquoDeterminationof dynamic fracture parameters using a semi-circular bendtechnique in split Hopkinson pressure bar testingrdquo Engi-neering Fracture Mechanics vol 76 no 9 pp 1268ndash12762009
[35] P Forquin ldquoAn optical correlation technique for character-izing the crack velocity in concreterdquo e European PhysicalJournal Special Topics vol 206 no 1 pp 89ndash95 2012
[36] Y Zhao S Gong C Zhang Z Zhang and Y Jiang ldquoFractalcharacteristics of crack propagation in coal under impactloadingrdquo Fractals vol 26 no 2 article 1840014 2018
[37] J T Gomez A Shukla and A Sharma ldquoStatic and dynamicbehavior of concrete and granite in tension with damagerdquoeoretical and Applied Fracture Mechanics vol 36 no 1pp 37ndash49 2001
[38] Q B Zhang and J Zhao ldquoDetermination of mechanicalproperties and full-field strain measurements of rock materialunder dynamic loadsrdquo International Journal of Rock Me-chanics and Mining Sciences vol 60 pp 423ndash439 2013
[39] W Yao Y Xu H-W Liu and K Xia ldquoQuantification ofthermally induced damage and its effect on dynamic fracturetoughness of two mortarsrdquo Engineering Fracture Mechanicsvol 169 pp 74ndash88 2017
[40] T S Yun Y J Jeong K Y Kim and K-B Min ldquoEvaluation ofrock anisotropy using 3D X-ray computed tomographyrdquoEngineering Geology vol 163 pp 11ndash19 2013
[41] T Yin X Li K Xia and S Huang ldquoEffect of thermaltreatment on the dynamic fracture toughness of Laurentiangraniterdquo Rock Mechanics and Rock Engineering vol 45 no 6pp 1087ndash1094 2012
[42] S Huang K Xia F Yan and X Feng ldquoAn experimental studyof the rate dependence of tensile strength softening ofLongyou sandstonerdquo Rock Mechanics and Rock Engineeringvol 43 no 6 pp 677ndash683 2010
[43] S N Luo B J Jensen D E Hooks et al ldquoGas gun shockexperiments with single-pulse X-ray phase contrast imagingand diffraction at the advanced photon sourcerdquo Review ofScientific Instruments vol 83 no 7 article 073903 2012
[44] M Hudspeth B Claus S Dubelman et al ldquoHigh speedsynchrotron X-ray phase contrast imaging of dynamic ma-terial response to split Hopkinson bar loadingrdquo Review ofScientific Instruments vol 84 no 2 article 025102 2013
[45] Y Li and K T Ramesh ldquoAn optical technique for mea-surement of material properties in the tension Kolsky barrdquoInternational Journal of Impact Engineering vol 34 no 4pp 784ndash798 2007
[46] G Gao S Huang K Xia and Z Li ldquoApplication of digitalimage correlation (DIC) in dynamic notched semi-circularbend (NSCB) testsrdquo Experimental Mechanics vol 55 no 1pp 95ndash104 2015
[47] B Pan K Qian H Xie and A Asundi ldquoTwo-dimensionaldigital image correlation for in-plane displacement and strain
measurement a reviewrdquo Measurement Science and Technol-ogy vol 20 no 6 article 062001 2009
[48] F Amiot M Bornert P Doumalin et al ldquoAssessment ofdigital image correlation measurement accuracy in the ulti-mate error regime main results of a collaborative bench-markrdquo Strain vol 49 no 6 pp 483ndash496 2013
[49] W Shi Y Wu and L Wu ldquoQuantitative analysis of theprojectile impact on rock using infrared thermographyrdquoInternational Journal of Impact Engineering vol 34 no 5pp 990ndash1002 2007
[50] D K Iakovidis T Goudas C V Smailis and I MaglogiannisldquoRatsnake a versatile image annotation tool with applicationto computer-aided diagnosisrdquo e Scientific World Journalvol 2014 Article ID 286856 12 pages 2014
[51] B A Han H Y Xiang Z Li and J J Huang ldquoDefects de-tection of sheet metal parts based on HALCON and regionmorphologyrdquo Applied Mechanics and Materials vol 365-366pp 729ndash732 2013
[52] D Ai Y Zhao Q Wang and C Li ldquoExperimental andnumerical investigation of crack propagation and dynamicproperties of rock in SHPB indirect tension testrdquo In-ternational Journal of Impact Engineering vol 126 pp 135ndash146 2019
[53] H Xie and D J Sanderson ldquoFractal effects of crack propa-gation on dynamic stress intensity factors and crack veloci-tiesrdquo International Journal of Fracture vol 74 no 1pp 29ndash42 1996
[54] F Dai R Chen and K Xia ldquoA semi-circular bend techniquefor determining dynamic fracture toughnessrdquo ExperimentalMechanics vol 50 no 6 pp 783ndash791 2010
[55] D Chakerian and B B Mandelbrot ldquo+e fractal geometry ofnaturerdquo College Mathematics Journal vol 15 no 2pp 175ndash177 1984
[56] K Falconer ldquoFractal geometry mathematical foundationsand applicationsrdquo Biometrics vol 46 no 3 pp 886-887 1990
[57] T-B Yin K Peng L Wang P Wang X-Y Yin andY-L Zhang ldquoStudy on impact damage and energy dissipationof coal rock exposed to high temperaturesrdquo Shock and Vi-bration vol 2016 Article ID 5121932 10 pages 2016
14 Shock and Vibration
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
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Active and Passive Electronic Components
VLSI Design
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Shock and Vibration
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Civil EngineeringAdvances in
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Submit your manuscripts atwwwhindawicom
has been well recognized that surface roughness in rock-likematerials exhibits self-similarity properties at least over a givenrange of length scales In other words the fracture surfacetopography of rock-like materials reveals inherent details as-sociated with energy dissipation mechanisms that govern thefracturing process +erefore the relationship between fractaldimension and absorbed energy was first calculated and theresult is shown in Figure 16(a) However it can be found thatthere is no obvious relationship between the two variables
On the other hand Figure 16(b) presents the total energyabsorbed WS versus the crack feature VAnis for the rockspecimens It can be seen that there is a linearly negativecorrelation between the two variables the greater the WSthe smaller the VAnis
422 Strain-Stress Parameters According to the incidentεi(t) reflected εr(t) and transmitted εt(t) strain signalsillustrated in Figure 14 and formulas (1)ndash(3) the max stressmax strain and mean strain rate of rocks under differentimpact velocities were calculated Combining with the crackcharacteristic parameters in the above section the re-lationship between the crack propagation process and dy-namic mechanical properties was analyzed
Figure 17 shows the max strain and mean strain rateversus the crack propagation velocity V while Figure 18shows the max strain and mean strain rate versus the crackpropagation velocity VAP
It can be seen that with theincrease of the V both the max strain and mean strain rateare gradually decreased and mean strain rate basically
000
001
002
003
004
005
006
007V D
(Dfr
ame)
2 4 6 8 10 12 14 16 180WS (J)
(a)
Fitting curve of WS and VAnis
2 4 6 8 10 12 14 16 180WS (J)
8
10
12
14
16
18
20
22
24
V Ani
s (an
isfr
ame)
(b)
Figure 16 (a) Relationship between WS and VD (b) relationship between WS and VAnis
Fitting curve of V and ε
66
68
70
72
74
76
78
εmiddot (sndash1
)
200 300 400 500
600 700100V (ms)
(a)
Fitting curve of V and εmax
200 300 400 500 600 700100V (ms)
25
30
35
40
45
50
55
60
65
70
ε max
(10ndash3
)
(b)
Figure 17 Curves of strain parameters with crack propagation velocity V and associated results after linear fitting (a) _ε as a function of V(b) εmax as a function of V
Shock and Vibration 11
remains the same when V ranges from 350ms to 650msSimilarly the max strain and mean strain rate also linearlydecrease with the increase of crack propagation velocityVAP
5 Conclusion
In this study the Brazil test of rock specimens was per-formed under different impact velocities using the SHPBsystem to explore fracture characterizations of rocks underdynamic loads Based on image processing technique crackpropagation process was quantitatively described from threeperspectives the crack propagation velocity crack fractalcharacteristic and crack morphological features Accordingto the recorded strain wave signals the dynamic mechanicalproperties of rocks were also calculated and the relationshipbetween impact velocity and crack propagation process wasexplored and analyzed +e main conclusions are listed asfollows
(1) Crack propagation velocities V and VAPboth in-
crease with increase of the crack fractals velocity VD
(2) +e proposed two crack features Compactness andAnisometery have a capacity of describing thefracture process of rock In specific VAnis linearlydecreases with the increase of impact velocity v whileVComp exhibits a negative relationship with crackfractals velocity VD
(3) +e energy absorbed by the rocks increases with theincrease of impact velocity v but shows a linearnegative trend with VAnis
(4) +e mean strain rate and max strain both decreasewith increase of crack propagation velocity whichshows that there is a certain relationship between thecrack propagation process and dynamic mechanicalproperties of rocks under dynamic loading
In the future work we will conduct the static tensile testsusing the BD specimen on the same rock material andcompare the static and dynamic results in terms of me-chanical properties and crack propagation process
Nomenclature
_ε Mean strain rate (sminus1)σmax Max stress (MPa)εmax Max strain (10minus3)A Cross-sectional area of the bar (mm2)A Crack length (mm)Ap Crack quantification area (pixels)AS Cross-sectional area of the specimen (mm2)Anis Crack feature descriptormdashanisometryC Longitudinal stress wave speed of the bar (ms)Comp Crack feature descriptormdashcompactnessD Fractal dimensionE Youngrsquos modulus of the bar (GPa)LS Length of rock specimen (mm)P1 P2 Dynamic forces on incident and transmitted ends
(N)rxy Pearsonrsquos correlation coefficientV Crack propagation velocity (ms)v Impact velocity (ms)VD Fractal dimension velocity (Dframe)VAP
Crack propagation velocity (pixelss)VAnis Anisometry velocity (anisframe)VComp Compactness velocity (compframe)WS Absorbed energy (J)
Data Availability
+e data utilized in this study are available from the cor-responding author upon request
00 50 times 106 10 times 107 15 times 107
Fitting curve of VAP and ε
20 times 107 25 times 107 30 times 107 35 times 107
VAP (pixelss)
66
68
70
72
74
76
78ε (
sndash1)
(a)
70
65
60
55
50
44
40
30
25
35
ε max
(10ndash3
)
Fitting curve of VAP and εmax
00 50 times 106 10 times 107 15 times 107 20 times 107 25 times 107 30 times 107 35 times 107
VAP (pixelss)
(b)
Figure 18 Curves of strain parameters with crack propagation velocity VAPand associated results after linear fitting (a) _ε as a function of
VAP (b) εmax as a function of VAP
12 Shock and Vibration
Conflicts of Interest
+e authors declare that they have no conflicts of interest
Acknowledgments
+is research was financially supported by the NationalNatural Science Foundation of China (nos 51274206 and51404277) +is support is greatly acknowledged andappreciated
References
[1] K Xia and W Yao ldquoDynamic rock tests using split Hop-kinson (Kolsky) bar systemmdasha reviewrdquo Journal of RockMechanics and Geotechnical Engineering vol 7 no 1pp 27ndash59 2015
[2] F Gong H Ye and Y Luo ldquo+e effect of high loading rate onthe behaviour and mechanical properties of coal-rock com-bined bodyrdquo Shock and Vibration vol 2018 Article ID4374530 9 pages 2018
[3] Y X Zhou K Xia X B Li et al ldquoSuggested methods fordetermining the dynamic strength parameters and mode-ifracture toughness of rock materialsrdquo International Journal ofRock Mechanics and Mining Sciences vol 49 no 1pp 105ndash112 2012
[4] Y Zhao G-F Zhao Y Jiang D Elsworth and Y HuangldquoEffects of bedding on the dynamic indirect tensile strength ofcoal Laboratory experiments and numerical simulationrdquoInternational Journal of Coal Geology vol 132 pp 81ndash932014
[5] F Dai K Xia and S N Luo ldquoSemicircular bend testing withsplit Hopkinson pressure bar for measuring dynamic tensilestrength of brittle solidsrdquo Review of Scientific Instrumentsvol 79 no 12 article 123903 2008
[6] F Dai K Xia and L Tang ldquoRate dependence of the flexuraltensile strength of Laurentian graniterdquo International Journalof Rock Mechanics and Mining Sciences vol 47 no 3pp 469ndash475 2010
[7] Y Wang ldquoRock dynamic fracture characteristics based onNSCB impact methodrdquo Shock and Vibration vol 2018 Ar-ticle ID 3105384 13 pages 2018
[8] Q B Zhang and J Zhao ldquoEffect of loading rate on fracturetoughness and failure micromechanisms in marblerdquo Engi-neering Fracture Mechanics vol 102 pp 288ndash309 2013
[9] M D Kuruppu Y Obara M R Ayatollahi K P Chong andT Funatsu ldquoISRM-suggested method for determining themode i static fracture toughness using semi-circular bendspecimenrdquo Rock Mechanics and Rock Engineering vol 47no 1 pp 267ndash274 2014
[10] M RM Aliha andM R Ayatollahi ldquoRock fracture toughnessstudy using cracked chevron notched Brazilian disc specimenunder pure modes I and II loadingmdasha statistical approachrdquoeoretical and Applied Fracture Mechanics vol 69 no 2pp 17ndash25 2014
[11] F Dai K Xia H Zheng and Y X Wang ldquoDetermination ofdynamic rock mode-i fracture parameters using crackedchevron notched semi-circular bend specimenrdquo EngineeringFracture Mechanics vol 78 no 15 pp 2633ndash2644 2011
[12] T Tang Z P Bazant S Yang and D Zollinger ldquoVariable-notch one-size test method for fracture energy and processzone lengthrdquo Engineering Fracture Mechanics vol 55 no 3pp 383ndash404 1996
[13] Q Z Wang S Zhang and H P Xie ldquoRock dynamic fracturetoughness tested with holed-cracked flattened Brazilian discsdiametrically impacted by SHPB and its size effectrdquo Experi-mental Mechanics vol 50 no 7 pp 877ndash885 2010
[14] B Lundberg ldquoA split Hopkinson bar study of energy ab-sorption in dynamic rock fragmentationrdquo InternationalJournal of Rock Mechanics and Mining Sciences amp Geo-mechanics Abstracts vol 13 no 6 pp 187ndash197 1976
[15] V Isheyskiy and M Marinin ldquoDetermination of rock massweakening coefficient after blasting in various fracture zonesrdquoEngineering Solid Mechanics vol 5 no 3 pp 199ndash204 2017
[16] G Gary and P Bailly ldquoBehaviour of quasi-brittle material athigh strain rate Experiment and modellingrdquo EuropeanJournal of Mechanics-ASolids vol 17 no 3 pp 403ndash4201998
[17] J Zhao H B Li and Y H ZhaoDynamic Strength Tests of theBukit Timah Granite Nanyang Technological UniversitySingapore 1998
[18] Q B Zhang and J Zhao ldquoA review of dynamic experimentaltechniques andmechanical behaviour of rockmaterialsrdquo RockMechanics and Rock Engineering vol 47 no 4 pp 1411ndash14782014
[19] J Zhao and H B Li ldquoExperimental determination of dynamictensile properties of a graniterdquo International Journal of RockMechanics and Mining Sciences vol 37 no 5 pp 861ndash8662000
[20] J R Klepaczko and A Brara ldquoAn experimental method fordynamic tensile testing of concrete by spallingrdquo InternationalJournal of Impact Engineering vol 25 no 4 pp 387ndash4092001
[21] S Kubota Y Ogata Y Wada G Simangunsong H Shimadaand K Matsui ldquoEstimation of dynamic tensile strength ofsandstonerdquo International Journal of Rock Mechanics andMining Sciences vol 45 no 3 pp 397ndash406 2008
[22] B Erzar and P Forquin ldquoAn experimental method to de-termine the tensile strength of concrete at high rates of strainrdquoExperimental Mechanics vol 50 no 7 pp 941ndash955 2010
[23] L Biolzi and J Labuz ldquoInstabilities in fracture of elastic-softening structuresrdquo Fracture of Engineering Materials andStructures vol 6 no 8 pp 821ndash826 1991
[24] Q ZWangW Li and H P Xie ldquoDynamic split tensile test offlattened Brazilian disc of rock with SHPB setuprdquo Mechanicsof Materials vol 41 no 3 pp 252ndash260 2009
[25] D Asprone E Cadoni A Prota and G Manfredi ldquoDynamicbehavior of a mediterranean natural stone under tensileloadingrdquo International Journal of Rock Mechanics and MiningSciences vol 46 no 3 pp 514ndash520 2009
[26] H Kolsky ldquoAn investigation of the mechanical properties ofmaterials at very high rates of loadingrdquo Proceedings of thePhysical Society Section B vol 62 no 11 pp 676ndash700 1949
[27] U S Lindholm ldquoSome experiments with the split Hopkinsonpressure barrdquo Journal of the Mechanics and Physics of Solidsvol 12 no 5 pp 317ndash335 1964
[28] G Subhash and G Ravichandran Split-Hopkinson PressureBar Testing of Ceramics pp 497ndash504 ASM InternationalMaterials Park OH USA 2000
[29] X Li T Zhou D Li and Z Wang ldquoExperimental and nu-merical investigations on feasibility and validity of prismaticrock specimen in SHPBrdquo Shock and Vibration vol 2016Article ID 7198980 13 pages 2016
[30] M R Ayatollahi and M Sistaninia ldquoMode __ fracture study ofrocks using Brazilian disk specimensrdquo International Journal ofRock Mechanics and Mining Sciences vol 48 no 5pp 819ndash826 2011
Shock and Vibration 13
[31] Q Z Wang X P Gou and H Fan ldquo+e minimum di-mensionless stress intensity factor and its upper bound forCCNBD fracture toughness specimen analyzed with straightthrough crack assumptionrdquo Engineering Fracture Mechanicsvol 82 pp 1ndash8 2012
[32] Q B Zhang and J Zhao ldquoQuasi-static and dynamic fracturebehaviour of rock materials phenomena and mechanismsrdquoInternational Journal of Fracture vol 189 no 1 pp 1ndash322014
[33] A Bertram and J F Kalthoff ldquoCrack propagation toughnessof rock for the range of low to very high crack speedsrdquo KeyEngineering Materials vol 251-252 pp 423ndash430 2003
[34] R Chen K Xia F Dai F Lu and S N Luo ldquoDeterminationof dynamic fracture parameters using a semi-circular bendtechnique in split Hopkinson pressure bar testingrdquo Engi-neering Fracture Mechanics vol 76 no 9 pp 1268ndash12762009
[35] P Forquin ldquoAn optical correlation technique for character-izing the crack velocity in concreterdquo e European PhysicalJournal Special Topics vol 206 no 1 pp 89ndash95 2012
[36] Y Zhao S Gong C Zhang Z Zhang and Y Jiang ldquoFractalcharacteristics of crack propagation in coal under impactloadingrdquo Fractals vol 26 no 2 article 1840014 2018
[37] J T Gomez A Shukla and A Sharma ldquoStatic and dynamicbehavior of concrete and granite in tension with damagerdquoeoretical and Applied Fracture Mechanics vol 36 no 1pp 37ndash49 2001
[38] Q B Zhang and J Zhao ldquoDetermination of mechanicalproperties and full-field strain measurements of rock materialunder dynamic loadsrdquo International Journal of Rock Me-chanics and Mining Sciences vol 60 pp 423ndash439 2013
[39] W Yao Y Xu H-W Liu and K Xia ldquoQuantification ofthermally induced damage and its effect on dynamic fracturetoughness of two mortarsrdquo Engineering Fracture Mechanicsvol 169 pp 74ndash88 2017
[40] T S Yun Y J Jeong K Y Kim and K-B Min ldquoEvaluation ofrock anisotropy using 3D X-ray computed tomographyrdquoEngineering Geology vol 163 pp 11ndash19 2013
[41] T Yin X Li K Xia and S Huang ldquoEffect of thermaltreatment on the dynamic fracture toughness of Laurentiangraniterdquo Rock Mechanics and Rock Engineering vol 45 no 6pp 1087ndash1094 2012
[42] S Huang K Xia F Yan and X Feng ldquoAn experimental studyof the rate dependence of tensile strength softening ofLongyou sandstonerdquo Rock Mechanics and Rock Engineeringvol 43 no 6 pp 677ndash683 2010
[43] S N Luo B J Jensen D E Hooks et al ldquoGas gun shockexperiments with single-pulse X-ray phase contrast imagingand diffraction at the advanced photon sourcerdquo Review ofScientific Instruments vol 83 no 7 article 073903 2012
[44] M Hudspeth B Claus S Dubelman et al ldquoHigh speedsynchrotron X-ray phase contrast imaging of dynamic ma-terial response to split Hopkinson bar loadingrdquo Review ofScientific Instruments vol 84 no 2 article 025102 2013
[45] Y Li and K T Ramesh ldquoAn optical technique for mea-surement of material properties in the tension Kolsky barrdquoInternational Journal of Impact Engineering vol 34 no 4pp 784ndash798 2007
[46] G Gao S Huang K Xia and Z Li ldquoApplication of digitalimage correlation (DIC) in dynamic notched semi-circularbend (NSCB) testsrdquo Experimental Mechanics vol 55 no 1pp 95ndash104 2015
[47] B Pan K Qian H Xie and A Asundi ldquoTwo-dimensionaldigital image correlation for in-plane displacement and strain
measurement a reviewrdquo Measurement Science and Technol-ogy vol 20 no 6 article 062001 2009
[48] F Amiot M Bornert P Doumalin et al ldquoAssessment ofdigital image correlation measurement accuracy in the ulti-mate error regime main results of a collaborative bench-markrdquo Strain vol 49 no 6 pp 483ndash496 2013
[49] W Shi Y Wu and L Wu ldquoQuantitative analysis of theprojectile impact on rock using infrared thermographyrdquoInternational Journal of Impact Engineering vol 34 no 5pp 990ndash1002 2007
[50] D K Iakovidis T Goudas C V Smailis and I MaglogiannisldquoRatsnake a versatile image annotation tool with applicationto computer-aided diagnosisrdquo e Scientific World Journalvol 2014 Article ID 286856 12 pages 2014
[51] B A Han H Y Xiang Z Li and J J Huang ldquoDefects de-tection of sheet metal parts based on HALCON and regionmorphologyrdquo Applied Mechanics and Materials vol 365-366pp 729ndash732 2013
[52] D Ai Y Zhao Q Wang and C Li ldquoExperimental andnumerical investigation of crack propagation and dynamicproperties of rock in SHPB indirect tension testrdquo In-ternational Journal of Impact Engineering vol 126 pp 135ndash146 2019
[53] H Xie and D J Sanderson ldquoFractal effects of crack propa-gation on dynamic stress intensity factors and crack veloci-tiesrdquo International Journal of Fracture vol 74 no 1pp 29ndash42 1996
[54] F Dai R Chen and K Xia ldquoA semi-circular bend techniquefor determining dynamic fracture toughnessrdquo ExperimentalMechanics vol 50 no 6 pp 783ndash791 2010
[55] D Chakerian and B B Mandelbrot ldquo+e fractal geometry ofnaturerdquo College Mathematics Journal vol 15 no 2pp 175ndash177 1984
[56] K Falconer ldquoFractal geometry mathematical foundationsand applicationsrdquo Biometrics vol 46 no 3 pp 886-887 1990
[57] T-B Yin K Peng L Wang P Wang X-Y Yin andY-L Zhang ldquoStudy on impact damage and energy dissipationof coal rock exposed to high temperaturesrdquo Shock and Vi-bration vol 2016 Article ID 5121932 10 pages 2016
14 Shock and Vibration
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
RoboticsJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
VLSI Design
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawiwwwhindawicom
Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Control Scienceand Engineering
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
SensorsJournal of
Hindawiwwwhindawicom Volume 2018
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
remains the same when V ranges from 350ms to 650msSimilarly the max strain and mean strain rate also linearlydecrease with the increase of crack propagation velocityVAP
5 Conclusion
In this study the Brazil test of rock specimens was per-formed under different impact velocities using the SHPBsystem to explore fracture characterizations of rocks underdynamic loads Based on image processing technique crackpropagation process was quantitatively described from threeperspectives the crack propagation velocity crack fractalcharacteristic and crack morphological features Accordingto the recorded strain wave signals the dynamic mechanicalproperties of rocks were also calculated and the relationshipbetween impact velocity and crack propagation process wasexplored and analyzed +e main conclusions are listed asfollows
(1) Crack propagation velocities V and VAPboth in-
crease with increase of the crack fractals velocity VD
(2) +e proposed two crack features Compactness andAnisometery have a capacity of describing thefracture process of rock In specific VAnis linearlydecreases with the increase of impact velocity v whileVComp exhibits a negative relationship with crackfractals velocity VD
(3) +e energy absorbed by the rocks increases with theincrease of impact velocity v but shows a linearnegative trend with VAnis
(4) +e mean strain rate and max strain both decreasewith increase of crack propagation velocity whichshows that there is a certain relationship between thecrack propagation process and dynamic mechanicalproperties of rocks under dynamic loading
In the future work we will conduct the static tensile testsusing the BD specimen on the same rock material andcompare the static and dynamic results in terms of me-chanical properties and crack propagation process
Nomenclature
_ε Mean strain rate (sminus1)σmax Max stress (MPa)εmax Max strain (10minus3)A Cross-sectional area of the bar (mm2)A Crack length (mm)Ap Crack quantification area (pixels)AS Cross-sectional area of the specimen (mm2)Anis Crack feature descriptormdashanisometryC Longitudinal stress wave speed of the bar (ms)Comp Crack feature descriptormdashcompactnessD Fractal dimensionE Youngrsquos modulus of the bar (GPa)LS Length of rock specimen (mm)P1 P2 Dynamic forces on incident and transmitted ends
(N)rxy Pearsonrsquos correlation coefficientV Crack propagation velocity (ms)v Impact velocity (ms)VD Fractal dimension velocity (Dframe)VAP
Crack propagation velocity (pixelss)VAnis Anisometry velocity (anisframe)VComp Compactness velocity (compframe)WS Absorbed energy (J)
Data Availability
+e data utilized in this study are available from the cor-responding author upon request
00 50 times 106 10 times 107 15 times 107
Fitting curve of VAP and ε
20 times 107 25 times 107 30 times 107 35 times 107
VAP (pixelss)
66
68
70
72
74
76
78ε (
sndash1)
(a)
70
65
60
55
50
44
40
30
25
35
ε max
(10ndash3
)
Fitting curve of VAP and εmax
00 50 times 106 10 times 107 15 times 107 20 times 107 25 times 107 30 times 107 35 times 107
VAP (pixelss)
(b)
Figure 18 Curves of strain parameters with crack propagation velocity VAPand associated results after linear fitting (a) _ε as a function of
VAP (b) εmax as a function of VAP
12 Shock and Vibration
Conflicts of Interest
+e authors declare that they have no conflicts of interest
Acknowledgments
+is research was financially supported by the NationalNatural Science Foundation of China (nos 51274206 and51404277) +is support is greatly acknowledged andappreciated
References
[1] K Xia and W Yao ldquoDynamic rock tests using split Hop-kinson (Kolsky) bar systemmdasha reviewrdquo Journal of RockMechanics and Geotechnical Engineering vol 7 no 1pp 27ndash59 2015
[2] F Gong H Ye and Y Luo ldquo+e effect of high loading rate onthe behaviour and mechanical properties of coal-rock com-bined bodyrdquo Shock and Vibration vol 2018 Article ID4374530 9 pages 2018
[3] Y X Zhou K Xia X B Li et al ldquoSuggested methods fordetermining the dynamic strength parameters and mode-ifracture toughness of rock materialsrdquo International Journal ofRock Mechanics and Mining Sciences vol 49 no 1pp 105ndash112 2012
[4] Y Zhao G-F Zhao Y Jiang D Elsworth and Y HuangldquoEffects of bedding on the dynamic indirect tensile strength ofcoal Laboratory experiments and numerical simulationrdquoInternational Journal of Coal Geology vol 132 pp 81ndash932014
[5] F Dai K Xia and S N Luo ldquoSemicircular bend testing withsplit Hopkinson pressure bar for measuring dynamic tensilestrength of brittle solidsrdquo Review of Scientific Instrumentsvol 79 no 12 article 123903 2008
[6] F Dai K Xia and L Tang ldquoRate dependence of the flexuraltensile strength of Laurentian graniterdquo International Journalof Rock Mechanics and Mining Sciences vol 47 no 3pp 469ndash475 2010
[7] Y Wang ldquoRock dynamic fracture characteristics based onNSCB impact methodrdquo Shock and Vibration vol 2018 Ar-ticle ID 3105384 13 pages 2018
[8] Q B Zhang and J Zhao ldquoEffect of loading rate on fracturetoughness and failure micromechanisms in marblerdquo Engi-neering Fracture Mechanics vol 102 pp 288ndash309 2013
[9] M D Kuruppu Y Obara M R Ayatollahi K P Chong andT Funatsu ldquoISRM-suggested method for determining themode i static fracture toughness using semi-circular bendspecimenrdquo Rock Mechanics and Rock Engineering vol 47no 1 pp 267ndash274 2014
[10] M RM Aliha andM R Ayatollahi ldquoRock fracture toughnessstudy using cracked chevron notched Brazilian disc specimenunder pure modes I and II loadingmdasha statistical approachrdquoeoretical and Applied Fracture Mechanics vol 69 no 2pp 17ndash25 2014
[11] F Dai K Xia H Zheng and Y X Wang ldquoDetermination ofdynamic rock mode-i fracture parameters using crackedchevron notched semi-circular bend specimenrdquo EngineeringFracture Mechanics vol 78 no 15 pp 2633ndash2644 2011
[12] T Tang Z P Bazant S Yang and D Zollinger ldquoVariable-notch one-size test method for fracture energy and processzone lengthrdquo Engineering Fracture Mechanics vol 55 no 3pp 383ndash404 1996
[13] Q Z Wang S Zhang and H P Xie ldquoRock dynamic fracturetoughness tested with holed-cracked flattened Brazilian discsdiametrically impacted by SHPB and its size effectrdquo Experi-mental Mechanics vol 50 no 7 pp 877ndash885 2010
[14] B Lundberg ldquoA split Hopkinson bar study of energy ab-sorption in dynamic rock fragmentationrdquo InternationalJournal of Rock Mechanics and Mining Sciences amp Geo-mechanics Abstracts vol 13 no 6 pp 187ndash197 1976
[15] V Isheyskiy and M Marinin ldquoDetermination of rock massweakening coefficient after blasting in various fracture zonesrdquoEngineering Solid Mechanics vol 5 no 3 pp 199ndash204 2017
[16] G Gary and P Bailly ldquoBehaviour of quasi-brittle material athigh strain rate Experiment and modellingrdquo EuropeanJournal of Mechanics-ASolids vol 17 no 3 pp 403ndash4201998
[17] J Zhao H B Li and Y H ZhaoDynamic Strength Tests of theBukit Timah Granite Nanyang Technological UniversitySingapore 1998
[18] Q B Zhang and J Zhao ldquoA review of dynamic experimentaltechniques andmechanical behaviour of rockmaterialsrdquo RockMechanics and Rock Engineering vol 47 no 4 pp 1411ndash14782014
[19] J Zhao and H B Li ldquoExperimental determination of dynamictensile properties of a graniterdquo International Journal of RockMechanics and Mining Sciences vol 37 no 5 pp 861ndash8662000
[20] J R Klepaczko and A Brara ldquoAn experimental method fordynamic tensile testing of concrete by spallingrdquo InternationalJournal of Impact Engineering vol 25 no 4 pp 387ndash4092001
[21] S Kubota Y Ogata Y Wada G Simangunsong H Shimadaand K Matsui ldquoEstimation of dynamic tensile strength ofsandstonerdquo International Journal of Rock Mechanics andMining Sciences vol 45 no 3 pp 397ndash406 2008
[22] B Erzar and P Forquin ldquoAn experimental method to de-termine the tensile strength of concrete at high rates of strainrdquoExperimental Mechanics vol 50 no 7 pp 941ndash955 2010
[23] L Biolzi and J Labuz ldquoInstabilities in fracture of elastic-softening structuresrdquo Fracture of Engineering Materials andStructures vol 6 no 8 pp 821ndash826 1991
[24] Q ZWangW Li and H P Xie ldquoDynamic split tensile test offlattened Brazilian disc of rock with SHPB setuprdquo Mechanicsof Materials vol 41 no 3 pp 252ndash260 2009
[25] D Asprone E Cadoni A Prota and G Manfredi ldquoDynamicbehavior of a mediterranean natural stone under tensileloadingrdquo International Journal of Rock Mechanics and MiningSciences vol 46 no 3 pp 514ndash520 2009
[26] H Kolsky ldquoAn investigation of the mechanical properties ofmaterials at very high rates of loadingrdquo Proceedings of thePhysical Society Section B vol 62 no 11 pp 676ndash700 1949
[27] U S Lindholm ldquoSome experiments with the split Hopkinsonpressure barrdquo Journal of the Mechanics and Physics of Solidsvol 12 no 5 pp 317ndash335 1964
[28] G Subhash and G Ravichandran Split-Hopkinson PressureBar Testing of Ceramics pp 497ndash504 ASM InternationalMaterials Park OH USA 2000
[29] X Li T Zhou D Li and Z Wang ldquoExperimental and nu-merical investigations on feasibility and validity of prismaticrock specimen in SHPBrdquo Shock and Vibration vol 2016Article ID 7198980 13 pages 2016
[30] M R Ayatollahi and M Sistaninia ldquoMode __ fracture study ofrocks using Brazilian disk specimensrdquo International Journal ofRock Mechanics and Mining Sciences vol 48 no 5pp 819ndash826 2011
Shock and Vibration 13
[31] Q Z Wang X P Gou and H Fan ldquo+e minimum di-mensionless stress intensity factor and its upper bound forCCNBD fracture toughness specimen analyzed with straightthrough crack assumptionrdquo Engineering Fracture Mechanicsvol 82 pp 1ndash8 2012
[32] Q B Zhang and J Zhao ldquoQuasi-static and dynamic fracturebehaviour of rock materials phenomena and mechanismsrdquoInternational Journal of Fracture vol 189 no 1 pp 1ndash322014
[33] A Bertram and J F Kalthoff ldquoCrack propagation toughnessof rock for the range of low to very high crack speedsrdquo KeyEngineering Materials vol 251-252 pp 423ndash430 2003
[34] R Chen K Xia F Dai F Lu and S N Luo ldquoDeterminationof dynamic fracture parameters using a semi-circular bendtechnique in split Hopkinson pressure bar testingrdquo Engi-neering Fracture Mechanics vol 76 no 9 pp 1268ndash12762009
[35] P Forquin ldquoAn optical correlation technique for character-izing the crack velocity in concreterdquo e European PhysicalJournal Special Topics vol 206 no 1 pp 89ndash95 2012
[36] Y Zhao S Gong C Zhang Z Zhang and Y Jiang ldquoFractalcharacteristics of crack propagation in coal under impactloadingrdquo Fractals vol 26 no 2 article 1840014 2018
[37] J T Gomez A Shukla and A Sharma ldquoStatic and dynamicbehavior of concrete and granite in tension with damagerdquoeoretical and Applied Fracture Mechanics vol 36 no 1pp 37ndash49 2001
[38] Q B Zhang and J Zhao ldquoDetermination of mechanicalproperties and full-field strain measurements of rock materialunder dynamic loadsrdquo International Journal of Rock Me-chanics and Mining Sciences vol 60 pp 423ndash439 2013
[39] W Yao Y Xu H-W Liu and K Xia ldquoQuantification ofthermally induced damage and its effect on dynamic fracturetoughness of two mortarsrdquo Engineering Fracture Mechanicsvol 169 pp 74ndash88 2017
[40] T S Yun Y J Jeong K Y Kim and K-B Min ldquoEvaluation ofrock anisotropy using 3D X-ray computed tomographyrdquoEngineering Geology vol 163 pp 11ndash19 2013
[41] T Yin X Li K Xia and S Huang ldquoEffect of thermaltreatment on the dynamic fracture toughness of Laurentiangraniterdquo Rock Mechanics and Rock Engineering vol 45 no 6pp 1087ndash1094 2012
[42] S Huang K Xia F Yan and X Feng ldquoAn experimental studyof the rate dependence of tensile strength softening ofLongyou sandstonerdquo Rock Mechanics and Rock Engineeringvol 43 no 6 pp 677ndash683 2010
[43] S N Luo B J Jensen D E Hooks et al ldquoGas gun shockexperiments with single-pulse X-ray phase contrast imagingand diffraction at the advanced photon sourcerdquo Review ofScientific Instruments vol 83 no 7 article 073903 2012
[44] M Hudspeth B Claus S Dubelman et al ldquoHigh speedsynchrotron X-ray phase contrast imaging of dynamic ma-terial response to split Hopkinson bar loadingrdquo Review ofScientific Instruments vol 84 no 2 article 025102 2013
[45] Y Li and K T Ramesh ldquoAn optical technique for mea-surement of material properties in the tension Kolsky barrdquoInternational Journal of Impact Engineering vol 34 no 4pp 784ndash798 2007
[46] G Gao S Huang K Xia and Z Li ldquoApplication of digitalimage correlation (DIC) in dynamic notched semi-circularbend (NSCB) testsrdquo Experimental Mechanics vol 55 no 1pp 95ndash104 2015
[47] B Pan K Qian H Xie and A Asundi ldquoTwo-dimensionaldigital image correlation for in-plane displacement and strain
measurement a reviewrdquo Measurement Science and Technol-ogy vol 20 no 6 article 062001 2009
[48] F Amiot M Bornert P Doumalin et al ldquoAssessment ofdigital image correlation measurement accuracy in the ulti-mate error regime main results of a collaborative bench-markrdquo Strain vol 49 no 6 pp 483ndash496 2013
[49] W Shi Y Wu and L Wu ldquoQuantitative analysis of theprojectile impact on rock using infrared thermographyrdquoInternational Journal of Impact Engineering vol 34 no 5pp 990ndash1002 2007
[50] D K Iakovidis T Goudas C V Smailis and I MaglogiannisldquoRatsnake a versatile image annotation tool with applicationto computer-aided diagnosisrdquo e Scientific World Journalvol 2014 Article ID 286856 12 pages 2014
[51] B A Han H Y Xiang Z Li and J J Huang ldquoDefects de-tection of sheet metal parts based on HALCON and regionmorphologyrdquo Applied Mechanics and Materials vol 365-366pp 729ndash732 2013
[52] D Ai Y Zhao Q Wang and C Li ldquoExperimental andnumerical investigation of crack propagation and dynamicproperties of rock in SHPB indirect tension testrdquo In-ternational Journal of Impact Engineering vol 126 pp 135ndash146 2019
[53] H Xie and D J Sanderson ldquoFractal effects of crack propa-gation on dynamic stress intensity factors and crack veloci-tiesrdquo International Journal of Fracture vol 74 no 1pp 29ndash42 1996
[54] F Dai R Chen and K Xia ldquoA semi-circular bend techniquefor determining dynamic fracture toughnessrdquo ExperimentalMechanics vol 50 no 6 pp 783ndash791 2010
[55] D Chakerian and B B Mandelbrot ldquo+e fractal geometry ofnaturerdquo College Mathematics Journal vol 15 no 2pp 175ndash177 1984
[56] K Falconer ldquoFractal geometry mathematical foundationsand applicationsrdquo Biometrics vol 46 no 3 pp 886-887 1990
[57] T-B Yin K Peng L Wang P Wang X-Y Yin andY-L Zhang ldquoStudy on impact damage and energy dissipationof coal rock exposed to high temperaturesrdquo Shock and Vi-bration vol 2016 Article ID 5121932 10 pages 2016
14 Shock and Vibration
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
RoboticsJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
VLSI Design
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawiwwwhindawicom
Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Control Scienceand Engineering
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
SensorsJournal of
Hindawiwwwhindawicom Volume 2018
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
Conflicts of Interest
+e authors declare that they have no conflicts of interest
Acknowledgments
+is research was financially supported by the NationalNatural Science Foundation of China (nos 51274206 and51404277) +is support is greatly acknowledged andappreciated
References
[1] K Xia and W Yao ldquoDynamic rock tests using split Hop-kinson (Kolsky) bar systemmdasha reviewrdquo Journal of RockMechanics and Geotechnical Engineering vol 7 no 1pp 27ndash59 2015
[2] F Gong H Ye and Y Luo ldquo+e effect of high loading rate onthe behaviour and mechanical properties of coal-rock com-bined bodyrdquo Shock and Vibration vol 2018 Article ID4374530 9 pages 2018
[3] Y X Zhou K Xia X B Li et al ldquoSuggested methods fordetermining the dynamic strength parameters and mode-ifracture toughness of rock materialsrdquo International Journal ofRock Mechanics and Mining Sciences vol 49 no 1pp 105ndash112 2012
[4] Y Zhao G-F Zhao Y Jiang D Elsworth and Y HuangldquoEffects of bedding on the dynamic indirect tensile strength ofcoal Laboratory experiments and numerical simulationrdquoInternational Journal of Coal Geology vol 132 pp 81ndash932014
[5] F Dai K Xia and S N Luo ldquoSemicircular bend testing withsplit Hopkinson pressure bar for measuring dynamic tensilestrength of brittle solidsrdquo Review of Scientific Instrumentsvol 79 no 12 article 123903 2008
[6] F Dai K Xia and L Tang ldquoRate dependence of the flexuraltensile strength of Laurentian graniterdquo International Journalof Rock Mechanics and Mining Sciences vol 47 no 3pp 469ndash475 2010
[7] Y Wang ldquoRock dynamic fracture characteristics based onNSCB impact methodrdquo Shock and Vibration vol 2018 Ar-ticle ID 3105384 13 pages 2018
[8] Q B Zhang and J Zhao ldquoEffect of loading rate on fracturetoughness and failure micromechanisms in marblerdquo Engi-neering Fracture Mechanics vol 102 pp 288ndash309 2013
[9] M D Kuruppu Y Obara M R Ayatollahi K P Chong andT Funatsu ldquoISRM-suggested method for determining themode i static fracture toughness using semi-circular bendspecimenrdquo Rock Mechanics and Rock Engineering vol 47no 1 pp 267ndash274 2014
[10] M RM Aliha andM R Ayatollahi ldquoRock fracture toughnessstudy using cracked chevron notched Brazilian disc specimenunder pure modes I and II loadingmdasha statistical approachrdquoeoretical and Applied Fracture Mechanics vol 69 no 2pp 17ndash25 2014
[11] F Dai K Xia H Zheng and Y X Wang ldquoDetermination ofdynamic rock mode-i fracture parameters using crackedchevron notched semi-circular bend specimenrdquo EngineeringFracture Mechanics vol 78 no 15 pp 2633ndash2644 2011
[12] T Tang Z P Bazant S Yang and D Zollinger ldquoVariable-notch one-size test method for fracture energy and processzone lengthrdquo Engineering Fracture Mechanics vol 55 no 3pp 383ndash404 1996
[13] Q Z Wang S Zhang and H P Xie ldquoRock dynamic fracturetoughness tested with holed-cracked flattened Brazilian discsdiametrically impacted by SHPB and its size effectrdquo Experi-mental Mechanics vol 50 no 7 pp 877ndash885 2010
[14] B Lundberg ldquoA split Hopkinson bar study of energy ab-sorption in dynamic rock fragmentationrdquo InternationalJournal of Rock Mechanics and Mining Sciences amp Geo-mechanics Abstracts vol 13 no 6 pp 187ndash197 1976
[15] V Isheyskiy and M Marinin ldquoDetermination of rock massweakening coefficient after blasting in various fracture zonesrdquoEngineering Solid Mechanics vol 5 no 3 pp 199ndash204 2017
[16] G Gary and P Bailly ldquoBehaviour of quasi-brittle material athigh strain rate Experiment and modellingrdquo EuropeanJournal of Mechanics-ASolids vol 17 no 3 pp 403ndash4201998
[17] J Zhao H B Li and Y H ZhaoDynamic Strength Tests of theBukit Timah Granite Nanyang Technological UniversitySingapore 1998
[18] Q B Zhang and J Zhao ldquoA review of dynamic experimentaltechniques andmechanical behaviour of rockmaterialsrdquo RockMechanics and Rock Engineering vol 47 no 4 pp 1411ndash14782014
[19] J Zhao and H B Li ldquoExperimental determination of dynamictensile properties of a graniterdquo International Journal of RockMechanics and Mining Sciences vol 37 no 5 pp 861ndash8662000
[20] J R Klepaczko and A Brara ldquoAn experimental method fordynamic tensile testing of concrete by spallingrdquo InternationalJournal of Impact Engineering vol 25 no 4 pp 387ndash4092001
[21] S Kubota Y Ogata Y Wada G Simangunsong H Shimadaand K Matsui ldquoEstimation of dynamic tensile strength ofsandstonerdquo International Journal of Rock Mechanics andMining Sciences vol 45 no 3 pp 397ndash406 2008
[22] B Erzar and P Forquin ldquoAn experimental method to de-termine the tensile strength of concrete at high rates of strainrdquoExperimental Mechanics vol 50 no 7 pp 941ndash955 2010
[23] L Biolzi and J Labuz ldquoInstabilities in fracture of elastic-softening structuresrdquo Fracture of Engineering Materials andStructures vol 6 no 8 pp 821ndash826 1991
[24] Q ZWangW Li and H P Xie ldquoDynamic split tensile test offlattened Brazilian disc of rock with SHPB setuprdquo Mechanicsof Materials vol 41 no 3 pp 252ndash260 2009
[25] D Asprone E Cadoni A Prota and G Manfredi ldquoDynamicbehavior of a mediterranean natural stone under tensileloadingrdquo International Journal of Rock Mechanics and MiningSciences vol 46 no 3 pp 514ndash520 2009
[26] H Kolsky ldquoAn investigation of the mechanical properties ofmaterials at very high rates of loadingrdquo Proceedings of thePhysical Society Section B vol 62 no 11 pp 676ndash700 1949
[27] U S Lindholm ldquoSome experiments with the split Hopkinsonpressure barrdquo Journal of the Mechanics and Physics of Solidsvol 12 no 5 pp 317ndash335 1964
[28] G Subhash and G Ravichandran Split-Hopkinson PressureBar Testing of Ceramics pp 497ndash504 ASM InternationalMaterials Park OH USA 2000
[29] X Li T Zhou D Li and Z Wang ldquoExperimental and nu-merical investigations on feasibility and validity of prismaticrock specimen in SHPBrdquo Shock and Vibration vol 2016Article ID 7198980 13 pages 2016
[30] M R Ayatollahi and M Sistaninia ldquoMode __ fracture study ofrocks using Brazilian disk specimensrdquo International Journal ofRock Mechanics and Mining Sciences vol 48 no 5pp 819ndash826 2011
Shock and Vibration 13
[31] Q Z Wang X P Gou and H Fan ldquo+e minimum di-mensionless stress intensity factor and its upper bound forCCNBD fracture toughness specimen analyzed with straightthrough crack assumptionrdquo Engineering Fracture Mechanicsvol 82 pp 1ndash8 2012
[32] Q B Zhang and J Zhao ldquoQuasi-static and dynamic fracturebehaviour of rock materials phenomena and mechanismsrdquoInternational Journal of Fracture vol 189 no 1 pp 1ndash322014
[33] A Bertram and J F Kalthoff ldquoCrack propagation toughnessof rock for the range of low to very high crack speedsrdquo KeyEngineering Materials vol 251-252 pp 423ndash430 2003
[34] R Chen K Xia F Dai F Lu and S N Luo ldquoDeterminationof dynamic fracture parameters using a semi-circular bendtechnique in split Hopkinson pressure bar testingrdquo Engi-neering Fracture Mechanics vol 76 no 9 pp 1268ndash12762009
[35] P Forquin ldquoAn optical correlation technique for character-izing the crack velocity in concreterdquo e European PhysicalJournal Special Topics vol 206 no 1 pp 89ndash95 2012
[36] Y Zhao S Gong C Zhang Z Zhang and Y Jiang ldquoFractalcharacteristics of crack propagation in coal under impactloadingrdquo Fractals vol 26 no 2 article 1840014 2018
[37] J T Gomez A Shukla and A Sharma ldquoStatic and dynamicbehavior of concrete and granite in tension with damagerdquoeoretical and Applied Fracture Mechanics vol 36 no 1pp 37ndash49 2001
[38] Q B Zhang and J Zhao ldquoDetermination of mechanicalproperties and full-field strain measurements of rock materialunder dynamic loadsrdquo International Journal of Rock Me-chanics and Mining Sciences vol 60 pp 423ndash439 2013
[39] W Yao Y Xu H-W Liu and K Xia ldquoQuantification ofthermally induced damage and its effect on dynamic fracturetoughness of two mortarsrdquo Engineering Fracture Mechanicsvol 169 pp 74ndash88 2017
[40] T S Yun Y J Jeong K Y Kim and K-B Min ldquoEvaluation ofrock anisotropy using 3D X-ray computed tomographyrdquoEngineering Geology vol 163 pp 11ndash19 2013
[41] T Yin X Li K Xia and S Huang ldquoEffect of thermaltreatment on the dynamic fracture toughness of Laurentiangraniterdquo Rock Mechanics and Rock Engineering vol 45 no 6pp 1087ndash1094 2012
[42] S Huang K Xia F Yan and X Feng ldquoAn experimental studyof the rate dependence of tensile strength softening ofLongyou sandstonerdquo Rock Mechanics and Rock Engineeringvol 43 no 6 pp 677ndash683 2010
[43] S N Luo B J Jensen D E Hooks et al ldquoGas gun shockexperiments with single-pulse X-ray phase contrast imagingand diffraction at the advanced photon sourcerdquo Review ofScientific Instruments vol 83 no 7 article 073903 2012
[44] M Hudspeth B Claus S Dubelman et al ldquoHigh speedsynchrotron X-ray phase contrast imaging of dynamic ma-terial response to split Hopkinson bar loadingrdquo Review ofScientific Instruments vol 84 no 2 article 025102 2013
[45] Y Li and K T Ramesh ldquoAn optical technique for mea-surement of material properties in the tension Kolsky barrdquoInternational Journal of Impact Engineering vol 34 no 4pp 784ndash798 2007
[46] G Gao S Huang K Xia and Z Li ldquoApplication of digitalimage correlation (DIC) in dynamic notched semi-circularbend (NSCB) testsrdquo Experimental Mechanics vol 55 no 1pp 95ndash104 2015
[47] B Pan K Qian H Xie and A Asundi ldquoTwo-dimensionaldigital image correlation for in-plane displacement and strain
measurement a reviewrdquo Measurement Science and Technol-ogy vol 20 no 6 article 062001 2009
[48] F Amiot M Bornert P Doumalin et al ldquoAssessment ofdigital image correlation measurement accuracy in the ulti-mate error regime main results of a collaborative bench-markrdquo Strain vol 49 no 6 pp 483ndash496 2013
[49] W Shi Y Wu and L Wu ldquoQuantitative analysis of theprojectile impact on rock using infrared thermographyrdquoInternational Journal of Impact Engineering vol 34 no 5pp 990ndash1002 2007
[50] D K Iakovidis T Goudas C V Smailis and I MaglogiannisldquoRatsnake a versatile image annotation tool with applicationto computer-aided diagnosisrdquo e Scientific World Journalvol 2014 Article ID 286856 12 pages 2014
[51] B A Han H Y Xiang Z Li and J J Huang ldquoDefects de-tection of sheet metal parts based on HALCON and regionmorphologyrdquo Applied Mechanics and Materials vol 365-366pp 729ndash732 2013
[52] D Ai Y Zhao Q Wang and C Li ldquoExperimental andnumerical investigation of crack propagation and dynamicproperties of rock in SHPB indirect tension testrdquo In-ternational Journal of Impact Engineering vol 126 pp 135ndash146 2019
[53] H Xie and D J Sanderson ldquoFractal effects of crack propa-gation on dynamic stress intensity factors and crack veloci-tiesrdquo International Journal of Fracture vol 74 no 1pp 29ndash42 1996
[54] F Dai R Chen and K Xia ldquoA semi-circular bend techniquefor determining dynamic fracture toughnessrdquo ExperimentalMechanics vol 50 no 6 pp 783ndash791 2010
[55] D Chakerian and B B Mandelbrot ldquo+e fractal geometry ofnaturerdquo College Mathematics Journal vol 15 no 2pp 175ndash177 1984
[56] K Falconer ldquoFractal geometry mathematical foundationsand applicationsrdquo Biometrics vol 46 no 3 pp 886-887 1990
[57] T-B Yin K Peng L Wang P Wang X-Y Yin andY-L Zhang ldquoStudy on impact damage and energy dissipationof coal rock exposed to high temperaturesrdquo Shock and Vi-bration vol 2016 Article ID 5121932 10 pages 2016
14 Shock and Vibration
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
RoboticsJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
VLSI Design
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawiwwwhindawicom
Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Control Scienceand Engineering
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
SensorsJournal of
Hindawiwwwhindawicom Volume 2018
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
[31] Q Z Wang X P Gou and H Fan ldquo+e minimum di-mensionless stress intensity factor and its upper bound forCCNBD fracture toughness specimen analyzed with straightthrough crack assumptionrdquo Engineering Fracture Mechanicsvol 82 pp 1ndash8 2012
[32] Q B Zhang and J Zhao ldquoQuasi-static and dynamic fracturebehaviour of rock materials phenomena and mechanismsrdquoInternational Journal of Fracture vol 189 no 1 pp 1ndash322014
[33] A Bertram and J F Kalthoff ldquoCrack propagation toughnessof rock for the range of low to very high crack speedsrdquo KeyEngineering Materials vol 251-252 pp 423ndash430 2003
[34] R Chen K Xia F Dai F Lu and S N Luo ldquoDeterminationof dynamic fracture parameters using a semi-circular bendtechnique in split Hopkinson pressure bar testingrdquo Engi-neering Fracture Mechanics vol 76 no 9 pp 1268ndash12762009
[35] P Forquin ldquoAn optical correlation technique for character-izing the crack velocity in concreterdquo e European PhysicalJournal Special Topics vol 206 no 1 pp 89ndash95 2012
[36] Y Zhao S Gong C Zhang Z Zhang and Y Jiang ldquoFractalcharacteristics of crack propagation in coal under impactloadingrdquo Fractals vol 26 no 2 article 1840014 2018
[37] J T Gomez A Shukla and A Sharma ldquoStatic and dynamicbehavior of concrete and granite in tension with damagerdquoeoretical and Applied Fracture Mechanics vol 36 no 1pp 37ndash49 2001
[38] Q B Zhang and J Zhao ldquoDetermination of mechanicalproperties and full-field strain measurements of rock materialunder dynamic loadsrdquo International Journal of Rock Me-chanics and Mining Sciences vol 60 pp 423ndash439 2013
[39] W Yao Y Xu H-W Liu and K Xia ldquoQuantification ofthermally induced damage and its effect on dynamic fracturetoughness of two mortarsrdquo Engineering Fracture Mechanicsvol 169 pp 74ndash88 2017
[40] T S Yun Y J Jeong K Y Kim and K-B Min ldquoEvaluation ofrock anisotropy using 3D X-ray computed tomographyrdquoEngineering Geology vol 163 pp 11ndash19 2013
[41] T Yin X Li K Xia and S Huang ldquoEffect of thermaltreatment on the dynamic fracture toughness of Laurentiangraniterdquo Rock Mechanics and Rock Engineering vol 45 no 6pp 1087ndash1094 2012
[42] S Huang K Xia F Yan and X Feng ldquoAn experimental studyof the rate dependence of tensile strength softening ofLongyou sandstonerdquo Rock Mechanics and Rock Engineeringvol 43 no 6 pp 677ndash683 2010
[43] S N Luo B J Jensen D E Hooks et al ldquoGas gun shockexperiments with single-pulse X-ray phase contrast imagingand diffraction at the advanced photon sourcerdquo Review ofScientific Instruments vol 83 no 7 article 073903 2012
[44] M Hudspeth B Claus S Dubelman et al ldquoHigh speedsynchrotron X-ray phase contrast imaging of dynamic ma-terial response to split Hopkinson bar loadingrdquo Review ofScientific Instruments vol 84 no 2 article 025102 2013
[45] Y Li and K T Ramesh ldquoAn optical technique for mea-surement of material properties in the tension Kolsky barrdquoInternational Journal of Impact Engineering vol 34 no 4pp 784ndash798 2007
[46] G Gao S Huang K Xia and Z Li ldquoApplication of digitalimage correlation (DIC) in dynamic notched semi-circularbend (NSCB) testsrdquo Experimental Mechanics vol 55 no 1pp 95ndash104 2015
[47] B Pan K Qian H Xie and A Asundi ldquoTwo-dimensionaldigital image correlation for in-plane displacement and strain
measurement a reviewrdquo Measurement Science and Technol-ogy vol 20 no 6 article 062001 2009
[48] F Amiot M Bornert P Doumalin et al ldquoAssessment ofdigital image correlation measurement accuracy in the ulti-mate error regime main results of a collaborative bench-markrdquo Strain vol 49 no 6 pp 483ndash496 2013
[49] W Shi Y Wu and L Wu ldquoQuantitative analysis of theprojectile impact on rock using infrared thermographyrdquoInternational Journal of Impact Engineering vol 34 no 5pp 990ndash1002 2007
[50] D K Iakovidis T Goudas C V Smailis and I MaglogiannisldquoRatsnake a versatile image annotation tool with applicationto computer-aided diagnosisrdquo e Scientific World Journalvol 2014 Article ID 286856 12 pages 2014
[51] B A Han H Y Xiang Z Li and J J Huang ldquoDefects de-tection of sheet metal parts based on HALCON and regionmorphologyrdquo Applied Mechanics and Materials vol 365-366pp 729ndash732 2013
[52] D Ai Y Zhao Q Wang and C Li ldquoExperimental andnumerical investigation of crack propagation and dynamicproperties of rock in SHPB indirect tension testrdquo In-ternational Journal of Impact Engineering vol 126 pp 135ndash146 2019
[53] H Xie and D J Sanderson ldquoFractal effects of crack propa-gation on dynamic stress intensity factors and crack veloci-tiesrdquo International Journal of Fracture vol 74 no 1pp 29ndash42 1996
[54] F Dai R Chen and K Xia ldquoA semi-circular bend techniquefor determining dynamic fracture toughnessrdquo ExperimentalMechanics vol 50 no 6 pp 783ndash791 2010
[55] D Chakerian and B B Mandelbrot ldquo+e fractal geometry ofnaturerdquo College Mathematics Journal vol 15 no 2pp 175ndash177 1984
[56] K Falconer ldquoFractal geometry mathematical foundationsand applicationsrdquo Biometrics vol 46 no 3 pp 886-887 1990
[57] T-B Yin K Peng L Wang P Wang X-Y Yin andY-L Zhang ldquoStudy on impact damage and energy dissipationof coal rock exposed to high temperaturesrdquo Shock and Vi-bration vol 2016 Article ID 5121932 10 pages 2016
14 Shock and Vibration
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
RoboticsJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
VLSI Design
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawiwwwhindawicom
Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Control Scienceand Engineering
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
SensorsJournal of
Hindawiwwwhindawicom Volume 2018
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
International Journal of
AerospaceEngineeringHindawiwwwhindawicom Volume 2018
RoboticsJournal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Active and Passive Electronic Components
VLSI Design
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Shock and Vibration
Hindawiwwwhindawicom Volume 2018
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawiwwwhindawicom
Volume 2018
Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom
The Scientific World Journal
Volume 2018
Control Scienceand Engineering
Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom
Journal ofEngineeringVolume 2018
SensorsJournal of
Hindawiwwwhindawicom Volume 2018
International Journal of
RotatingMachinery
Hindawiwwwhindawicom Volume 2018
Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom