Research ArticleDynamic Crack Propagation and Fracture Behavior ofPre-cracked Specimens under Impact Loading by SplitHopkinson Pressure Bar

Shijun Zhao 12 and Qing Zhang 1

1College of Mechanics and Materials Hohai University Nanjing 211100 China2Department of Mechanical and Materials Engineering University of Nebraska-Lincoln Lincoln NE 68588 USA

Correspondence should be addressed to Qing Zhang lxzhangqinghhueducn

Received 25 March 2019 Revised 7 May 2019 Accepted 20 May 2019 Published 23 June 2019

Guest Editor Grzegorz Lesiuk

Copyright copy 2019 Shijun Zhao and Qing Zhang -is is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in anymedium provided the original work isproperly cited

Deformation and fracture of brittle materials especially crack propagation have drawn wide attention in recent years But dynamiccrack propagation under impact loading was not well understood In this paper we experimentally tested Brazilian disk (BD) finesandstone specimens containing pre-cracks under cyclic impact loading by the Φ 74mm diameter split Hopkinson pressure bar(SHPB) test device -e pre-cracked specimens were named central straight through crack flattened Brazilian disk (CSCFBD) Byusing the low air-pressure loading conditions (01MPa equal to the impact velocity of 376ms) a series of dynamic impact tests weredetected successfully and the effects of pre-cracks on dynamic properties were analyzed Experimental results show that the multiplecracks mostly initiate ator near the pre-crack tips and then propagate in different paths and directions varying by inclination anglesleading to the ultimate failure Compared to static or quasi-static loading dynamic crack propagation and fracture behavior areobviously different Furthermore we characterized the crack propagation paths directions and fracture patterns and discussed theinfluences of the pre-cracks during the breakage process We concluded that the results obtained are significant in investigating thefailure mechanism and mechanical properties of brittle materials under impact loading

1 Introduction

Dynamic deformation and fracture of brittle materials arecomplex processes Mining tunnel excavation and naturaldisasters such as landslides and earthquakes are all involvedin the problems of dynamic damage -e failure of brittlematerials is usually associated with crack propagation ini-tiated from natural or artificial pre-existing defects More-over the mechanical properties of brittle materials areclosely related to external loading conditions such asloading rate and load magnitude [1ndash3] Rock is one of themost complex brittle materials containing different scalevoids cracks and other defects as shown in Figure 1 whichare the main mechanical factors that affect the rock de-formation and failure [4] Crack growth and catastrophicfailures initiated from pre-existing defects subjected to

multiaxial loads are the main concerns for geotechnicalengineers and designers of underground structures -edefects in rock can promote the initiation of new defectswhich in turnmay propagate and coalesce with other defectsand then can further decrease the strength of the rock mass[5ndash8] -e presence of pre-cracks may obviously reduce thefracture toughness dynamic uniaxial compressive strengthand dynamic tensile strength and lead to fragmentation andmultiple crack interactions branching and coalescence [9]

Due to the difficulties of in-situ tests the laboratoryexperiment is an important and effective research method toinvestigate rock failure modes and fracture mechanismsOver the past few decades many experiments have beendevoted to use semi-circular core in the three-point bending(SCB) specimen [10] Brazilian disk (BD) specimen withchevron flaws or other pre-existing flaws [11] radial cracked

HindawiAdvances in Materials Science and EngineeringVolume 2019 Article ID 2383861 11 pageshttpsdoiorg10115520192383861

ring (RCR) specimen [12] and modified ring (MR) specimen[13] to investigate fracture toughness and crack propagationNote that in previous studies the fracture behavior and crackpropagation of brittle materials were mainly investigatedunder staticquasi-static loading or used in intact specimensIrwin et al [14ndash16] divided the simple cracks into three typesin the basic failure process Mode I (the tensionopeningmode) crack Mode II (the sliding mode) and Mode III (thetearing mode) crack In engineering Mode I cracks are ofprime importance More complicated cracks can form fromthese simple cracks called mixed-mode cracks Many ex-perimental studies have been conducted to explain the crackinitiation propagation and coalescence in pre-cracked brittlematerials under static or quasi-static loading [17ndash21] -e BDtest is an effective way to study crack propagation and fracturebehavior of brittle materials [22 23] Al-Shayea [24] studiedcrack propagation paths in pre-cracked limestone centralstraight though crack Brazilian disk (CSCBD) specimensloaded with diametrical compression and they investigatedthe possibility of using outcrop specimens to estimate thefracture toughness behavior of the reservoir rock at in-situconditions of temperature and confining pressure Haeri et al[25ndash27] used Portland Pozzolana Cement (PPC) experi-mentally and studied crack propagation and crack co-alescence of BD pre-cracked and pre-holed specimens underquasi-static compressive and tensile loading Aliha andBahmani [28] investigated fracture toughness under mixed-mode loading using different cylindrical and disc shapes forthe brittle material However in deep strata the damage anddestruction of rock mass are often caused by dynamic evencyclic dynamic loading None of these investigations listedabove has ever captured the dynamic multiple crack propa-gation In such cases it is of great significance and essential toinvestigate the dynamic crack propagation and fracturepatterns of rock in deep strata under impactcyclic impactloading

Various experiments devices have been used to explore awide range of strain rates Split Hopkinson pressure bar(SHPB) technique which decouples cleverly the inertia effectin structures and strain rate effect in materials has beenwidely used to characterize the dynamic performance ofvarious engineering materials at high strain rate such as rock[29ndash33] concrete [34ndash38] and ceramics [39 40] at high strain

rates (102sim104 sminus1) -e strain rate sensitive behavior of brittlematerials has been under investigation for several decades-e strain rate sensitivities are mainly measured by strengthor the strains at themaximum stress [41 42] In recent years avariety of researchers have investigated and demonstrated thedynamic properties of natural or artificial brittle materials[43ndash47] and they found that the dynamic strength (includingdynamic compressive strength and dynamic tensile strength)and impact toughness increases with strain rate and the strainrate sensitivity of brittle materials

In this paper we defined some central straight throughcrack flattened Brazilian disk (CSCFBD) specimens to in-vestigate dynamic crack propagation and fracture patternsunder impact loading by the SHPB device and the termldquopre-crack(s)rdquo is used to describe the artificially createdcrack -e motivation for this work will focus on the fol-lowing two points (1) investigating the dynamic fracturepatterns multiple crack propagation paths and directions inpre-cracked specimens (2) characterizing and analyzing thecrack types initiated from pre-cracks under cyclic impactloading -is paper is organized as follows in Section 2 thepreparation of tested CSCFBD specimens and experimentalprocedure are discussed -e SHPB experimental scheme isalso introduced In Section 3 we present the experimentalresults We look at both the multiple crack propagationpaths and directions In Section 4 we discuss the experi-mental results and characterize the dynamic fracture pat-terns and failure modes -e conclusions concluded uponthe foregoing results are given in Section 5

2 Preparation of Disk Specimens andExperimental Procedure

Due to the crystalline and blocky structures fine sandstone iswidely used to investigate the fracture behavior and crackpropagation of defected brittle materials In this paper weused fine sandstone to study the dynamic crack propagationunder impact loading -e fine sandstone samples wereexcavated by geologic drilling from about 900-meter depthunderground strata in Juye coalfield whose Cenozoic for-mation is very thick -e average thickness of strata in thefourth system is 15843m and the average thickness of theupper tertiary strata is 49701m And the thickness of thenew boundary layer is 530sim720m mainly composed of claysandy clay sand fine sand and gravel Main coal seam roofand floor sandstone thickness is 480sim7565m mainly finesandstone local sandstone and siltstone [4] -e pre-cracked specimensrsquo preparation and experimental pro-cedures will be explained as follows

21 Preparation of CSCFBD Specimens For manufacturingCSCFBD specimens the whole tests used six samples witheach one cored into 30sim50 cm long diameter D= 62mmcylindrical columns in the construction site In order toavoid external environmental influence the surface of thesamples was wrapped in the multilayer food preservationfilm after removing from the formation-e specimens werecut into BD shapes with the size of Φ 62times 30mm -ree

Figure 1 Schematic view of pre-existing defects in the natural rockmass [4]

2 Advances in Materials Science and Engineering

specimens with same pre-crack geometry were prepared toguarantee the reproducibility of these experimental testsand a total number of 21 CSCFBD specimens were manu-factured in this work -e physical and mechanical prop-erties of the tested fine sandstone are listed in Table 1

Various Brazilian tests were conducted on CSCFBDspecimens containing a single crack with different in-clination angles -ese pre-cracks were created by the high-speed water jet cutting machine [4] as shown in Figure 2Figure 3 shows pre-cracked specimens with different in-clination angles and the crack inclination angle β (the anglebetween the normal line of the pre-crack surface and thevertical direction of the impact load) β= 0deg 15deg 30deg 45deg 60deg75deg and 90deg Figure 4 shows a schematic view of CSCFBDspecimens -e pre-cracks length 2b (b is the half of pre-crack length) is equal to 10mm and the crack width is1mm -e radius and thickness of the CSCFBD specimenare R= 31mm and H= 30mm Crack length ratio is animportant parameter for the pattern trajectory and thenumber of fractures in this work the ratio bR is 016

22 SHPB Experimental Procedure In this work the dy-namic tests were taken in the structure laboratory of HohaiUniversity adopting Φ 74mm diameter straight tapervariable cross sections SHPB device -e Φ 74mm diameterSHPB device mainly composes of the power system (whichpropelled by a gas gun) elastic bars (an incident bar atransmitter bar and an absorbing bar) a damper energyabsorbing setup high dynamic strain indicator and dataprocessing systems -e power system consists of an aircompressor and pressure vessel -e impact velocity ismeasured by the light electric tachometer Schematic of theSHPB test device is shown in Figure 5

-e SHPB device is based on the one-dimensional theoryof elastic wave and uses Lagrangian coordinates to describeall the physical parameters -e control equations of wavesin the bars are on the following assumptions One-dimensional assumption speed v and the strain ε are onlythe function of point X and time t and the assumption thatthe strain rate is independent Assuming axial wave prop-agation and homogeneous stress distribution in the speci-men the resulting stress σs(t) strain εs(t) and strain rate_ε(t) of the specimen are obtained by the following equation[48]

σs(t) SBE

2SSεt(t) + εr(t) + εi(t)1113858 1113859

_εs(t) C0

Lsεt(t) + εr(t)minus εi(t)1113858 1113859

εt(t) C0

LS1113946

t

0εt(t) + εr(t)minus εi(t)1113858 1113859dτ

(1)

where SB E and C0 are the cross-sectional area (mm2)Youngrsquos modulus (GPa) and the wave velocity (kms) ofthe bar material and LS and Ss are the length (mm) andcross-sectional area (mm2) of the specimen εi(t) εr(t) andεt(t) are the strain singles in specimen -e diameter

Youngrsquos modulus and density of the elastic bars are 74mm210 GPa and 7850 kgm3 respectively

In fact during the experimental tests by BD specimensthe cracks of samples are first produced by the center andthen expanded along the radial direction Wang et al [49]presented that if the samples between two planes parallel tothe plane of the degree of smoothness and not less than005mm then they can ensure that the fracture initiatedfrom the specimen center -e loading areas corresponding

Table 1 Physical and mechanical properties of the tested finesandstone

Properties ValueYoungrsquos modulus E (GPa) 111Compressive strength σc (MPa) 841Brazilian tensile strength σt (MPa) 30Longitudinal wave velocity VP (ms) 35264Porosity () 83Poissonrsquos ratio v 033Density ρ (kgm3) 2692

Figure 2 Pre-crack preparation in CSCFBD specimens using awater jet cutting machine [4]

Figure 3 Schematic view of CSCFBD specimens with differentinclination angles of pre-cracks

Advances in Materials Science and Engineering 3

to the center angle 2α to meet 20degle 2αle 30deg Figure 6 showsthe attened BD specimen under radial loading Before theinstallation of the specimens a layer of Vaseline is evenlyapplied to the contact between the end of the specimen andthe end of the compression bar and the specimens need tobe tightened between the incident bar and the transmitterbar During SHPB tests the brittle materials may fail beforestress uniformly is achieved within the specimens Modi -cation of the incident pulse to closely match the elasticresponse is required e pulse shaping technique has beenwidely applied in SHPB testing of engineering materials andit is especially used for investigating the dynamic response ofbrittle materials In this paper we used a pulse shapingtechnique a thin copper disk (12 mm-diameter and 1mm-thickness) which was placed on the impact side of the in-cident bar e pulse shape can attenuate high-frequencyoscillations of the incident stress wave to improve the stresswave shape Pulse shaping technique allows for controllingthe damage of brittle materials [29 30]

3 Experimental Results

31 Impact Time Analysis of CSCFBD Specimens Duringtesting the air pressure in the gas gun chamber was keptconstant 01MPa equal to the impact velocity 376ms andthe bullet must be brought back to its original positionbefore the next loading e times of impacts were recordedfor each specimen until nal failure As shown in Figure 7 toreach the nal crack propagation paths forms 6 times

impact loading are needed when β= 0deg and the impact timesare 3 4 6 4 2 and 2 when β= 15deg 30deg 45deg 60deg 75deg and 90degrespectively It is obvious that the impact times in nalfailure are related to the pre-existing inclination anglesBecause pre-cracks can make the specimen strength to re-duce so when β= 15deg 75deg and 90deg the impact times areusually less than the cases of β= 0deg 30deg 45deg and 90deg

32 Dynamic Crack Propagation Paths and Directions ofCSCFBD Specimens In this paper we investigated the dy-namic crack propagation paths and directions in CSCFBDspecimens In Figure 8 the crack propagation paths in

BufferAbsorbing bar

Strain gauge

High-dynamic strain indicator

Waveform memory Data processing systems

Light electric tachometer

BulletLauncher Incident bar Specimen Transmitter bar

Figure 5 Schematic of the split Hopkinson pressure bar (SHPB) device

2α2αP P

Specimen62 mm

Incident bar Transmitterbar

Figure 6 Flattened BD specimen under radial impact loading

P

β2b

P

Figure 4 Schematic view of the ne sandstone CSCFBD specimen

4 Advances in Materials Science and Engineering

CSCFBD specimens with dierent inclination angles areindicated and for all gures the upper plane edges of thespecimens are contacted with the incident bar As shown inFigures 8(b)ndash8(g) cracks initiated from the tips of pre-cracksand approximately propagated towards the direction of themaximum stress It should be noted that in Figure 8(a)there is a crack initiated from the middle portion of the pre-crack when β= 0deg

Figure 8(a) shows that ve crack propagation pathsappeared two cracks started from the pre-existing crackrsquosleft-end tip and propagated to the specimenrsquos lower planeedge two cracks started from the pre-existing crackrsquos right-end tip the rest one crack propagated to the upper and lowerplane edges However because of the high values of crackorientation with respect to the loading direction there is onecrack which did not propagate from the tip of the pre-crackIn Figures 8(c) and 8(d) β= 30deg 45deg respectively ve crackpropagation paths appeared Figure 8(c) shows that there aretwo cracks that started from the pre-crack upper tip andpropagated to the upper plane edge two cracks started fromthe pre-crack lower tip and propagated to the lower planeedge and the rest one crack started from the pre-crack uppertip and propagated to the lower plane edge While inFigure 8(d) there is one crack that started from the pre-cracklower tip and propagated to the upper plane edge InFigures 8(b) 8(e) and 8(f ) β= 15deg 60deg and 75deg respectivelyfour main crack propagation paths appeared and two ofthem started from the pre-crack upper tip and propagated tothe upper plane edge e other two started from the pre-crack lower tip and propagated to the lower plane edge InFigure 8(b) an intermittent crack appeared starting fromthe pre-crack lower tip and has a downward trend to thelower plane edge Figure 8(e) shows that the scatter of thefour cracks presents regular symmetrical characteristic Asshown in Figure 8(g) β= 90deg and the upper pre-crack tippropagated two crack propagation paths to the upper planeedge and one to the lower plane edge

From Figures 8(a)ndash8(g) it can be clearly seen that the nal dynamic crack propagation paths and fracture pat-terns under impact loading are obviously dierent

compared to those under static or quasi-static loading(eg Figure 9 [4]) In many studies there is only onefracture that propagates from each tip of BD specimensunder static or quasi-static loading But under impactloading in the SHPB test due to fractures with high strainrate there are multiple crack propagation paths eresults also show the pre-existing inclination angles aectthe multiple crack propagation paths and directionsinitiated from tips of the pre-cracks under cyclic dynamicloading

4 Discussion

e crack propagation patterns were obtained in previousinvestigations of brittle materials with pre-cracks as shownin Figure 10 [1 2] From the experimental results above twotypes of cracks were observed wing cracks and secondarycracks Usually the wing cracks are tensile cracks and thesecondary cracks are shear cracks (oblique shear cracks andcoplanar or quasi-coplanar shear) Table 2 summarizes cracktypes initiated from the pre-cracks in CSCFBD specimensunder cyclic impact loading Most of the tensile cracks andshear cracks initiated from the tips of pre-cracks at an angleand then propagate to the parallel to the compressive di-rection Shear cracksrsquo initiation patterns depend on theinclination angles of the pre-cracks Under impact loadingshear cracks caused the failure of the tested specimensmostly

Fracture and failure of pre-cracked CSCFBD specimensunder cyclic impact loading involve tensile and shear cracktypes Because of pre-cracks the fracture patterns andfailure modes are much more complex than those of intactbrittle materials Note that all the CSCFBD specimenspresent multiply crack propagation paths But the geom-etries of pre-cracks appear to play limited eects on thecrack type of CSCFBD specimens under cyclic impactloading

In this paper we studied the dynamic crack propa-gation and fracture patterns in pre-cracked CSCFBDspecimens from deep underground strata under cyclicimpact loading e dynamic crack propagation paths anddirections are obviously dierent from those under staticor quasi-static loading in the previous studies and theexperimental results present some regular symmetricalcharacteristics e dynamic crack propagation paths andpropagation directions are not only determined by ma-terial related but also dependent on the geometries of thepre-cracks However the geometries of pre-cracks appearto play limited eects on the nal dynamic fracture pat-terns and failure modes of CSCFBD specimens undercyclic impact loading Further research may be a focus onthe dynamic crack propagation mechanism of brittlematerials studied by experimental and numerical simu-lation comprehensively Various numerical simulationmethods eg nite element method (FEM) extended nite element method (XFEM) nite dierentialmethod (FDM) and dierent criteria eg strain energydensity (SED) criterion cohesive zone model (CZM) [50]for theoretical analysis have been developed to investigate

ndash151

2

3Impa

ct ti

mes

4

5

6

0 15 30 45β angle (degrees)

60 75 90

Figure 7 Impact times in nal crack propagation path forms whenβ 0deg 15deg 30deg 45deg 60deg 75deg and 90deg

Advances in Materials Science and Engineering 5

Crack propagationpath

Crack propagationpath

(a)

Crack propagation path

Crack propagation path

(b)

Crack propagationpath

Crack propagation path

(c)

Crack propagationpath

Crack propagation path

(d)

Crack propagation path

Crack propagation path

(e)

Crack propagationpath

Crack propagation path

(f )

Figure 8 Continued

6 Advances in Materials Science and Engineering

Wing crack

Wing crack

(a)

Wing crack

Wing crack

(b)

Wing crack

Wing crack

(c)

Wing crack

Wing crack

(d)

Figure 9 Continued

Crack propagation path

Crack propagation path

(g)

Figure 8 Crack propagation paths in ne sandstone CSCFBD specimens with dierent inclination angles of pre-cracks (a) β 0 (b) β 15deg(c) β 30deg (d) β 45deg (e) β 60deg (f ) β 75deg (g) β 90deg

Advances in Materials Science and Engineering 7

Wing crack

Wing crack

(e)

Wing crack

Wing crack

(f )

Wing crack

Wing crack

(g)

Figure 9 Experimental results of crack propagation paths in tested specimens with dierent inclination angles of pre-cracks (a) β 0(b) β 15deg (c) β 30deg (d) β 45deg (e) β 60deg (f ) β 75deg (g) β 90deg [4]

T

TType IT

T

Type II

T

T

Type IIIT

T

S

S

Type IV

S

S

Type V

S

Type VI

S

SType VII

Figure 10 Various crack types initiated from the pre-cracks identi ed in the present studies (Tand S denote tensile and shear cracks)Type Itensile crack Type II tensile crack Type III tensile crack Type IV mixed tensile-shear crack Type V shear crack Type VI shear crack(coplanar or quasi-coplanar shear crack) Type VII shear crack (oblique shear crack) [1 2]

8 Advances in Materials Science and Engineering

crack propagation fracture patterns and failure modes inbrittle materials but have not shown satisfactoryeffectiveness in modeling dynamic damage evolutionand crack propagation [51ndash53] Using mesh-free particlemethods to numerically study dynamic crack propagationmay be an effective way Especially in peridynamics cracksare part of the solution not part of the problem [54]-erefore using peridynamics to simulate dynamicmultiple crack propagation and fracture patterns in brittlematerials under impact or cyclic impact loading would bevery meaningful which we plan for in the future

5 Conclusions

In this paper we provide experimental results of dynamicfracture tests carried out on fine sandstone CSCFBDspecimens under cyclic impact loading by the Φ 74mm-diameter SHPB device Dynamic crack propagation andfracture mechanism are rather complicated processes Fromthe results presented and analyzed above the followingconclusions could be drawn

(1) Compared to static or quasi-static loading the dy-namic crack propagation and fracture behavior aremuch more complex and it presents multiple crackpropagation paths and directions in dynamicfracture

(2) Both tensile and shear cracks were observed most ofthemmainly initiated from tips of the pre-cracks andpropagated in a stable manner According to thedifferent geometries of pre-cracks the testedCSCFBD specimens experienced tensile or shearcrack propagation failure

(3) -e natural or artificial pre-existing defects canchange the crack propagation paths especially di-rections under impact loading compared to static orquasi-static loading However the geometries ofpre-cracks appear to play limited effects on crackstype of CSCFBD specimens under cyclic impactloading

(4) Dynamic crack propagation and fracture mecha-nism are rather complicated processes -is studyrevealed multiple dynamic crack propagationbehavior that had not been observed previouslyNumerical simulation is further needed to besummarized and explored which we plan for in thefuture

Data Availability

-e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-e research described in this paper was financially supportedby the National Key Technologies Research amp DevelopmentProgram (nos 2018YFC0406703 and 2017YFC1502600) theNational Natural Science Foundation of China (nos 11672101and 11372099) the Postgraduate Research amp Practice In-novation Program of Jiangsu Province (no KYLX16_0700)and the Fundamental Research Funds for the Central Uni-versities (no 2016B45214)

References

[1] L N Y Wong and H H Einstein ldquoCrack coalescence inmolded gypsum and Carrara marble part 1mdashmacroscopicobservations and interpretationrdquo Rock Mechanics and RockEngineering vol 42 no 3 pp 475ndash511 2009

[2] L N Y Wong and H H Einstein ldquoCrack coalescence inmolded gypsum and carrara marble part 2mdashmicroscopicobservations and interpretationrdquo Rock Mechanics and RockEngineering vol 42 no 3 pp 513ndash545 2009

[3] H Cheng X Zhou J Zhu and Q Qian ldquo-e effects of crackopenings on crack initiation propagation and coalescencebehavior in rock-like materials under uniaxial compressionrdquoRock Mechanics and Rock Engineering vol 49 no 9pp 3481ndash3494 2016

[4] S J Zhao Q Zhang and L M Liu ldquoCrack initiationpropagation and coalescence experiments in sandstone Bra-zilian disks containing pre-existing flawsrdquo Advances in CivilEngineering vol 2019 Article ID 9816067 11 pages 2019

[5] A Bobet and H H Einstein ldquoFracture coalescence in rock-type materials under uniaxial and biaxial compressionrdquo In-ternational Journal of Rock Mechanics and Mining Sciencesvol 35 no 7 pp 863ndash888 1998

[6] E Hoek and C D Martin ldquoFracture initiation and propa-gation in intact rockmdasha reviewrdquo Journal of Rock Mechanicsand Geotechnical Engineering vol 6 no 4 pp 287ndash300 2014

[7] X Zhuang J Chun and H Zhu ldquoA comparative study onunfilled and filled crack propagation for rock-like brittlematerialrdquo=eoretical and Applied Fracture Mechanics vol 72pp 110ndash120 2014

Table 2 Types of cracks initiated from pre-cracked CSCFBD specimens under cyclic impact loading

Tested CSCFBDspecimen no

Crack typesType I tensile Type II tensile Type III tensile Type IV tensile-shear Type V shear Type VI shear Type VII shear

β 0deg radic radic radic radicβ 15deg radic radic radicβ 30deg radic radic radic radic radicβ 45deg radic radic radic radicβ 60deg radic radic radicβ 75deg radic radic radicβ 90deg radic radic radic

Advances in Materials Science and Engineering 9

[8] P Cao T Liu C Pu and H Lin ldquoCrack propagation andcoalescence of brittle rock-like specimens with pre-existingcracks in compressionrdquo Engineering Geology vol 187pp 113ndash121 2015

[9] 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

[10] 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

[11] M D Kuruppu ldquoFracture toughness measurement usingchevron notched semi-circular bend specimenrdquo InternationalJournal of Fracture vol 86 no 4 pp L33ndashL38 1997

[12] A M Shiryaev and A M Kotkis ldquoMethods for determiningfracture toughness of brittle porous materialsrdquo IndustrialLaboratory vol 48 no 9 pp 917-918 1983

[13] M -iercelin and J C Roegiers ldquoFracture toughness de-termination with the modified ring testrdquo in Proceedings of theInternational Symposium on Engineering in Complex RockFormations pp 1ndash8 Beijing China November 1986

[14] G R Irwin ldquoAnalysis of stress and strains near the end of acrack traversing a platerdquo Journal of AppliedMechanics vol 24no 3 pp 361ndash364 1957

[15] J B Walsh ldquo-e effect of cracks on the compressibility ofrockrdquo Journal of Geophysical Research vol 70 no 2pp 381ndash389 1965

[16] E Hoek and Z T Bieniawski ldquoBrittle fracture propagation inrock under compressionrdquo International Journal of FractureMechanics vol 1 no 3 pp 137ndash155 1965

[17] S Q Yang Y H Dai L J Han and Z Q Jin ldquoExperimentalstudy on mechanical behavior of brittle marble samplescontaining different flaws under uniaxial compressionrdquo En-gineering Fracture Mechanics vol 76 no 12 pp 1833ndash18452009

[18] C H Park and A Bobet ldquoCrack coalescence in specimenswith open and closed flaws a comparisonrdquo InternationalJournal of Rock Mechanics and Mining Sciences vol 46 no 5pp 819ndash829 2009

[19] R P Janeiro and H H Einstein ldquoExperimental study of thecracking behavior of specimens containing inclusions (underuniaxial compression)rdquo International Journal of Fracturevol 164 no 1 pp 83ndash102 2010

[20] S Q Yang ldquoCrack coalescence behavior of brittle sandstonesamples containing two coplanar fissures in the process ofdeformation failurerdquo Engineering Fracture Mechanics vol 78no 17 pp 3059ndash3081 2011

[21] M R M Aliha M Sistaninia D J Smith M J Pavier andM R Ayatollahi ldquoGeometry effects and statistical analysis ofmode I fracture in guiting limestonerdquo International Journal ofRock Mechanics and Mining Sciences vol 51 pp 128ndash1352012

[22] M R Ayatollahi and M R M Aliha ldquoOn the use of Braziliandisc specimen for calculating mixed mode I-II fracturetoughness of rock materialsrdquo Engineering Fracture Mechanicsvol 75 no 16 pp 4631ndash4641 2008

[23] A Ghazvinian H R Nejati V Sarfarazi and M R HadeildquoMixed mode crack propagation in low brittle rock-likematerialsrdquo Arabian Journal of Geosciences vol 6 no 11pp 4435ndash4444 2013

[24] N A Al-Shayea ldquoCrack propagation trajectories for rocksunder mixed mode I-II fracturerdquo Engineering Geology vol 81no 1 pp 84ndash97 2005

[25] H Haeri K Shahriar M F Marji and P MoarefvandldquoExperimental and numerical study of crack propagation andcoalescence in pre-cracked rock-like disksrdquo InternationalJournal of Rock Mechanics and Mining Sciences vol 67 no 6pp 20ndash28 2014

[26] H Haeri A Khaloo and M F Marji ldquoFracture analyses ofdifferent pre-holed concrete specimens under compressionrdquoActa Mechanica Sinica vol 31 no 6 pp 855ndash870 2015

[27] H Haeri V Sarfarazi and A Hedayat ldquoSuggesting a newtesting device for determination of tensile strength of con-creterdquo Structural Engineering and Mechanics vol 60 no 6pp 939ndash952 2016

[28] M R M Aliha and A Bahmani ldquoRock fracture toughnessstudy under mixed mode IIII loadingrdquo Rock Mechanics andRock Engineering vol 50 no 7 pp 1739ndash1751 2017

[29] D J Frew M J Forrestal and W W Chen ldquoPulse shapingtechniques for testing brittle materials with a split Hopkinsonpressure barrdquo Experimental Mechanics vol 42 no 1pp 93ndash106 2002

[30] D J Frew M J Forrestal and W Chen ldquoPulse shapingtechniques for testing elastic-plastic materials with a splitHopkinson pressure barrdquo Experimental Mechanics vol 45no 2 pp 186ndash195 2005

[31] X Li T Zhou and D Li ldquoDynamic strength and fracturingbehavior of single-flawed prismatic marble specimens underimpact loading with a split-Hopkinson pressure barrdquo RockMechanics and Rock Engineering vol 50 no 1 pp 29ndash442017

[32] Q Z Wang J R Yang C G Zhang et al ldquoSequential de-termination of dynamic initiation and propagation toughnessof rock using an experimental-numerical-analytical methodrdquoEngineering Fracture Mechanics vol 141 pp 78ndash94 2015

[33] F Dai S Huang K Xia and Z Tan ldquoSome fundamentalissues in dynamic compression and tension tests of rocksusing split Hopkinson pressure barrdquo Rock Mechanics andRock Engineering vol 43 no 6 pp 657ndash666 2010

[34] W Li and J Xu ldquoMechanical properties of basalt fiberreinforced geopolymeric concrete under impact loadingrdquoMaterials Science and Engineering A vol 505 no 1-2pp 178ndash186 2009

[35] Z L Wang H H Zhu and J G Wang ldquoRepeated-impactresponse of ultrashort steel fiber reinforced concreterdquo Ex-perimental Techniques vol 37 no 4 pp 6ndash13 2013

[36] X Chen S Wu and J Zhou ldquoExperimental and modelingstudy of dynamic mechanical properties of cement pastemortar and concreterdquo Construction and Building Materialsvol 47 pp 419ndash430 2013

[37] X D Chen L M Ge J K Zhou and S X Wu ldquoDynamicBrazilian test of concrete using split Hopkinson pressure barrdquoMaterials and Structures vol 50 no 1 2017

[38] M Zhang H J Wu Q M Li and F L Huang ldquoFurtherinvestigation on the dynamic compressive strength en-hancement of concrete-like materials based on split Hop-kinson pressure bar testsmdashpart I experimentsrdquo InternationalJournal of Impact Engineering vol 36 no 12 pp 1327ndash13342009

[39] W Chen and G Ravichandran ldquoFailure mode transition inceramics under dynamic multiaxial compressionrdquo In-ternational Journal of Fracture vol 101 no 1-2 pp 141ndash1592000

10 Advances in Materials Science and Engineering

[40] H Wang and K T Ramesh ldquoDynamic strength and frag-mentation of hot-pressed silicon carbide under uniaxialcompressionrdquo Acta Materialia vol 52 no 2 pp 355ndash3672004

[41] T Ficker ldquoQuasi-static compressive strength of cement-basedmaterialsrdquo Cement and Concrete Research vol 41 no 1pp 129ndash132 2011

[42] H Hao and B G Tarasov ldquoExperimental study of dynamicmaterial properties of clay brick and mortar at different strainratesrdquo Australian Journal of Structural Engineering vol 8no 2 pp 117ndash132 2008

[43] M Wu C Qin and C Zhang ldquoHigh strain rate splittingtensile tests of concrete and numerical simulation by meso-scale particle elementsrdquo Journal of Materials in Civil Engi-neering vol 26 no 1 pp 71ndash82 2014

[44] J Xiao L Li L Shen and C S Poon ldquoCompressive behaviourof recycled aggregate concrete under impact loadingrdquo Cementand Concrete Research vol 71 pp 46ndash55 2015

[45] W Wu W Zhang and G Ma ldquoMechanical properties ofcopper slag reinforced concrete under dynamic compressionrdquoConstruction and Building Materials vol 24 no 6 pp 910ndash917 2010

[46] H Su and J Xu ldquoDynamic compressive behavior of ceramicfiber reinforced concrete under impact loadrdquo Constructionand Building Materials vol 45 pp 306ndash313 2013

[47] Y Al-Salloum T Almusallam S M Ibrahim H Abbas andS Alsayed ldquoRate dependent behavior and modeling ofconcrete based on SHPB experimentsrdquo Cement and ConcreteComposites vol 55 pp 34ndash44 2015

[48] C A Ross P Y -ompson and J W Tedesco ldquoSplit-Hopkinson pressure-bar tests on concrete and mortar intension and compressionrdquo ACI Materials Journal vol 86no 5 pp 475ndash481 1989

[49] Q Z Wang X M Jia S Q Kou Z X Zhang andP-A Lindqvist ldquo-e flattened Brazilian disc specimen usedfor testing elastic modulus tensile strength and fracturetoughness of brittle rocks analytical and numerical resultsrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 41 no 2 pp 245ndash253 2004

[50] F Berto and J Gomez ldquoNotched plates in mixed modeloading (I+II) a review based on the local strain energydensity and the cohesive zone modelrdquo Engineering SolidMechanics vol 5 pp 1ndash8 2017

[51] D Huang Q Zhang and P Qiao ldquoDamage and progressivefailure of concrete structures using non-local peridynamicmodelingrdquo Science China Technological Sciences vol 54 no 3pp 591ndash596 2011

[52] D Huang Q Zhang P Z Qiao and F Shen ldquoA review onperidynamics (PD) method and its applicationsrdquo Advances inMechanics vol 40 no 4 pp 448ndash459 2010

[53] H Haeri K Shahriar M F Marji and P Moarefvand ldquoAcoupled numerical-experimental study of the breakage pro-cess of brittle substancesrdquo Arabian Journal of Geosciencesvol 8 no 2 pp 809ndash825 2015

[54] Y D Ha and F Bobaru ldquoStudies of dynamic crack propa-gation and crack branching with peridynamicsrdquo InternationalJournal of Fracture vol 162 no 1-2 pp 229ndash244 2010

Advances in Materials Science and Engineering 11

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Submit your manuscripts atwwwhindawicom

specimens with same pre-crack geometry were prepared toguarantee the reproducibility of these experimental testsand a total number of 21 CSCFBD specimens were manu-factured in this work -e physical and mechanical prop-erties of the tested fine sandstone are listed in Table 1

Various Brazilian tests were conducted on CSCFBDspecimens containing a single crack with different in-clination angles -ese pre-cracks were created by the high-speed water jet cutting machine [4] as shown in Figure 2Figure 3 shows pre-cracked specimens with different in-clination angles and the crack inclination angle β (the anglebetween the normal line of the pre-crack surface and thevertical direction of the impact load) β= 0deg 15deg 30deg 45deg 60deg75deg and 90deg Figure 4 shows a schematic view of CSCFBDspecimens -e pre-cracks length 2b (b is the half of pre-crack length) is equal to 10mm and the crack width is1mm -e radius and thickness of the CSCFBD specimenare R= 31mm and H= 30mm Crack length ratio is animportant parameter for the pattern trajectory and thenumber of fractures in this work the ratio bR is 016

22 SHPB Experimental Procedure In this work the dy-namic tests were taken in the structure laboratory of HohaiUniversity adopting Φ 74mm diameter straight tapervariable cross sections SHPB device -e Φ 74mm diameterSHPB device mainly composes of the power system (whichpropelled by a gas gun) elastic bars (an incident bar atransmitter bar and an absorbing bar) a damper energyabsorbing setup high dynamic strain indicator and dataprocessing systems -e power system consists of an aircompressor and pressure vessel -e impact velocity ismeasured by the light electric tachometer Schematic of theSHPB test device is shown in Figure 5

-e SHPB device is based on the one-dimensional theoryof elastic wave and uses Lagrangian coordinates to describeall the physical parameters -e control equations of wavesin the bars are on the following assumptions One-dimensional assumption speed v and the strain ε are onlythe function of point X and time t and the assumption thatthe strain rate is independent Assuming axial wave prop-agation and homogeneous stress distribution in the speci-men the resulting stress σs(t) strain εs(t) and strain rate_ε(t) of the specimen are obtained by the following equation[48]

σs(t) SBE

2SSεt(t) + εr(t) + εi(t)1113858 1113859

_εs(t) C0

Lsεt(t) + εr(t)minus εi(t)1113858 1113859

εt(t) C0

LS1113946

t

0εt(t) + εr(t)minus εi(t)1113858 1113859dτ

(1)

where SB E and C0 are the cross-sectional area (mm2)Youngrsquos modulus (GPa) and the wave velocity (kms) ofthe bar material and LS and Ss are the length (mm) andcross-sectional area (mm2) of the specimen εi(t) εr(t) andεt(t) are the strain singles in specimen -e diameter

Youngrsquos modulus and density of the elastic bars are 74mm210 GPa and 7850 kgm3 respectively

In fact during the experimental tests by BD specimensthe cracks of samples are first produced by the center andthen expanded along the radial direction Wang et al [49]presented that if the samples between two planes parallel tothe plane of the degree of smoothness and not less than005mm then they can ensure that the fracture initiatedfrom the specimen center -e loading areas corresponding

Table 1 Physical and mechanical properties of the tested finesandstone

Properties ValueYoungrsquos modulus E (GPa) 111Compressive strength σc (MPa) 841Brazilian tensile strength σt (MPa) 30Longitudinal wave velocity VP (ms) 35264Porosity () 83Poissonrsquos ratio v 033Density ρ (kgm3) 2692

Figure 2 Pre-crack preparation in CSCFBD specimens using awater jet cutting machine [4]

Figure 3 Schematic view of CSCFBD specimens with differentinclination angles of pre-cracks

Advances in Materials Science and Engineering 3

to the center angle 2α to meet 20degle 2αle 30deg Figure 6 showsthe attened BD specimen under radial loading Before theinstallation of the specimens a layer of Vaseline is evenlyapplied to the contact between the end of the specimen andthe end of the compression bar and the specimens need tobe tightened between the incident bar and the transmitterbar During SHPB tests the brittle materials may fail beforestress uniformly is achieved within the specimens Modi -cation of the incident pulse to closely match the elasticresponse is required e pulse shaping technique has beenwidely applied in SHPB testing of engineering materials andit is especially used for investigating the dynamic response ofbrittle materials In this paper we used a pulse shapingtechnique a thin copper disk (12 mm-diameter and 1mm-thickness) which was placed on the impact side of the in-cident bar e pulse shape can attenuate high-frequencyoscillations of the incident stress wave to improve the stresswave shape Pulse shaping technique allows for controllingthe damage of brittle materials [29 30]

3 Experimental Results

31 Impact Time Analysis of CSCFBD Specimens Duringtesting the air pressure in the gas gun chamber was keptconstant 01MPa equal to the impact velocity 376ms andthe bullet must be brought back to its original positionbefore the next loading e times of impacts were recordedfor each specimen until nal failure As shown in Figure 7 toreach the nal crack propagation paths forms 6 times

impact loading are needed when β= 0deg and the impact timesare 3 4 6 4 2 and 2 when β= 15deg 30deg 45deg 60deg 75deg and 90degrespectively It is obvious that the impact times in nalfailure are related to the pre-existing inclination anglesBecause pre-cracks can make the specimen strength to re-duce so when β= 15deg 75deg and 90deg the impact times areusually less than the cases of β= 0deg 30deg 45deg and 90deg

32 Dynamic Crack Propagation Paths and Directions ofCSCFBD Specimens In this paper we investigated the dy-namic crack propagation paths and directions in CSCFBDspecimens In Figure 8 the crack propagation paths in

BufferAbsorbing bar

Strain gauge

High-dynamic strain indicator

Waveform memory Data processing systems

Light electric tachometer

BulletLauncher Incident bar Specimen Transmitter bar

Figure 5 Schematic of the split Hopkinson pressure bar (SHPB) device

2α2αP P

Specimen62 mm

Incident bar Transmitterbar

Figure 6 Flattened BD specimen under radial impact loading

P

β2b

P

Figure 4 Schematic view of the ne sandstone CSCFBD specimen

4 Advances in Materials Science and Engineering

CSCFBD specimens with dierent inclination angles areindicated and for all gures the upper plane edges of thespecimens are contacted with the incident bar As shown inFigures 8(b)ndash8(g) cracks initiated from the tips of pre-cracksand approximately propagated towards the direction of themaximum stress It should be noted that in Figure 8(a)there is a crack initiated from the middle portion of the pre-crack when β= 0deg

Figure 8(a) shows that ve crack propagation pathsappeared two cracks started from the pre-existing crackrsquosleft-end tip and propagated to the specimenrsquos lower planeedge two cracks started from the pre-existing crackrsquos right-end tip the rest one crack propagated to the upper and lowerplane edges However because of the high values of crackorientation with respect to the loading direction there is onecrack which did not propagate from the tip of the pre-crackIn Figures 8(c) and 8(d) β= 30deg 45deg respectively ve crackpropagation paths appeared Figure 8(c) shows that there aretwo cracks that started from the pre-crack upper tip andpropagated to the upper plane edge two cracks started fromthe pre-crack lower tip and propagated to the lower planeedge and the rest one crack started from the pre-crack uppertip and propagated to the lower plane edge While inFigure 8(d) there is one crack that started from the pre-cracklower tip and propagated to the upper plane edge InFigures 8(b) 8(e) and 8(f ) β= 15deg 60deg and 75deg respectivelyfour main crack propagation paths appeared and two ofthem started from the pre-crack upper tip and propagated tothe upper plane edge e other two started from the pre-crack lower tip and propagated to the lower plane edge InFigure 8(b) an intermittent crack appeared starting fromthe pre-crack lower tip and has a downward trend to thelower plane edge Figure 8(e) shows that the scatter of thefour cracks presents regular symmetrical characteristic Asshown in Figure 8(g) β= 90deg and the upper pre-crack tippropagated two crack propagation paths to the upper planeedge and one to the lower plane edge

From Figures 8(a)ndash8(g) it can be clearly seen that the nal dynamic crack propagation paths and fracture pat-terns under impact loading are obviously dierent

compared to those under static or quasi-static loading(eg Figure 9 [4]) In many studies there is only onefracture that propagates from each tip of BD specimensunder static or quasi-static loading But under impactloading in the SHPB test due to fractures with high strainrate there are multiple crack propagation paths eresults also show the pre-existing inclination angles aectthe multiple crack propagation paths and directionsinitiated from tips of the pre-cracks under cyclic dynamicloading

4 Discussion

e crack propagation patterns were obtained in previousinvestigations of brittle materials with pre-cracks as shownin Figure 10 [1 2] From the experimental results above twotypes of cracks were observed wing cracks and secondarycracks Usually the wing cracks are tensile cracks and thesecondary cracks are shear cracks (oblique shear cracks andcoplanar or quasi-coplanar shear) Table 2 summarizes cracktypes initiated from the pre-cracks in CSCFBD specimensunder cyclic impact loading Most of the tensile cracks andshear cracks initiated from the tips of pre-cracks at an angleand then propagate to the parallel to the compressive di-rection Shear cracksrsquo initiation patterns depend on theinclination angles of the pre-cracks Under impact loadingshear cracks caused the failure of the tested specimensmostly

Fracture and failure of pre-cracked CSCFBD specimensunder cyclic impact loading involve tensile and shear cracktypes Because of pre-cracks the fracture patterns andfailure modes are much more complex than those of intactbrittle materials Note that all the CSCFBD specimenspresent multiply crack propagation paths But the geom-etries of pre-cracks appear to play limited eects on thecrack type of CSCFBD specimens under cyclic impactloading

In this paper we studied the dynamic crack propa-gation and fracture patterns in pre-cracked CSCFBDspecimens from deep underground strata under cyclicimpact loading e dynamic crack propagation paths anddirections are obviously dierent from those under staticor quasi-static loading in the previous studies and theexperimental results present some regular symmetricalcharacteristics e dynamic crack propagation paths andpropagation directions are not only determined by ma-terial related but also dependent on the geometries of thepre-cracks However the geometries of pre-cracks appearto play limited eects on the nal dynamic fracture pat-terns and failure modes of CSCFBD specimens undercyclic impact loading Further research may be a focus onthe dynamic crack propagation mechanism of brittlematerials studied by experimental and numerical simu-lation comprehensively Various numerical simulationmethods eg nite element method (FEM) extended nite element method (XFEM) nite dierentialmethod (FDM) and dierent criteria eg strain energydensity (SED) criterion cohesive zone model (CZM) [50]for theoretical analysis have been developed to investigate

ndash151

2

3Impa

ct ti

mes

4

5

6

0 15 30 45β angle (degrees)

60 75 90

Figure 7 Impact times in nal crack propagation path forms whenβ 0deg 15deg 30deg 45deg 60deg 75deg and 90deg

Advances in Materials Science and Engineering 5

Crack propagationpath

Crack propagationpath

(a)

Crack propagation path

Crack propagation path

(b)

Crack propagationpath

Crack propagation path

(c)

Crack propagationpath

Crack propagation path

(d)

Crack propagation path

Crack propagation path

(e)

Crack propagationpath

Crack propagation path

(f )

Figure 8 Continued

6 Advances in Materials Science and Engineering

Wing crack

Wing crack

(a)

Wing crack

Wing crack

(b)

Wing crack

Wing crack

(c)

Wing crack

Wing crack

(d)

Figure 9 Continued

Crack propagation path

Crack propagation path

(g)

Figure 8 Crack propagation paths in ne sandstone CSCFBD specimens with dierent inclination angles of pre-cracks (a) β 0 (b) β 15deg(c) β 30deg (d) β 45deg (e) β 60deg (f ) β 75deg (g) β 90deg

Advances in Materials Science and Engineering 7

Wing crack

Wing crack

(e)

Wing crack

Wing crack

(f )

Wing crack

Wing crack

(g)

Figure 9 Experimental results of crack propagation paths in tested specimens with dierent inclination angles of pre-cracks (a) β 0(b) β 15deg (c) β 30deg (d) β 45deg (e) β 60deg (f ) β 75deg (g) β 90deg [4]

T

TType IT

T

Type II

T

T

Type IIIT

T

S

S

Type IV

S

S

Type V

S

Type VI

S

SType VII

Figure 10 Various crack types initiated from the pre-cracks identi ed in the present studies (Tand S denote tensile and shear cracks)Type Itensile crack Type II tensile crack Type III tensile crack Type IV mixed tensile-shear crack Type V shear crack Type VI shear crack(coplanar or quasi-coplanar shear crack) Type VII shear crack (oblique shear crack) [1 2]

8 Advances in Materials Science and Engineering

crack propagation fracture patterns and failure modes inbrittle materials but have not shown satisfactoryeffectiveness in modeling dynamic damage evolutionand crack propagation [51ndash53] Using mesh-free particlemethods to numerically study dynamic crack propagationmay be an effective way Especially in peridynamics cracksare part of the solution not part of the problem [54]-erefore using peridynamics to simulate dynamicmultiple crack propagation and fracture patterns in brittlematerials under impact or cyclic impact loading would bevery meaningful which we plan for in the future

5 Conclusions

In this paper we provide experimental results of dynamicfracture tests carried out on fine sandstone CSCFBDspecimens under cyclic impact loading by the Φ 74mm-diameter SHPB device Dynamic crack propagation andfracture mechanism are rather complicated processes Fromthe results presented and analyzed above the followingconclusions could be drawn

(1) Compared to static or quasi-static loading the dy-namic crack propagation and fracture behavior aremuch more complex and it presents multiple crackpropagation paths and directions in dynamicfracture

(2) Both tensile and shear cracks were observed most ofthemmainly initiated from tips of the pre-cracks andpropagated in a stable manner According to thedifferent geometries of pre-cracks the testedCSCFBD specimens experienced tensile or shearcrack propagation failure

(3) -e natural or artificial pre-existing defects canchange the crack propagation paths especially di-rections under impact loading compared to static orquasi-static loading However the geometries ofpre-cracks appear to play limited effects on crackstype of CSCFBD specimens under cyclic impactloading

(4) Dynamic crack propagation and fracture mecha-nism are rather complicated processes -is studyrevealed multiple dynamic crack propagationbehavior that had not been observed previouslyNumerical simulation is further needed to besummarized and explored which we plan for in thefuture

Data Availability

-e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-e research described in this paper was financially supportedby the National Key Technologies Research amp DevelopmentProgram (nos 2018YFC0406703 and 2017YFC1502600) theNational Natural Science Foundation of China (nos 11672101and 11372099) the Postgraduate Research amp Practice In-novation Program of Jiangsu Province (no KYLX16_0700)and the Fundamental Research Funds for the Central Uni-versities (no 2016B45214)

References

[1] L N Y Wong and H H Einstein ldquoCrack coalescence inmolded gypsum and Carrara marble part 1mdashmacroscopicobservations and interpretationrdquo Rock Mechanics and RockEngineering vol 42 no 3 pp 475ndash511 2009

[2] L N Y Wong and H H Einstein ldquoCrack coalescence inmolded gypsum and carrara marble part 2mdashmicroscopicobservations and interpretationrdquo Rock Mechanics and RockEngineering vol 42 no 3 pp 513ndash545 2009

[3] H Cheng X Zhou J Zhu and Q Qian ldquo-e effects of crackopenings on crack initiation propagation and coalescencebehavior in rock-like materials under uniaxial compressionrdquoRock Mechanics and Rock Engineering vol 49 no 9pp 3481ndash3494 2016

[4] S J Zhao Q Zhang and L M Liu ldquoCrack initiationpropagation and coalescence experiments in sandstone Bra-zilian disks containing pre-existing flawsrdquo Advances in CivilEngineering vol 2019 Article ID 9816067 11 pages 2019

[5] A Bobet and H H Einstein ldquoFracture coalescence in rock-type materials under uniaxial and biaxial compressionrdquo In-ternational Journal of Rock Mechanics and Mining Sciencesvol 35 no 7 pp 863ndash888 1998

[6] E Hoek and C D Martin ldquoFracture initiation and propa-gation in intact rockmdasha reviewrdquo Journal of Rock Mechanicsand Geotechnical Engineering vol 6 no 4 pp 287ndash300 2014

[7] X Zhuang J Chun and H Zhu ldquoA comparative study onunfilled and filled crack propagation for rock-like brittlematerialrdquo=eoretical and Applied Fracture Mechanics vol 72pp 110ndash120 2014

Table 2 Types of cracks initiated from pre-cracked CSCFBD specimens under cyclic impact loading

Tested CSCFBDspecimen no

Crack typesType I tensile Type II tensile Type III tensile Type IV tensile-shear Type V shear Type VI shear Type VII shear

β 0deg radic radic radic radicβ 15deg radic radic radicβ 30deg radic radic radic radic radicβ 45deg radic radic radic radicβ 60deg radic radic radicβ 75deg radic radic radicβ 90deg radic radic radic

Advances in Materials Science and Engineering 9

[8] P Cao T Liu C Pu and H Lin ldquoCrack propagation andcoalescence of brittle rock-like specimens with pre-existingcracks in compressionrdquo Engineering Geology vol 187pp 113ndash121 2015

[9] 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

[10] 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

[11] M D Kuruppu ldquoFracture toughness measurement usingchevron notched semi-circular bend specimenrdquo InternationalJournal of Fracture vol 86 no 4 pp L33ndashL38 1997

[12] A M Shiryaev and A M Kotkis ldquoMethods for determiningfracture toughness of brittle porous materialsrdquo IndustrialLaboratory vol 48 no 9 pp 917-918 1983

[13] M -iercelin and J C Roegiers ldquoFracture toughness de-termination with the modified ring testrdquo in Proceedings of theInternational Symposium on Engineering in Complex RockFormations pp 1ndash8 Beijing China November 1986

[14] G R Irwin ldquoAnalysis of stress and strains near the end of acrack traversing a platerdquo Journal of AppliedMechanics vol 24no 3 pp 361ndash364 1957

[15] J B Walsh ldquo-e effect of cracks on the compressibility ofrockrdquo Journal of Geophysical Research vol 70 no 2pp 381ndash389 1965

[16] E Hoek and Z T Bieniawski ldquoBrittle fracture propagation inrock under compressionrdquo International Journal of FractureMechanics vol 1 no 3 pp 137ndash155 1965

[17] S Q Yang Y H Dai L J Han and Z Q Jin ldquoExperimentalstudy on mechanical behavior of brittle marble samplescontaining different flaws under uniaxial compressionrdquo En-gineering Fracture Mechanics vol 76 no 12 pp 1833ndash18452009

[18] C H Park and A Bobet ldquoCrack coalescence in specimenswith open and closed flaws a comparisonrdquo InternationalJournal of Rock Mechanics and Mining Sciences vol 46 no 5pp 819ndash829 2009

[19] R P Janeiro and H H Einstein ldquoExperimental study of thecracking behavior of specimens containing inclusions (underuniaxial compression)rdquo International Journal of Fracturevol 164 no 1 pp 83ndash102 2010

[20] S Q Yang ldquoCrack coalescence behavior of brittle sandstonesamples containing two coplanar fissures in the process ofdeformation failurerdquo Engineering Fracture Mechanics vol 78no 17 pp 3059ndash3081 2011

[21] M R M Aliha M Sistaninia D J Smith M J Pavier andM R Ayatollahi ldquoGeometry effects and statistical analysis ofmode I fracture in guiting limestonerdquo International Journal ofRock Mechanics and Mining Sciences vol 51 pp 128ndash1352012

[22] M R Ayatollahi and M R M Aliha ldquoOn the use of Braziliandisc specimen for calculating mixed mode I-II fracturetoughness of rock materialsrdquo Engineering Fracture Mechanicsvol 75 no 16 pp 4631ndash4641 2008

[23] A Ghazvinian H R Nejati V Sarfarazi and M R HadeildquoMixed mode crack propagation in low brittle rock-likematerialsrdquo Arabian Journal of Geosciences vol 6 no 11pp 4435ndash4444 2013

[24] N A Al-Shayea ldquoCrack propagation trajectories for rocksunder mixed mode I-II fracturerdquo Engineering Geology vol 81no 1 pp 84ndash97 2005

[25] H Haeri K Shahriar M F Marji and P MoarefvandldquoExperimental and numerical study of crack propagation andcoalescence in pre-cracked rock-like disksrdquo InternationalJournal of Rock Mechanics and Mining Sciences vol 67 no 6pp 20ndash28 2014

[26] H Haeri A Khaloo and M F Marji ldquoFracture analyses ofdifferent pre-holed concrete specimens under compressionrdquoActa Mechanica Sinica vol 31 no 6 pp 855ndash870 2015

[27] H Haeri V Sarfarazi and A Hedayat ldquoSuggesting a newtesting device for determination of tensile strength of con-creterdquo Structural Engineering and Mechanics vol 60 no 6pp 939ndash952 2016

[28] M R M Aliha and A Bahmani ldquoRock fracture toughnessstudy under mixed mode IIII loadingrdquo Rock Mechanics andRock Engineering vol 50 no 7 pp 1739ndash1751 2017

[29] D J Frew M J Forrestal and W W Chen ldquoPulse shapingtechniques for testing brittle materials with a split Hopkinsonpressure barrdquo Experimental Mechanics vol 42 no 1pp 93ndash106 2002

[30] D J Frew M J Forrestal and W Chen ldquoPulse shapingtechniques for testing elastic-plastic materials with a splitHopkinson pressure barrdquo Experimental Mechanics vol 45no 2 pp 186ndash195 2005

[31] X Li T Zhou and D Li ldquoDynamic strength and fracturingbehavior of single-flawed prismatic marble specimens underimpact loading with a split-Hopkinson pressure barrdquo RockMechanics and Rock Engineering vol 50 no 1 pp 29ndash442017

[32] Q Z Wang J R Yang C G Zhang et al ldquoSequential de-termination of dynamic initiation and propagation toughnessof rock using an experimental-numerical-analytical methodrdquoEngineering Fracture Mechanics vol 141 pp 78ndash94 2015

[33] F Dai S Huang K Xia and Z Tan ldquoSome fundamentalissues in dynamic compression and tension tests of rocksusing split Hopkinson pressure barrdquo Rock Mechanics andRock Engineering vol 43 no 6 pp 657ndash666 2010

[34] W Li and J Xu ldquoMechanical properties of basalt fiberreinforced geopolymeric concrete under impact loadingrdquoMaterials Science and Engineering A vol 505 no 1-2pp 178ndash186 2009

[35] Z L Wang H H Zhu and J G Wang ldquoRepeated-impactresponse of ultrashort steel fiber reinforced concreterdquo Ex-perimental Techniques vol 37 no 4 pp 6ndash13 2013

[36] X Chen S Wu and J Zhou ldquoExperimental and modelingstudy of dynamic mechanical properties of cement pastemortar and concreterdquo Construction and Building Materialsvol 47 pp 419ndash430 2013

[37] X D Chen L M Ge J K Zhou and S X Wu ldquoDynamicBrazilian test of concrete using split Hopkinson pressure barrdquoMaterials and Structures vol 50 no 1 2017

[38] M Zhang H J Wu Q M Li and F L Huang ldquoFurtherinvestigation on the dynamic compressive strength en-hancement of concrete-like materials based on split Hop-kinson pressure bar testsmdashpart I experimentsrdquo InternationalJournal of Impact Engineering vol 36 no 12 pp 1327ndash13342009

[39] W Chen and G Ravichandran ldquoFailure mode transition inceramics under dynamic multiaxial compressionrdquo In-ternational Journal of Fracture vol 101 no 1-2 pp 141ndash1592000

10 Advances in Materials Science and Engineering

[40] H Wang and K T Ramesh ldquoDynamic strength and frag-mentation of hot-pressed silicon carbide under uniaxialcompressionrdquo Acta Materialia vol 52 no 2 pp 355ndash3672004

[41] T Ficker ldquoQuasi-static compressive strength of cement-basedmaterialsrdquo Cement and Concrete Research vol 41 no 1pp 129ndash132 2011

[42] H Hao and B G Tarasov ldquoExperimental study of dynamicmaterial properties of clay brick and mortar at different strainratesrdquo Australian Journal of Structural Engineering vol 8no 2 pp 117ndash132 2008

[43] M Wu C Qin and C Zhang ldquoHigh strain rate splittingtensile tests of concrete and numerical simulation by meso-scale particle elementsrdquo Journal of Materials in Civil Engi-neering vol 26 no 1 pp 71ndash82 2014

[44] J Xiao L Li L Shen and C S Poon ldquoCompressive behaviourof recycled aggregate concrete under impact loadingrdquo Cementand Concrete Research vol 71 pp 46ndash55 2015

[45] W Wu W Zhang and G Ma ldquoMechanical properties ofcopper slag reinforced concrete under dynamic compressionrdquoConstruction and Building Materials vol 24 no 6 pp 910ndash917 2010

[46] H Su and J Xu ldquoDynamic compressive behavior of ceramicfiber reinforced concrete under impact loadrdquo Constructionand Building Materials vol 45 pp 306ndash313 2013

[47] Y Al-Salloum T Almusallam S M Ibrahim H Abbas andS Alsayed ldquoRate dependent behavior and modeling ofconcrete based on SHPB experimentsrdquo Cement and ConcreteComposites vol 55 pp 34ndash44 2015

[48] C A Ross P Y -ompson and J W Tedesco ldquoSplit-Hopkinson pressure-bar tests on concrete and mortar intension and compressionrdquo ACI Materials Journal vol 86no 5 pp 475ndash481 1989

[49] Q Z Wang X M Jia S Q Kou Z X Zhang andP-A Lindqvist ldquo-e flattened Brazilian disc specimen usedfor testing elastic modulus tensile strength and fracturetoughness of brittle rocks analytical and numerical resultsrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 41 no 2 pp 245ndash253 2004

[50] F Berto and J Gomez ldquoNotched plates in mixed modeloading (I+II) a review based on the local strain energydensity and the cohesive zone modelrdquo Engineering SolidMechanics vol 5 pp 1ndash8 2017

[51] D Huang Q Zhang and P Qiao ldquoDamage and progressivefailure of concrete structures using non-local peridynamicmodelingrdquo Science China Technological Sciences vol 54 no 3pp 591ndash596 2011

[52] D Huang Q Zhang P Z Qiao and F Shen ldquoA review onperidynamics (PD) method and its applicationsrdquo Advances inMechanics vol 40 no 4 pp 448ndash459 2010

[53] H Haeri K Shahriar M F Marji and P Moarefvand ldquoAcoupled numerical-experimental study of the breakage pro-cess of brittle substancesrdquo Arabian Journal of Geosciencesvol 8 no 2 pp 809ndash825 2015

[54] Y D Ha and F Bobaru ldquoStudies of dynamic crack propa-gation and crack branching with peridynamicsrdquo InternationalJournal of Fracture vol 162 no 1-2 pp 229ndash244 2010

Advances in Materials Science and Engineering 11

CorrosionInternational Journal of

Hindawiwwwhindawicom Volume 2018

Advances in

Materials Science and EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Analytical ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

ScienticaHindawiwwwhindawicom Volume 2018

Polymer ScienceInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Advances in Condensed Matter Physics

Hindawiwwwhindawicom Volume 2018

International Journal of

BiomaterialsHindawiwwwhindawicom

Journal ofEngineeringVolume 2018

Applied ChemistryJournal of

Hindawiwwwhindawicom Volume 2018

NanotechnologyHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

High Energy PhysicsAdvances in

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

TribologyAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

ChemistryAdvances in

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

Hindawiwwwhindawicom Volume 2018

BioMed Research InternationalMaterials

Journal of

Hindawiwwwhindawicom Volume 2018

Na

nom

ate

ria

ls

Hindawiwwwhindawicom Volume 2018

Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom

to the center angle 2α to meet 20degle 2αle 30deg Figure 6 showsthe attened BD specimen under radial loading Before theinstallation of the specimens a layer of Vaseline is evenlyapplied to the contact between the end of the specimen andthe end of the compression bar and the specimens need tobe tightened between the incident bar and the transmitterbar During SHPB tests the brittle materials may fail beforestress uniformly is achieved within the specimens Modi -cation of the incident pulse to closely match the elasticresponse is required e pulse shaping technique has beenwidely applied in SHPB testing of engineering materials andit is especially used for investigating the dynamic response ofbrittle materials In this paper we used a pulse shapingtechnique a thin copper disk (12 mm-diameter and 1mm-thickness) which was placed on the impact side of the in-cident bar e pulse shape can attenuate high-frequencyoscillations of the incident stress wave to improve the stresswave shape Pulse shaping technique allows for controllingthe damage of brittle materials [29 30]

3 Experimental Results

31 Impact Time Analysis of CSCFBD Specimens Duringtesting the air pressure in the gas gun chamber was keptconstant 01MPa equal to the impact velocity 376ms andthe bullet must be brought back to its original positionbefore the next loading e times of impacts were recordedfor each specimen until nal failure As shown in Figure 7 toreach the nal crack propagation paths forms 6 times

impact loading are needed when β= 0deg and the impact timesare 3 4 6 4 2 and 2 when β= 15deg 30deg 45deg 60deg 75deg and 90degrespectively It is obvious that the impact times in nalfailure are related to the pre-existing inclination anglesBecause pre-cracks can make the specimen strength to re-duce so when β= 15deg 75deg and 90deg the impact times areusually less than the cases of β= 0deg 30deg 45deg and 90deg

32 Dynamic Crack Propagation Paths and Directions ofCSCFBD Specimens In this paper we investigated the dy-namic crack propagation paths and directions in CSCFBDspecimens In Figure 8 the crack propagation paths in

BufferAbsorbing bar

Strain gauge

High-dynamic strain indicator

Waveform memory Data processing systems

Light electric tachometer

BulletLauncher Incident bar Specimen Transmitter bar

Figure 5 Schematic of the split Hopkinson pressure bar (SHPB) device

2α2αP P

Specimen62 mm

Incident bar Transmitterbar

Figure 6 Flattened BD specimen under radial impact loading

P

β2b

P

Figure 4 Schematic view of the ne sandstone CSCFBD specimen

4 Advances in Materials Science and Engineering

CSCFBD specimens with dierent inclination angles areindicated and for all gures the upper plane edges of thespecimens are contacted with the incident bar As shown inFigures 8(b)ndash8(g) cracks initiated from the tips of pre-cracksand approximately propagated towards the direction of themaximum stress It should be noted that in Figure 8(a)there is a crack initiated from the middle portion of the pre-crack when β= 0deg

Figure 8(a) shows that ve crack propagation pathsappeared two cracks started from the pre-existing crackrsquosleft-end tip and propagated to the specimenrsquos lower planeedge two cracks started from the pre-existing crackrsquos right-end tip the rest one crack propagated to the upper and lowerplane edges However because of the high values of crackorientation with respect to the loading direction there is onecrack which did not propagate from the tip of the pre-crackIn Figures 8(c) and 8(d) β= 30deg 45deg respectively ve crackpropagation paths appeared Figure 8(c) shows that there aretwo cracks that started from the pre-crack upper tip andpropagated to the upper plane edge two cracks started fromthe pre-crack lower tip and propagated to the lower planeedge and the rest one crack started from the pre-crack uppertip and propagated to the lower plane edge While inFigure 8(d) there is one crack that started from the pre-cracklower tip and propagated to the upper plane edge InFigures 8(b) 8(e) and 8(f ) β= 15deg 60deg and 75deg respectivelyfour main crack propagation paths appeared and two ofthem started from the pre-crack upper tip and propagated tothe upper plane edge e other two started from the pre-crack lower tip and propagated to the lower plane edge InFigure 8(b) an intermittent crack appeared starting fromthe pre-crack lower tip and has a downward trend to thelower plane edge Figure 8(e) shows that the scatter of thefour cracks presents regular symmetrical characteristic Asshown in Figure 8(g) β= 90deg and the upper pre-crack tippropagated two crack propagation paths to the upper planeedge and one to the lower plane edge

From Figures 8(a)ndash8(g) it can be clearly seen that the nal dynamic crack propagation paths and fracture pat-terns under impact loading are obviously dierent

compared to those under static or quasi-static loading(eg Figure 9 [4]) In many studies there is only onefracture that propagates from each tip of BD specimensunder static or quasi-static loading But under impactloading in the SHPB test due to fractures with high strainrate there are multiple crack propagation paths eresults also show the pre-existing inclination angles aectthe multiple crack propagation paths and directionsinitiated from tips of the pre-cracks under cyclic dynamicloading

4 Discussion

e crack propagation patterns were obtained in previousinvestigations of brittle materials with pre-cracks as shownin Figure 10 [1 2] From the experimental results above twotypes of cracks were observed wing cracks and secondarycracks Usually the wing cracks are tensile cracks and thesecondary cracks are shear cracks (oblique shear cracks andcoplanar or quasi-coplanar shear) Table 2 summarizes cracktypes initiated from the pre-cracks in CSCFBD specimensunder cyclic impact loading Most of the tensile cracks andshear cracks initiated from the tips of pre-cracks at an angleand then propagate to the parallel to the compressive di-rection Shear cracksrsquo initiation patterns depend on theinclination angles of the pre-cracks Under impact loadingshear cracks caused the failure of the tested specimensmostly

Fracture and failure of pre-cracked CSCFBD specimensunder cyclic impact loading involve tensile and shear cracktypes Because of pre-cracks the fracture patterns andfailure modes are much more complex than those of intactbrittle materials Note that all the CSCFBD specimenspresent multiply crack propagation paths But the geom-etries of pre-cracks appear to play limited eects on thecrack type of CSCFBD specimens under cyclic impactloading

In this paper we studied the dynamic crack propa-gation and fracture patterns in pre-cracked CSCFBDspecimens from deep underground strata under cyclicimpact loading e dynamic crack propagation paths anddirections are obviously dierent from those under staticor quasi-static loading in the previous studies and theexperimental results present some regular symmetricalcharacteristics e dynamic crack propagation paths andpropagation directions are not only determined by ma-terial related but also dependent on the geometries of thepre-cracks However the geometries of pre-cracks appearto play limited eects on the nal dynamic fracture pat-terns and failure modes of CSCFBD specimens undercyclic impact loading Further research may be a focus onthe dynamic crack propagation mechanism of brittlematerials studied by experimental and numerical simu-lation comprehensively Various numerical simulationmethods eg nite element method (FEM) extended nite element method (XFEM) nite dierentialmethod (FDM) and dierent criteria eg strain energydensity (SED) criterion cohesive zone model (CZM) [50]for theoretical analysis have been developed to investigate

ndash151

2

3Impa

ct ti

mes

4

5

6

0 15 30 45β angle (degrees)

60 75 90

Figure 7 Impact times in nal crack propagation path forms whenβ 0deg 15deg 30deg 45deg 60deg 75deg and 90deg

Advances in Materials Science and Engineering 5

Crack propagationpath

Crack propagationpath

(a)

Crack propagation path

Crack propagation path

(b)

Crack propagationpath

Crack propagation path

(c)

Crack propagationpath

Crack propagation path

(d)

Crack propagation path

Crack propagation path

(e)

Crack propagationpath

Crack propagation path

(f )

Figure 8 Continued

6 Advances in Materials Science and Engineering

Wing crack

Wing crack

(a)

Wing crack

Wing crack

(b)

Wing crack

Wing crack

(c)

Wing crack

Wing crack

(d)

Figure 9 Continued

Crack propagation path

Crack propagation path

(g)

Figure 8 Crack propagation paths in ne sandstone CSCFBD specimens with dierent inclination angles of pre-cracks (a) β 0 (b) β 15deg(c) β 30deg (d) β 45deg (e) β 60deg (f ) β 75deg (g) β 90deg

Advances in Materials Science and Engineering 7

Wing crack

Wing crack

(e)

Wing crack

Wing crack

(f )

Wing crack

Wing crack

(g)

Figure 9 Experimental results of crack propagation paths in tested specimens with dierent inclination angles of pre-cracks (a) β 0(b) β 15deg (c) β 30deg (d) β 45deg (e) β 60deg (f ) β 75deg (g) β 90deg [4]

T

TType IT

T

Type II

T

T

Type IIIT

T

S

S

Type IV

S

S

Type V

S

Type VI

S

SType VII

Figure 10 Various crack types initiated from the pre-cracks identi ed in the present studies (Tand S denote tensile and shear cracks)Type Itensile crack Type II tensile crack Type III tensile crack Type IV mixed tensile-shear crack Type V shear crack Type VI shear crack(coplanar or quasi-coplanar shear crack) Type VII shear crack (oblique shear crack) [1 2]

8 Advances in Materials Science and Engineering

crack propagation fracture patterns and failure modes inbrittle materials but have not shown satisfactoryeffectiveness in modeling dynamic damage evolutionand crack propagation [51ndash53] Using mesh-free particlemethods to numerically study dynamic crack propagationmay be an effective way Especially in peridynamics cracksare part of the solution not part of the problem [54]-erefore using peridynamics to simulate dynamicmultiple crack propagation and fracture patterns in brittlematerials under impact or cyclic impact loading would bevery meaningful which we plan for in the future

5 Conclusions

In this paper we provide experimental results of dynamicfracture tests carried out on fine sandstone CSCFBDspecimens under cyclic impact loading by the Φ 74mm-diameter SHPB device Dynamic crack propagation andfracture mechanism are rather complicated processes Fromthe results presented and analyzed above the followingconclusions could be drawn

(1) Compared to static or quasi-static loading the dy-namic crack propagation and fracture behavior aremuch more complex and it presents multiple crackpropagation paths and directions in dynamicfracture

(2) Both tensile and shear cracks were observed most ofthemmainly initiated from tips of the pre-cracks andpropagated in a stable manner According to thedifferent geometries of pre-cracks the testedCSCFBD specimens experienced tensile or shearcrack propagation failure

(3) -e natural or artificial pre-existing defects canchange the crack propagation paths especially di-rections under impact loading compared to static orquasi-static loading However the geometries ofpre-cracks appear to play limited effects on crackstype of CSCFBD specimens under cyclic impactloading

(4) Dynamic crack propagation and fracture mecha-nism are rather complicated processes -is studyrevealed multiple dynamic crack propagationbehavior that had not been observed previouslyNumerical simulation is further needed to besummarized and explored which we plan for in thefuture

Data Availability

-e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-e research described in this paper was financially supportedby the National Key Technologies Research amp DevelopmentProgram (nos 2018YFC0406703 and 2017YFC1502600) theNational Natural Science Foundation of China (nos 11672101and 11372099) the Postgraduate Research amp Practice In-novation Program of Jiangsu Province (no KYLX16_0700)and the Fundamental Research Funds for the Central Uni-versities (no 2016B45214)

References

[1] L N Y Wong and H H Einstein ldquoCrack coalescence inmolded gypsum and Carrara marble part 1mdashmacroscopicobservations and interpretationrdquo Rock Mechanics and RockEngineering vol 42 no 3 pp 475ndash511 2009

[2] L N Y Wong and H H Einstein ldquoCrack coalescence inmolded gypsum and carrara marble part 2mdashmicroscopicobservations and interpretationrdquo Rock Mechanics and RockEngineering vol 42 no 3 pp 513ndash545 2009

[3] H Cheng X Zhou J Zhu and Q Qian ldquo-e effects of crackopenings on crack initiation propagation and coalescencebehavior in rock-like materials under uniaxial compressionrdquoRock Mechanics and Rock Engineering vol 49 no 9pp 3481ndash3494 2016

[4] S J Zhao Q Zhang and L M Liu ldquoCrack initiationpropagation and coalescence experiments in sandstone Bra-zilian disks containing pre-existing flawsrdquo Advances in CivilEngineering vol 2019 Article ID 9816067 11 pages 2019

[5] A Bobet and H H Einstein ldquoFracture coalescence in rock-type materials under uniaxial and biaxial compressionrdquo In-ternational Journal of Rock Mechanics and Mining Sciencesvol 35 no 7 pp 863ndash888 1998

[6] E Hoek and C D Martin ldquoFracture initiation and propa-gation in intact rockmdasha reviewrdquo Journal of Rock Mechanicsand Geotechnical Engineering vol 6 no 4 pp 287ndash300 2014

[7] X Zhuang J Chun and H Zhu ldquoA comparative study onunfilled and filled crack propagation for rock-like brittlematerialrdquo=eoretical and Applied Fracture Mechanics vol 72pp 110ndash120 2014

Table 2 Types of cracks initiated from pre-cracked CSCFBD specimens under cyclic impact loading

Tested CSCFBDspecimen no

Crack typesType I tensile Type II tensile Type III tensile Type IV tensile-shear Type V shear Type VI shear Type VII shear

β 0deg radic radic radic radicβ 15deg radic radic radicβ 30deg radic radic radic radic radicβ 45deg radic radic radic radicβ 60deg radic radic radicβ 75deg radic radic radicβ 90deg radic radic radic

Advances in Materials Science and Engineering 9

[8] P Cao T Liu C Pu and H Lin ldquoCrack propagation andcoalescence of brittle rock-like specimens with pre-existingcracks in compressionrdquo Engineering Geology vol 187pp 113ndash121 2015

[9] 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

[10] 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

[11] M D Kuruppu ldquoFracture toughness measurement usingchevron notched semi-circular bend specimenrdquo InternationalJournal of Fracture vol 86 no 4 pp L33ndashL38 1997

[12] A M Shiryaev and A M Kotkis ldquoMethods for determiningfracture toughness of brittle porous materialsrdquo IndustrialLaboratory vol 48 no 9 pp 917-918 1983

[13] M -iercelin and J C Roegiers ldquoFracture toughness de-termination with the modified ring testrdquo in Proceedings of theInternational Symposium on Engineering in Complex RockFormations pp 1ndash8 Beijing China November 1986

[14] G R Irwin ldquoAnalysis of stress and strains near the end of acrack traversing a platerdquo Journal of AppliedMechanics vol 24no 3 pp 361ndash364 1957

[15] J B Walsh ldquo-e effect of cracks on the compressibility ofrockrdquo Journal of Geophysical Research vol 70 no 2pp 381ndash389 1965

[16] E Hoek and Z T Bieniawski ldquoBrittle fracture propagation inrock under compressionrdquo International Journal of FractureMechanics vol 1 no 3 pp 137ndash155 1965

[17] S Q Yang Y H Dai L J Han and Z Q Jin ldquoExperimentalstudy on mechanical behavior of brittle marble samplescontaining different flaws under uniaxial compressionrdquo En-gineering Fracture Mechanics vol 76 no 12 pp 1833ndash18452009

[18] C H Park and A Bobet ldquoCrack coalescence in specimenswith open and closed flaws a comparisonrdquo InternationalJournal of Rock Mechanics and Mining Sciences vol 46 no 5pp 819ndash829 2009

[19] R P Janeiro and H H Einstein ldquoExperimental study of thecracking behavior of specimens containing inclusions (underuniaxial compression)rdquo International Journal of Fracturevol 164 no 1 pp 83ndash102 2010

[20] S Q Yang ldquoCrack coalescence behavior of brittle sandstonesamples containing two coplanar fissures in the process ofdeformation failurerdquo Engineering Fracture Mechanics vol 78no 17 pp 3059ndash3081 2011

[21] M R M Aliha M Sistaninia D J Smith M J Pavier andM R Ayatollahi ldquoGeometry effects and statistical analysis ofmode I fracture in guiting limestonerdquo International Journal ofRock Mechanics and Mining Sciences vol 51 pp 128ndash1352012

[22] M R Ayatollahi and M R M Aliha ldquoOn the use of Braziliandisc specimen for calculating mixed mode I-II fracturetoughness of rock materialsrdquo Engineering Fracture Mechanicsvol 75 no 16 pp 4631ndash4641 2008

[23] A Ghazvinian H R Nejati V Sarfarazi and M R HadeildquoMixed mode crack propagation in low brittle rock-likematerialsrdquo Arabian Journal of Geosciences vol 6 no 11pp 4435ndash4444 2013

[24] N A Al-Shayea ldquoCrack propagation trajectories for rocksunder mixed mode I-II fracturerdquo Engineering Geology vol 81no 1 pp 84ndash97 2005

[25] H Haeri K Shahriar M F Marji and P MoarefvandldquoExperimental and numerical study of crack propagation andcoalescence in pre-cracked rock-like disksrdquo InternationalJournal of Rock Mechanics and Mining Sciences vol 67 no 6pp 20ndash28 2014

[26] H Haeri A Khaloo and M F Marji ldquoFracture analyses ofdifferent pre-holed concrete specimens under compressionrdquoActa Mechanica Sinica vol 31 no 6 pp 855ndash870 2015

[27] H Haeri V Sarfarazi and A Hedayat ldquoSuggesting a newtesting device for determination of tensile strength of con-creterdquo Structural Engineering and Mechanics vol 60 no 6pp 939ndash952 2016

[28] M R M Aliha and A Bahmani ldquoRock fracture toughnessstudy under mixed mode IIII loadingrdquo Rock Mechanics andRock Engineering vol 50 no 7 pp 1739ndash1751 2017

[29] D J Frew M J Forrestal and W W Chen ldquoPulse shapingtechniques for testing brittle materials with a split Hopkinsonpressure barrdquo Experimental Mechanics vol 42 no 1pp 93ndash106 2002

[30] D J Frew M J Forrestal and W Chen ldquoPulse shapingtechniques for testing elastic-plastic materials with a splitHopkinson pressure barrdquo Experimental Mechanics vol 45no 2 pp 186ndash195 2005

[31] X Li T Zhou and D Li ldquoDynamic strength and fracturingbehavior of single-flawed prismatic marble specimens underimpact loading with a split-Hopkinson pressure barrdquo RockMechanics and Rock Engineering vol 50 no 1 pp 29ndash442017

[32] Q Z Wang J R Yang C G Zhang et al ldquoSequential de-termination of dynamic initiation and propagation toughnessof rock using an experimental-numerical-analytical methodrdquoEngineering Fracture Mechanics vol 141 pp 78ndash94 2015

[33] F Dai S Huang K Xia and Z Tan ldquoSome fundamentalissues in dynamic compression and tension tests of rocksusing split Hopkinson pressure barrdquo Rock Mechanics andRock Engineering vol 43 no 6 pp 657ndash666 2010

[34] W Li and J Xu ldquoMechanical properties of basalt fiberreinforced geopolymeric concrete under impact loadingrdquoMaterials Science and Engineering A vol 505 no 1-2pp 178ndash186 2009

[35] Z L Wang H H Zhu and J G Wang ldquoRepeated-impactresponse of ultrashort steel fiber reinforced concreterdquo Ex-perimental Techniques vol 37 no 4 pp 6ndash13 2013

[36] X Chen S Wu and J Zhou ldquoExperimental and modelingstudy of dynamic mechanical properties of cement pastemortar and concreterdquo Construction and Building Materialsvol 47 pp 419ndash430 2013

[37] X D Chen L M Ge J K Zhou and S X Wu ldquoDynamicBrazilian test of concrete using split Hopkinson pressure barrdquoMaterials and Structures vol 50 no 1 2017

[38] M Zhang H J Wu Q M Li and F L Huang ldquoFurtherinvestigation on the dynamic compressive strength en-hancement of concrete-like materials based on split Hop-kinson pressure bar testsmdashpart I experimentsrdquo InternationalJournal of Impact Engineering vol 36 no 12 pp 1327ndash13342009

[39] W Chen and G Ravichandran ldquoFailure mode transition inceramics under dynamic multiaxial compressionrdquo In-ternational Journal of Fracture vol 101 no 1-2 pp 141ndash1592000

10 Advances in Materials Science and Engineering

[40] H Wang and K T Ramesh ldquoDynamic strength and frag-mentation of hot-pressed silicon carbide under uniaxialcompressionrdquo Acta Materialia vol 52 no 2 pp 355ndash3672004

[41] T Ficker ldquoQuasi-static compressive strength of cement-basedmaterialsrdquo Cement and Concrete Research vol 41 no 1pp 129ndash132 2011

[42] H Hao and B G Tarasov ldquoExperimental study of dynamicmaterial properties of clay brick and mortar at different strainratesrdquo Australian Journal of Structural Engineering vol 8no 2 pp 117ndash132 2008

[43] M Wu C Qin and C Zhang ldquoHigh strain rate splittingtensile tests of concrete and numerical simulation by meso-scale particle elementsrdquo Journal of Materials in Civil Engi-neering vol 26 no 1 pp 71ndash82 2014

[44] J Xiao L Li L Shen and C S Poon ldquoCompressive behaviourof recycled aggregate concrete under impact loadingrdquo Cementand Concrete Research vol 71 pp 46ndash55 2015

[45] W Wu W Zhang and G Ma ldquoMechanical properties ofcopper slag reinforced concrete under dynamic compressionrdquoConstruction and Building Materials vol 24 no 6 pp 910ndash917 2010

[46] H Su and J Xu ldquoDynamic compressive behavior of ceramicfiber reinforced concrete under impact loadrdquo Constructionand Building Materials vol 45 pp 306ndash313 2013

[47] Y Al-Salloum T Almusallam S M Ibrahim H Abbas andS Alsayed ldquoRate dependent behavior and modeling ofconcrete based on SHPB experimentsrdquo Cement and ConcreteComposites vol 55 pp 34ndash44 2015

[48] C A Ross P Y -ompson and J W Tedesco ldquoSplit-Hopkinson pressure-bar tests on concrete and mortar intension and compressionrdquo ACI Materials Journal vol 86no 5 pp 475ndash481 1989

[49] Q Z Wang X M Jia S Q Kou Z X Zhang andP-A Lindqvist ldquo-e flattened Brazilian disc specimen usedfor testing elastic modulus tensile strength and fracturetoughness of brittle rocks analytical and numerical resultsrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 41 no 2 pp 245ndash253 2004

[50] F Berto and J Gomez ldquoNotched plates in mixed modeloading (I+II) a review based on the local strain energydensity and the cohesive zone modelrdquo Engineering SolidMechanics vol 5 pp 1ndash8 2017

[51] D Huang Q Zhang and P Qiao ldquoDamage and progressivefailure of concrete structures using non-local peridynamicmodelingrdquo Science China Technological Sciences vol 54 no 3pp 591ndash596 2011

[52] D Huang Q Zhang P Z Qiao and F Shen ldquoA review onperidynamics (PD) method and its applicationsrdquo Advances inMechanics vol 40 no 4 pp 448ndash459 2010

[53] H Haeri K Shahriar M F Marji and P Moarefvand ldquoAcoupled numerical-experimental study of the breakage pro-cess of brittle substancesrdquo Arabian Journal of Geosciencesvol 8 no 2 pp 809ndash825 2015

[54] Y D Ha and F Bobaru ldquoStudies of dynamic crack propa-gation and crack branching with peridynamicsrdquo InternationalJournal of Fracture vol 162 no 1-2 pp 229ndash244 2010

Advances in Materials Science and Engineering 11

CorrosionInternational Journal of

Hindawiwwwhindawicom Volume 2018

Advances in

Materials Science and EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Analytical ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

ScienticaHindawiwwwhindawicom Volume 2018

Polymer ScienceInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Advances in Condensed Matter Physics

Hindawiwwwhindawicom Volume 2018

International Journal of

BiomaterialsHindawiwwwhindawicom

Journal ofEngineeringVolume 2018

Applied ChemistryJournal of

Hindawiwwwhindawicom Volume 2018

NanotechnologyHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

High Energy PhysicsAdvances in

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

TribologyAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

ChemistryAdvances in

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

Hindawiwwwhindawicom Volume 2018

BioMed Research InternationalMaterials

Journal of

Hindawiwwwhindawicom Volume 2018

Na

nom

ate

ria

ls

Hindawiwwwhindawicom Volume 2018

Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom

CSCFBD specimens with dierent inclination angles areindicated and for all gures the upper plane edges of thespecimens are contacted with the incident bar As shown inFigures 8(b)ndash8(g) cracks initiated from the tips of pre-cracksand approximately propagated towards the direction of themaximum stress It should be noted that in Figure 8(a)there is a crack initiated from the middle portion of the pre-crack when β= 0deg

Figure 8(a) shows that ve crack propagation pathsappeared two cracks started from the pre-existing crackrsquosleft-end tip and propagated to the specimenrsquos lower planeedge two cracks started from the pre-existing crackrsquos right-end tip the rest one crack propagated to the upper and lowerplane edges However because of the high values of crackorientation with respect to the loading direction there is onecrack which did not propagate from the tip of the pre-crackIn Figures 8(c) and 8(d) β= 30deg 45deg respectively ve crackpropagation paths appeared Figure 8(c) shows that there aretwo cracks that started from the pre-crack upper tip andpropagated to the upper plane edge two cracks started fromthe pre-crack lower tip and propagated to the lower planeedge and the rest one crack started from the pre-crack uppertip and propagated to the lower plane edge While inFigure 8(d) there is one crack that started from the pre-cracklower tip and propagated to the upper plane edge InFigures 8(b) 8(e) and 8(f ) β= 15deg 60deg and 75deg respectivelyfour main crack propagation paths appeared and two ofthem started from the pre-crack upper tip and propagated tothe upper plane edge e other two started from the pre-crack lower tip and propagated to the lower plane edge InFigure 8(b) an intermittent crack appeared starting fromthe pre-crack lower tip and has a downward trend to thelower plane edge Figure 8(e) shows that the scatter of thefour cracks presents regular symmetrical characteristic Asshown in Figure 8(g) β= 90deg and the upper pre-crack tippropagated two crack propagation paths to the upper planeedge and one to the lower plane edge

From Figures 8(a)ndash8(g) it can be clearly seen that the nal dynamic crack propagation paths and fracture pat-terns under impact loading are obviously dierent

compared to those under static or quasi-static loading(eg Figure 9 [4]) In many studies there is only onefracture that propagates from each tip of BD specimensunder static or quasi-static loading But under impactloading in the SHPB test due to fractures with high strainrate there are multiple crack propagation paths eresults also show the pre-existing inclination angles aectthe multiple crack propagation paths and directionsinitiated from tips of the pre-cracks under cyclic dynamicloading

4 Discussion

e crack propagation patterns were obtained in previousinvestigations of brittle materials with pre-cracks as shownin Figure 10 [1 2] From the experimental results above twotypes of cracks were observed wing cracks and secondarycracks Usually the wing cracks are tensile cracks and thesecondary cracks are shear cracks (oblique shear cracks andcoplanar or quasi-coplanar shear) Table 2 summarizes cracktypes initiated from the pre-cracks in CSCFBD specimensunder cyclic impact loading Most of the tensile cracks andshear cracks initiated from the tips of pre-cracks at an angleand then propagate to the parallel to the compressive di-rection Shear cracksrsquo initiation patterns depend on theinclination angles of the pre-cracks Under impact loadingshear cracks caused the failure of the tested specimensmostly

Fracture and failure of pre-cracked CSCFBD specimensunder cyclic impact loading involve tensile and shear cracktypes Because of pre-cracks the fracture patterns andfailure modes are much more complex than those of intactbrittle materials Note that all the CSCFBD specimenspresent multiply crack propagation paths But the geom-etries of pre-cracks appear to play limited eects on thecrack type of CSCFBD specimens under cyclic impactloading

In this paper we studied the dynamic crack propa-gation and fracture patterns in pre-cracked CSCFBDspecimens from deep underground strata under cyclicimpact loading e dynamic crack propagation paths anddirections are obviously dierent from those under staticor quasi-static loading in the previous studies and theexperimental results present some regular symmetricalcharacteristics e dynamic crack propagation paths andpropagation directions are not only determined by ma-terial related but also dependent on the geometries of thepre-cracks However the geometries of pre-cracks appearto play limited eects on the nal dynamic fracture pat-terns and failure modes of CSCFBD specimens undercyclic impact loading Further research may be a focus onthe dynamic crack propagation mechanism of brittlematerials studied by experimental and numerical simu-lation comprehensively Various numerical simulationmethods eg nite element method (FEM) extended nite element method (XFEM) nite dierentialmethod (FDM) and dierent criteria eg strain energydensity (SED) criterion cohesive zone model (CZM) [50]for theoretical analysis have been developed to investigate

ndash151

2

3Impa

ct ti

mes

4

5

6

0 15 30 45β angle (degrees)

60 75 90

Figure 7 Impact times in nal crack propagation path forms whenβ 0deg 15deg 30deg 45deg 60deg 75deg and 90deg

Advances in Materials Science and Engineering 5

Crack propagationpath

Crack propagationpath

(a)

Crack propagation path

Crack propagation path

(b)

Crack propagationpath

Crack propagation path

(c)

Crack propagationpath

Crack propagation path

(d)

Crack propagation path

Crack propagation path

(e)

Crack propagationpath

Crack propagation path

(f )

Figure 8 Continued

6 Advances in Materials Science and Engineering

Wing crack

Wing crack

(a)

Wing crack

Wing crack

(b)

Wing crack

Wing crack

(c)

Wing crack

Wing crack

(d)

Figure 9 Continued

Crack propagation path

Crack propagation path

(g)

Figure 8 Crack propagation paths in ne sandstone CSCFBD specimens with dierent inclination angles of pre-cracks (a) β 0 (b) β 15deg(c) β 30deg (d) β 45deg (e) β 60deg (f ) β 75deg (g) β 90deg

Advances in Materials Science and Engineering 7

Wing crack

Wing crack

(e)

Wing crack

Wing crack

(f )

Wing crack

Wing crack

(g)

Figure 9 Experimental results of crack propagation paths in tested specimens with dierent inclination angles of pre-cracks (a) β 0(b) β 15deg (c) β 30deg (d) β 45deg (e) β 60deg (f ) β 75deg (g) β 90deg [4]

T

TType IT

T

Type II

T

T

Type IIIT

T

S

S

Type IV

S

S

Type V

S

Type VI

S

SType VII

Figure 10 Various crack types initiated from the pre-cracks identi ed in the present studies (Tand S denote tensile and shear cracks)Type Itensile crack Type II tensile crack Type III tensile crack Type IV mixed tensile-shear crack Type V shear crack Type VI shear crack(coplanar or quasi-coplanar shear crack) Type VII shear crack (oblique shear crack) [1 2]

8 Advances in Materials Science and Engineering

crack propagation fracture patterns and failure modes inbrittle materials but have not shown satisfactoryeffectiveness in modeling dynamic damage evolutionand crack propagation [51ndash53] Using mesh-free particlemethods to numerically study dynamic crack propagationmay be an effective way Especially in peridynamics cracksare part of the solution not part of the problem [54]-erefore using peridynamics to simulate dynamicmultiple crack propagation and fracture patterns in brittlematerials under impact or cyclic impact loading would bevery meaningful which we plan for in the future

5 Conclusions

In this paper we provide experimental results of dynamicfracture tests carried out on fine sandstone CSCFBDspecimens under cyclic impact loading by the Φ 74mm-diameter SHPB device Dynamic crack propagation andfracture mechanism are rather complicated processes Fromthe results presented and analyzed above the followingconclusions could be drawn

(1) Compared to static or quasi-static loading the dy-namic crack propagation and fracture behavior aremuch more complex and it presents multiple crackpropagation paths and directions in dynamicfracture

(2) Both tensile and shear cracks were observed most ofthemmainly initiated from tips of the pre-cracks andpropagated in a stable manner According to thedifferent geometries of pre-cracks the testedCSCFBD specimens experienced tensile or shearcrack propagation failure

(3) -e natural or artificial pre-existing defects canchange the crack propagation paths especially di-rections under impact loading compared to static orquasi-static loading However the geometries ofpre-cracks appear to play limited effects on crackstype of CSCFBD specimens under cyclic impactloading

(4) Dynamic crack propagation and fracture mecha-nism are rather complicated processes -is studyrevealed multiple dynamic crack propagationbehavior that had not been observed previouslyNumerical simulation is further needed to besummarized and explored which we plan for in thefuture

Data Availability

-e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-e research described in this paper was financially supportedby the National Key Technologies Research amp DevelopmentProgram (nos 2018YFC0406703 and 2017YFC1502600) theNational Natural Science Foundation of China (nos 11672101and 11372099) the Postgraduate Research amp Practice In-novation Program of Jiangsu Province (no KYLX16_0700)and the Fundamental Research Funds for the Central Uni-versities (no 2016B45214)

References

[1] L N Y Wong and H H Einstein ldquoCrack coalescence inmolded gypsum and Carrara marble part 1mdashmacroscopicobservations and interpretationrdquo Rock Mechanics and RockEngineering vol 42 no 3 pp 475ndash511 2009

[2] L N Y Wong and H H Einstein ldquoCrack coalescence inmolded gypsum and carrara marble part 2mdashmicroscopicobservations and interpretationrdquo Rock Mechanics and RockEngineering vol 42 no 3 pp 513ndash545 2009

[3] H Cheng X Zhou J Zhu and Q Qian ldquo-e effects of crackopenings on crack initiation propagation and coalescencebehavior in rock-like materials under uniaxial compressionrdquoRock Mechanics and Rock Engineering vol 49 no 9pp 3481ndash3494 2016

[4] S J Zhao Q Zhang and L M Liu ldquoCrack initiationpropagation and coalescence experiments in sandstone Bra-zilian disks containing pre-existing flawsrdquo Advances in CivilEngineering vol 2019 Article ID 9816067 11 pages 2019

[5] A Bobet and H H Einstein ldquoFracture coalescence in rock-type materials under uniaxial and biaxial compressionrdquo In-ternational Journal of Rock Mechanics and Mining Sciencesvol 35 no 7 pp 863ndash888 1998

[6] E Hoek and C D Martin ldquoFracture initiation and propa-gation in intact rockmdasha reviewrdquo Journal of Rock Mechanicsand Geotechnical Engineering vol 6 no 4 pp 287ndash300 2014

[7] X Zhuang J Chun and H Zhu ldquoA comparative study onunfilled and filled crack propagation for rock-like brittlematerialrdquo=eoretical and Applied Fracture Mechanics vol 72pp 110ndash120 2014

Table 2 Types of cracks initiated from pre-cracked CSCFBD specimens under cyclic impact loading

Tested CSCFBDspecimen no

Crack typesType I tensile Type II tensile Type III tensile Type IV tensile-shear Type V shear Type VI shear Type VII shear

β 0deg radic radic radic radicβ 15deg radic radic radicβ 30deg radic radic radic radic radicβ 45deg radic radic radic radicβ 60deg radic radic radicβ 75deg radic radic radicβ 90deg radic radic radic

Advances in Materials Science and Engineering 9

[8] P Cao T Liu C Pu and H Lin ldquoCrack propagation andcoalescence of brittle rock-like specimens with pre-existingcracks in compressionrdquo Engineering Geology vol 187pp 113ndash121 2015

[9] 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

[10] 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

[11] M D Kuruppu ldquoFracture toughness measurement usingchevron notched semi-circular bend specimenrdquo InternationalJournal of Fracture vol 86 no 4 pp L33ndashL38 1997

[12] A M Shiryaev and A M Kotkis ldquoMethods for determiningfracture toughness of brittle porous materialsrdquo IndustrialLaboratory vol 48 no 9 pp 917-918 1983

[13] M -iercelin and J C Roegiers ldquoFracture toughness de-termination with the modified ring testrdquo in Proceedings of theInternational Symposium on Engineering in Complex RockFormations pp 1ndash8 Beijing China November 1986

[14] G R Irwin ldquoAnalysis of stress and strains near the end of acrack traversing a platerdquo Journal of AppliedMechanics vol 24no 3 pp 361ndash364 1957

[15] J B Walsh ldquo-e effect of cracks on the compressibility ofrockrdquo Journal of Geophysical Research vol 70 no 2pp 381ndash389 1965

[16] E Hoek and Z T Bieniawski ldquoBrittle fracture propagation inrock under compressionrdquo International Journal of FractureMechanics vol 1 no 3 pp 137ndash155 1965

[17] S Q Yang Y H Dai L J Han and Z Q Jin ldquoExperimentalstudy on mechanical behavior of brittle marble samplescontaining different flaws under uniaxial compressionrdquo En-gineering Fracture Mechanics vol 76 no 12 pp 1833ndash18452009

[18] C H Park and A Bobet ldquoCrack coalescence in specimenswith open and closed flaws a comparisonrdquo InternationalJournal of Rock Mechanics and Mining Sciences vol 46 no 5pp 819ndash829 2009

[19] R P Janeiro and H H Einstein ldquoExperimental study of thecracking behavior of specimens containing inclusions (underuniaxial compression)rdquo International Journal of Fracturevol 164 no 1 pp 83ndash102 2010

[20] S Q Yang ldquoCrack coalescence behavior of brittle sandstonesamples containing two coplanar fissures in the process ofdeformation failurerdquo Engineering Fracture Mechanics vol 78no 17 pp 3059ndash3081 2011

[21] M R M Aliha M Sistaninia D J Smith M J Pavier andM R Ayatollahi ldquoGeometry effects and statistical analysis ofmode I fracture in guiting limestonerdquo International Journal ofRock Mechanics and Mining Sciences vol 51 pp 128ndash1352012

[22] M R Ayatollahi and M R M Aliha ldquoOn the use of Braziliandisc specimen for calculating mixed mode I-II fracturetoughness of rock materialsrdquo Engineering Fracture Mechanicsvol 75 no 16 pp 4631ndash4641 2008

[23] A Ghazvinian H R Nejati V Sarfarazi and M R HadeildquoMixed mode crack propagation in low brittle rock-likematerialsrdquo Arabian Journal of Geosciences vol 6 no 11pp 4435ndash4444 2013

[24] N A Al-Shayea ldquoCrack propagation trajectories for rocksunder mixed mode I-II fracturerdquo Engineering Geology vol 81no 1 pp 84ndash97 2005

[25] H Haeri K Shahriar M F Marji and P MoarefvandldquoExperimental and numerical study of crack propagation andcoalescence in pre-cracked rock-like disksrdquo InternationalJournal of Rock Mechanics and Mining Sciences vol 67 no 6pp 20ndash28 2014

[26] H Haeri A Khaloo and M F Marji ldquoFracture analyses ofdifferent pre-holed concrete specimens under compressionrdquoActa Mechanica Sinica vol 31 no 6 pp 855ndash870 2015

[27] H Haeri V Sarfarazi and A Hedayat ldquoSuggesting a newtesting device for determination of tensile strength of con-creterdquo Structural Engineering and Mechanics vol 60 no 6pp 939ndash952 2016

[28] M R M Aliha and A Bahmani ldquoRock fracture toughnessstudy under mixed mode IIII loadingrdquo Rock Mechanics andRock Engineering vol 50 no 7 pp 1739ndash1751 2017

[29] D J Frew M J Forrestal and W W Chen ldquoPulse shapingtechniques for testing brittle materials with a split Hopkinsonpressure barrdquo Experimental Mechanics vol 42 no 1pp 93ndash106 2002

[30] D J Frew M J Forrestal and W Chen ldquoPulse shapingtechniques for testing elastic-plastic materials with a splitHopkinson pressure barrdquo Experimental Mechanics vol 45no 2 pp 186ndash195 2005

[31] X Li T Zhou and D Li ldquoDynamic strength and fracturingbehavior of single-flawed prismatic marble specimens underimpact loading with a split-Hopkinson pressure barrdquo RockMechanics and Rock Engineering vol 50 no 1 pp 29ndash442017

[32] Q Z Wang J R Yang C G Zhang et al ldquoSequential de-termination of dynamic initiation and propagation toughnessof rock using an experimental-numerical-analytical methodrdquoEngineering Fracture Mechanics vol 141 pp 78ndash94 2015

[33] F Dai S Huang K Xia and Z Tan ldquoSome fundamentalissues in dynamic compression and tension tests of rocksusing split Hopkinson pressure barrdquo Rock Mechanics andRock Engineering vol 43 no 6 pp 657ndash666 2010

[34] W Li and J Xu ldquoMechanical properties of basalt fiberreinforced geopolymeric concrete under impact loadingrdquoMaterials Science and Engineering A vol 505 no 1-2pp 178ndash186 2009

[35] Z L Wang H H Zhu and J G Wang ldquoRepeated-impactresponse of ultrashort steel fiber reinforced concreterdquo Ex-perimental Techniques vol 37 no 4 pp 6ndash13 2013

[36] X Chen S Wu and J Zhou ldquoExperimental and modelingstudy of dynamic mechanical properties of cement pastemortar and concreterdquo Construction and Building Materialsvol 47 pp 419ndash430 2013

[37] X D Chen L M Ge J K Zhou and S X Wu ldquoDynamicBrazilian test of concrete using split Hopkinson pressure barrdquoMaterials and Structures vol 50 no 1 2017

[38] M Zhang H J Wu Q M Li and F L Huang ldquoFurtherinvestigation on the dynamic compressive strength en-hancement of concrete-like materials based on split Hop-kinson pressure bar testsmdashpart I experimentsrdquo InternationalJournal of Impact Engineering vol 36 no 12 pp 1327ndash13342009

[39] W Chen and G Ravichandran ldquoFailure mode transition inceramics under dynamic multiaxial compressionrdquo In-ternational Journal of Fracture vol 101 no 1-2 pp 141ndash1592000

10 Advances in Materials Science and Engineering

[40] H Wang and K T Ramesh ldquoDynamic strength and frag-mentation of hot-pressed silicon carbide under uniaxialcompressionrdquo Acta Materialia vol 52 no 2 pp 355ndash3672004

[41] T Ficker ldquoQuasi-static compressive strength of cement-basedmaterialsrdquo Cement and Concrete Research vol 41 no 1pp 129ndash132 2011

[42] H Hao and B G Tarasov ldquoExperimental study of dynamicmaterial properties of clay brick and mortar at different strainratesrdquo Australian Journal of Structural Engineering vol 8no 2 pp 117ndash132 2008

[43] M Wu C Qin and C Zhang ldquoHigh strain rate splittingtensile tests of concrete and numerical simulation by meso-scale particle elementsrdquo Journal of Materials in Civil Engi-neering vol 26 no 1 pp 71ndash82 2014

[44] J Xiao L Li L Shen and C S Poon ldquoCompressive behaviourof recycled aggregate concrete under impact loadingrdquo Cementand Concrete Research vol 71 pp 46ndash55 2015

[45] W Wu W Zhang and G Ma ldquoMechanical properties ofcopper slag reinforced concrete under dynamic compressionrdquoConstruction and Building Materials vol 24 no 6 pp 910ndash917 2010

[46] H Su and J Xu ldquoDynamic compressive behavior of ceramicfiber reinforced concrete under impact loadrdquo Constructionand Building Materials vol 45 pp 306ndash313 2013

[47] Y Al-Salloum T Almusallam S M Ibrahim H Abbas andS Alsayed ldquoRate dependent behavior and modeling ofconcrete based on SHPB experimentsrdquo Cement and ConcreteComposites vol 55 pp 34ndash44 2015

[48] C A Ross P Y -ompson and J W Tedesco ldquoSplit-Hopkinson pressure-bar tests on concrete and mortar intension and compressionrdquo ACI Materials Journal vol 86no 5 pp 475ndash481 1989

[49] Q Z Wang X M Jia S Q Kou Z X Zhang andP-A Lindqvist ldquo-e flattened Brazilian disc specimen usedfor testing elastic modulus tensile strength and fracturetoughness of brittle rocks analytical and numerical resultsrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 41 no 2 pp 245ndash253 2004

[50] F Berto and J Gomez ldquoNotched plates in mixed modeloading (I+II) a review based on the local strain energydensity and the cohesive zone modelrdquo Engineering SolidMechanics vol 5 pp 1ndash8 2017

[51] D Huang Q Zhang and P Qiao ldquoDamage and progressivefailure of concrete structures using non-local peridynamicmodelingrdquo Science China Technological Sciences vol 54 no 3pp 591ndash596 2011

[52] D Huang Q Zhang P Z Qiao and F Shen ldquoA review onperidynamics (PD) method and its applicationsrdquo Advances inMechanics vol 40 no 4 pp 448ndash459 2010

[53] H Haeri K Shahriar M F Marji and P Moarefvand ldquoAcoupled numerical-experimental study of the breakage pro-cess of brittle substancesrdquo Arabian Journal of Geosciencesvol 8 no 2 pp 809ndash825 2015

[54] Y D Ha and F Bobaru ldquoStudies of dynamic crack propa-gation and crack branching with peridynamicsrdquo InternationalJournal of Fracture vol 162 no 1-2 pp 229ndash244 2010

Advances in Materials Science and Engineering 11

CorrosionInternational Journal of

Hindawiwwwhindawicom Volume 2018

Advances in

Materials Science and EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Analytical ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

ScienticaHindawiwwwhindawicom Volume 2018

Polymer ScienceInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Advances in Condensed Matter Physics

Hindawiwwwhindawicom Volume 2018

International Journal of

BiomaterialsHindawiwwwhindawicom

Journal ofEngineeringVolume 2018

Applied ChemistryJournal of

Hindawiwwwhindawicom Volume 2018

NanotechnologyHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

High Energy PhysicsAdvances in

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

TribologyAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

ChemistryAdvances in

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

Hindawiwwwhindawicom Volume 2018

BioMed Research InternationalMaterials

Journal of

Hindawiwwwhindawicom Volume 2018

Na

nom

ate

ria

ls

Hindawiwwwhindawicom Volume 2018

Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom

Crack propagationpath

Crack propagationpath

(a)

Crack propagation path

Crack propagation path

(b)

Crack propagationpath

Crack propagation path

(c)

Crack propagationpath

Crack propagation path

(d)

Crack propagation path

Crack propagation path

(e)

Crack propagationpath

Crack propagation path

(f )

Figure 8 Continued

6 Advances in Materials Science and Engineering

Wing crack

Wing crack

(a)

Wing crack

Wing crack

(b)

Wing crack

Wing crack

(c)

Wing crack

Wing crack

(d)

Figure 9 Continued

Crack propagation path

Crack propagation path

(g)

Figure 8 Crack propagation paths in ne sandstone CSCFBD specimens with dierent inclination angles of pre-cracks (a) β 0 (b) β 15deg(c) β 30deg (d) β 45deg (e) β 60deg (f ) β 75deg (g) β 90deg

Advances in Materials Science and Engineering 7

Wing crack

Wing crack

(e)

Wing crack

Wing crack

(f )

Wing crack

Wing crack

(g)

Figure 9 Experimental results of crack propagation paths in tested specimens with dierent inclination angles of pre-cracks (a) β 0(b) β 15deg (c) β 30deg (d) β 45deg (e) β 60deg (f ) β 75deg (g) β 90deg [4]

T

TType IT

T

Type II

T

T

Type IIIT

T

S

S

Type IV

S

S

Type V

S

Type VI

S

SType VII

Figure 10 Various crack types initiated from the pre-cracks identi ed in the present studies (Tand S denote tensile and shear cracks)Type Itensile crack Type II tensile crack Type III tensile crack Type IV mixed tensile-shear crack Type V shear crack Type VI shear crack(coplanar or quasi-coplanar shear crack) Type VII shear crack (oblique shear crack) [1 2]

8 Advances in Materials Science and Engineering

crack propagation fracture patterns and failure modes inbrittle materials but have not shown satisfactoryeffectiveness in modeling dynamic damage evolutionand crack propagation [51ndash53] Using mesh-free particlemethods to numerically study dynamic crack propagationmay be an effective way Especially in peridynamics cracksare part of the solution not part of the problem [54]-erefore using peridynamics to simulate dynamicmultiple crack propagation and fracture patterns in brittlematerials under impact or cyclic impact loading would bevery meaningful which we plan for in the future

5 Conclusions

In this paper we provide experimental results of dynamicfracture tests carried out on fine sandstone CSCFBDspecimens under cyclic impact loading by the Φ 74mm-diameter SHPB device Dynamic crack propagation andfracture mechanism are rather complicated processes Fromthe results presented and analyzed above the followingconclusions could be drawn

(1) Compared to static or quasi-static loading the dy-namic crack propagation and fracture behavior aremuch more complex and it presents multiple crackpropagation paths and directions in dynamicfracture

(2) Both tensile and shear cracks were observed most ofthemmainly initiated from tips of the pre-cracks andpropagated in a stable manner According to thedifferent geometries of pre-cracks the testedCSCFBD specimens experienced tensile or shearcrack propagation failure

(3) -e natural or artificial pre-existing defects canchange the crack propagation paths especially di-rections under impact loading compared to static orquasi-static loading However the geometries ofpre-cracks appear to play limited effects on crackstype of CSCFBD specimens under cyclic impactloading

(4) Dynamic crack propagation and fracture mecha-nism are rather complicated processes -is studyrevealed multiple dynamic crack propagationbehavior that had not been observed previouslyNumerical simulation is further needed to besummarized and explored which we plan for in thefuture

Data Availability

-e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-e research described in this paper was financially supportedby the National Key Technologies Research amp DevelopmentProgram (nos 2018YFC0406703 and 2017YFC1502600) theNational Natural Science Foundation of China (nos 11672101and 11372099) the Postgraduate Research amp Practice In-novation Program of Jiangsu Province (no KYLX16_0700)and the Fundamental Research Funds for the Central Uni-versities (no 2016B45214)

References

[1] L N Y Wong and H H Einstein ldquoCrack coalescence inmolded gypsum and Carrara marble part 1mdashmacroscopicobservations and interpretationrdquo Rock Mechanics and RockEngineering vol 42 no 3 pp 475ndash511 2009

[2] L N Y Wong and H H Einstein ldquoCrack coalescence inmolded gypsum and carrara marble part 2mdashmicroscopicobservations and interpretationrdquo Rock Mechanics and RockEngineering vol 42 no 3 pp 513ndash545 2009

[3] H Cheng X Zhou J Zhu and Q Qian ldquo-e effects of crackopenings on crack initiation propagation and coalescencebehavior in rock-like materials under uniaxial compressionrdquoRock Mechanics and Rock Engineering vol 49 no 9pp 3481ndash3494 2016

[4] S J Zhao Q Zhang and L M Liu ldquoCrack initiationpropagation and coalescence experiments in sandstone Bra-zilian disks containing pre-existing flawsrdquo Advances in CivilEngineering vol 2019 Article ID 9816067 11 pages 2019

[5] A Bobet and H H Einstein ldquoFracture coalescence in rock-type materials under uniaxial and biaxial compressionrdquo In-ternational Journal of Rock Mechanics and Mining Sciencesvol 35 no 7 pp 863ndash888 1998

[6] E Hoek and C D Martin ldquoFracture initiation and propa-gation in intact rockmdasha reviewrdquo Journal of Rock Mechanicsand Geotechnical Engineering vol 6 no 4 pp 287ndash300 2014

[7] X Zhuang J Chun and H Zhu ldquoA comparative study onunfilled and filled crack propagation for rock-like brittlematerialrdquo=eoretical and Applied Fracture Mechanics vol 72pp 110ndash120 2014

Table 2 Types of cracks initiated from pre-cracked CSCFBD specimens under cyclic impact loading

Tested CSCFBDspecimen no

Crack typesType I tensile Type II tensile Type III tensile Type IV tensile-shear Type V shear Type VI shear Type VII shear

β 0deg radic radic radic radicβ 15deg radic radic radicβ 30deg radic radic radic radic radicβ 45deg radic radic radic radicβ 60deg radic radic radicβ 75deg radic radic radicβ 90deg radic radic radic

Advances in Materials Science and Engineering 9

[8] P Cao T Liu C Pu and H Lin ldquoCrack propagation andcoalescence of brittle rock-like specimens with pre-existingcracks in compressionrdquo Engineering Geology vol 187pp 113ndash121 2015

[9] 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

[10] 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

[11] M D Kuruppu ldquoFracture toughness measurement usingchevron notched semi-circular bend specimenrdquo InternationalJournal of Fracture vol 86 no 4 pp L33ndashL38 1997

[12] A M Shiryaev and A M Kotkis ldquoMethods for determiningfracture toughness of brittle porous materialsrdquo IndustrialLaboratory vol 48 no 9 pp 917-918 1983

[13] M -iercelin and J C Roegiers ldquoFracture toughness de-termination with the modified ring testrdquo in Proceedings of theInternational Symposium on Engineering in Complex RockFormations pp 1ndash8 Beijing China November 1986

[14] G R Irwin ldquoAnalysis of stress and strains near the end of acrack traversing a platerdquo Journal of AppliedMechanics vol 24no 3 pp 361ndash364 1957

[15] J B Walsh ldquo-e effect of cracks on the compressibility ofrockrdquo Journal of Geophysical Research vol 70 no 2pp 381ndash389 1965

[16] E Hoek and Z T Bieniawski ldquoBrittle fracture propagation inrock under compressionrdquo International Journal of FractureMechanics vol 1 no 3 pp 137ndash155 1965

[17] S Q Yang Y H Dai L J Han and Z Q Jin ldquoExperimentalstudy on mechanical behavior of brittle marble samplescontaining different flaws under uniaxial compressionrdquo En-gineering Fracture Mechanics vol 76 no 12 pp 1833ndash18452009

[18] C H Park and A Bobet ldquoCrack coalescence in specimenswith open and closed flaws a comparisonrdquo InternationalJournal of Rock Mechanics and Mining Sciences vol 46 no 5pp 819ndash829 2009

[19] R P Janeiro and H H Einstein ldquoExperimental study of thecracking behavior of specimens containing inclusions (underuniaxial compression)rdquo International Journal of Fracturevol 164 no 1 pp 83ndash102 2010

[20] S Q Yang ldquoCrack coalescence behavior of brittle sandstonesamples containing two coplanar fissures in the process ofdeformation failurerdquo Engineering Fracture Mechanics vol 78no 17 pp 3059ndash3081 2011

[21] M R M Aliha M Sistaninia D J Smith M J Pavier andM R Ayatollahi ldquoGeometry effects and statistical analysis ofmode I fracture in guiting limestonerdquo International Journal ofRock Mechanics and Mining Sciences vol 51 pp 128ndash1352012

[22] M R Ayatollahi and M R M Aliha ldquoOn the use of Braziliandisc specimen for calculating mixed mode I-II fracturetoughness of rock materialsrdquo Engineering Fracture Mechanicsvol 75 no 16 pp 4631ndash4641 2008

[23] A Ghazvinian H R Nejati V Sarfarazi and M R HadeildquoMixed mode crack propagation in low brittle rock-likematerialsrdquo Arabian Journal of Geosciences vol 6 no 11pp 4435ndash4444 2013

[24] N A Al-Shayea ldquoCrack propagation trajectories for rocksunder mixed mode I-II fracturerdquo Engineering Geology vol 81no 1 pp 84ndash97 2005

[25] H Haeri K Shahriar M F Marji and P MoarefvandldquoExperimental and numerical study of crack propagation andcoalescence in pre-cracked rock-like disksrdquo InternationalJournal of Rock Mechanics and Mining Sciences vol 67 no 6pp 20ndash28 2014

[26] H Haeri A Khaloo and M F Marji ldquoFracture analyses ofdifferent pre-holed concrete specimens under compressionrdquoActa Mechanica Sinica vol 31 no 6 pp 855ndash870 2015

[27] H Haeri V Sarfarazi and A Hedayat ldquoSuggesting a newtesting device for determination of tensile strength of con-creterdquo Structural Engineering and Mechanics vol 60 no 6pp 939ndash952 2016

[28] M R M Aliha and A Bahmani ldquoRock fracture toughnessstudy under mixed mode IIII loadingrdquo Rock Mechanics andRock Engineering vol 50 no 7 pp 1739ndash1751 2017

[29] D J Frew M J Forrestal and W W Chen ldquoPulse shapingtechniques for testing brittle materials with a split Hopkinsonpressure barrdquo Experimental Mechanics vol 42 no 1pp 93ndash106 2002

[30] D J Frew M J Forrestal and W Chen ldquoPulse shapingtechniques for testing elastic-plastic materials with a splitHopkinson pressure barrdquo Experimental Mechanics vol 45no 2 pp 186ndash195 2005

[31] X Li T Zhou and D Li ldquoDynamic strength and fracturingbehavior of single-flawed prismatic marble specimens underimpact loading with a split-Hopkinson pressure barrdquo RockMechanics and Rock Engineering vol 50 no 1 pp 29ndash442017

[32] Q Z Wang J R Yang C G Zhang et al ldquoSequential de-termination of dynamic initiation and propagation toughnessof rock using an experimental-numerical-analytical methodrdquoEngineering Fracture Mechanics vol 141 pp 78ndash94 2015

[33] F Dai S Huang K Xia and Z Tan ldquoSome fundamentalissues in dynamic compression and tension tests of rocksusing split Hopkinson pressure barrdquo Rock Mechanics andRock Engineering vol 43 no 6 pp 657ndash666 2010

[34] W Li and J Xu ldquoMechanical properties of basalt fiberreinforced geopolymeric concrete under impact loadingrdquoMaterials Science and Engineering A vol 505 no 1-2pp 178ndash186 2009

[35] Z L Wang H H Zhu and J G Wang ldquoRepeated-impactresponse of ultrashort steel fiber reinforced concreterdquo Ex-perimental Techniques vol 37 no 4 pp 6ndash13 2013

[36] X Chen S Wu and J Zhou ldquoExperimental and modelingstudy of dynamic mechanical properties of cement pastemortar and concreterdquo Construction and Building Materialsvol 47 pp 419ndash430 2013

[37] X D Chen L M Ge J K Zhou and S X Wu ldquoDynamicBrazilian test of concrete using split Hopkinson pressure barrdquoMaterials and Structures vol 50 no 1 2017

[38] M Zhang H J Wu Q M Li and F L Huang ldquoFurtherinvestigation on the dynamic compressive strength en-hancement of concrete-like materials based on split Hop-kinson pressure bar testsmdashpart I experimentsrdquo InternationalJournal of Impact Engineering vol 36 no 12 pp 1327ndash13342009

[39] W Chen and G Ravichandran ldquoFailure mode transition inceramics under dynamic multiaxial compressionrdquo In-ternational Journal of Fracture vol 101 no 1-2 pp 141ndash1592000

10 Advances in Materials Science and Engineering

[40] H Wang and K T Ramesh ldquoDynamic strength and frag-mentation of hot-pressed silicon carbide under uniaxialcompressionrdquo Acta Materialia vol 52 no 2 pp 355ndash3672004

[41] T Ficker ldquoQuasi-static compressive strength of cement-basedmaterialsrdquo Cement and Concrete Research vol 41 no 1pp 129ndash132 2011

[42] H Hao and B G Tarasov ldquoExperimental study of dynamicmaterial properties of clay brick and mortar at different strainratesrdquo Australian Journal of Structural Engineering vol 8no 2 pp 117ndash132 2008

[43] M Wu C Qin and C Zhang ldquoHigh strain rate splittingtensile tests of concrete and numerical simulation by meso-scale particle elementsrdquo Journal of Materials in Civil Engi-neering vol 26 no 1 pp 71ndash82 2014

[44] J Xiao L Li L Shen and C S Poon ldquoCompressive behaviourof recycled aggregate concrete under impact loadingrdquo Cementand Concrete Research vol 71 pp 46ndash55 2015

[45] W Wu W Zhang and G Ma ldquoMechanical properties ofcopper slag reinforced concrete under dynamic compressionrdquoConstruction and Building Materials vol 24 no 6 pp 910ndash917 2010

[46] H Su and J Xu ldquoDynamic compressive behavior of ceramicfiber reinforced concrete under impact loadrdquo Constructionand Building Materials vol 45 pp 306ndash313 2013

[47] Y Al-Salloum T Almusallam S M Ibrahim H Abbas andS Alsayed ldquoRate dependent behavior and modeling ofconcrete based on SHPB experimentsrdquo Cement and ConcreteComposites vol 55 pp 34ndash44 2015

[48] C A Ross P Y -ompson and J W Tedesco ldquoSplit-Hopkinson pressure-bar tests on concrete and mortar intension and compressionrdquo ACI Materials Journal vol 86no 5 pp 475ndash481 1989

[49] Q Z Wang X M Jia S Q Kou Z X Zhang andP-A Lindqvist ldquo-e flattened Brazilian disc specimen usedfor testing elastic modulus tensile strength and fracturetoughness of brittle rocks analytical and numerical resultsrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 41 no 2 pp 245ndash253 2004

[50] F Berto and J Gomez ldquoNotched plates in mixed modeloading (I+II) a review based on the local strain energydensity and the cohesive zone modelrdquo Engineering SolidMechanics vol 5 pp 1ndash8 2017

[51] D Huang Q Zhang and P Qiao ldquoDamage and progressivefailure of concrete structures using non-local peridynamicmodelingrdquo Science China Technological Sciences vol 54 no 3pp 591ndash596 2011

[52] D Huang Q Zhang P Z Qiao and F Shen ldquoA review onperidynamics (PD) method and its applicationsrdquo Advances inMechanics vol 40 no 4 pp 448ndash459 2010

[53] H Haeri K Shahriar M F Marji and P Moarefvand ldquoAcoupled numerical-experimental study of the breakage pro-cess of brittle substancesrdquo Arabian Journal of Geosciencesvol 8 no 2 pp 809ndash825 2015

[54] Y D Ha and F Bobaru ldquoStudies of dynamic crack propa-gation and crack branching with peridynamicsrdquo InternationalJournal of Fracture vol 162 no 1-2 pp 229ndash244 2010

Advances in Materials Science and Engineering 11

CorrosionInternational Journal of

Hindawiwwwhindawicom Volume 2018

Advances in

Materials Science and EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Analytical ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

ScienticaHindawiwwwhindawicom Volume 2018

Polymer ScienceInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Advances in Condensed Matter Physics

Hindawiwwwhindawicom Volume 2018

International Journal of

BiomaterialsHindawiwwwhindawicom

Journal ofEngineeringVolume 2018

Applied ChemistryJournal of

Hindawiwwwhindawicom Volume 2018

NanotechnologyHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

High Energy PhysicsAdvances in

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

TribologyAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

ChemistryAdvances in

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

Hindawiwwwhindawicom Volume 2018

BioMed Research InternationalMaterials

Journal of

Hindawiwwwhindawicom Volume 2018

Na

nom

ate

ria

ls

Hindawiwwwhindawicom Volume 2018

Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom

Wing crack

Wing crack

(a)

Wing crack

Wing crack

(b)

Wing crack

Wing crack

(c)

Wing crack

Wing crack

(d)

Figure 9 Continued

Crack propagation path

Crack propagation path

(g)

Figure 8 Crack propagation paths in ne sandstone CSCFBD specimens with dierent inclination angles of pre-cracks (a) β 0 (b) β 15deg(c) β 30deg (d) β 45deg (e) β 60deg (f ) β 75deg (g) β 90deg

Advances in Materials Science and Engineering 7

Wing crack

Wing crack

(e)

Wing crack

Wing crack

(f )

Wing crack

Wing crack

(g)

Figure 9 Experimental results of crack propagation paths in tested specimens with dierent inclination angles of pre-cracks (a) β 0(b) β 15deg (c) β 30deg (d) β 45deg (e) β 60deg (f ) β 75deg (g) β 90deg [4]

T

TType IT

T

Type II

T

T

Type IIIT

T

S

S

Type IV

S

S

Type V

S

Type VI

S

SType VII

Figure 10 Various crack types initiated from the pre-cracks identi ed in the present studies (Tand S denote tensile and shear cracks)Type Itensile crack Type II tensile crack Type III tensile crack Type IV mixed tensile-shear crack Type V shear crack Type VI shear crack(coplanar or quasi-coplanar shear crack) Type VII shear crack (oblique shear crack) [1 2]

8 Advances in Materials Science and Engineering

crack propagation fracture patterns and failure modes inbrittle materials but have not shown satisfactoryeffectiveness in modeling dynamic damage evolutionand crack propagation [51ndash53] Using mesh-free particlemethods to numerically study dynamic crack propagationmay be an effective way Especially in peridynamics cracksare part of the solution not part of the problem [54]-erefore using peridynamics to simulate dynamicmultiple crack propagation and fracture patterns in brittlematerials under impact or cyclic impact loading would bevery meaningful which we plan for in the future

5 Conclusions

In this paper we provide experimental results of dynamicfracture tests carried out on fine sandstone CSCFBDspecimens under cyclic impact loading by the Φ 74mm-diameter SHPB device Dynamic crack propagation andfracture mechanism are rather complicated processes Fromthe results presented and analyzed above the followingconclusions could be drawn

(1) Compared to static or quasi-static loading the dy-namic crack propagation and fracture behavior aremuch more complex and it presents multiple crackpropagation paths and directions in dynamicfracture

(2) Both tensile and shear cracks were observed most ofthemmainly initiated from tips of the pre-cracks andpropagated in a stable manner According to thedifferent geometries of pre-cracks the testedCSCFBD specimens experienced tensile or shearcrack propagation failure

(3) -e natural or artificial pre-existing defects canchange the crack propagation paths especially di-rections under impact loading compared to static orquasi-static loading However the geometries ofpre-cracks appear to play limited effects on crackstype of CSCFBD specimens under cyclic impactloading

(4) Dynamic crack propagation and fracture mecha-nism are rather complicated processes -is studyrevealed multiple dynamic crack propagationbehavior that had not been observed previouslyNumerical simulation is further needed to besummarized and explored which we plan for in thefuture

Data Availability

-e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-e research described in this paper was financially supportedby the National Key Technologies Research amp DevelopmentProgram (nos 2018YFC0406703 and 2017YFC1502600) theNational Natural Science Foundation of China (nos 11672101and 11372099) the Postgraduate Research amp Practice In-novation Program of Jiangsu Province (no KYLX16_0700)and the Fundamental Research Funds for the Central Uni-versities (no 2016B45214)

References

[1] L N Y Wong and H H Einstein ldquoCrack coalescence inmolded gypsum and Carrara marble part 1mdashmacroscopicobservations and interpretationrdquo Rock Mechanics and RockEngineering vol 42 no 3 pp 475ndash511 2009

[2] L N Y Wong and H H Einstein ldquoCrack coalescence inmolded gypsum and carrara marble part 2mdashmicroscopicobservations and interpretationrdquo Rock Mechanics and RockEngineering vol 42 no 3 pp 513ndash545 2009

[3] H Cheng X Zhou J Zhu and Q Qian ldquo-e effects of crackopenings on crack initiation propagation and coalescencebehavior in rock-like materials under uniaxial compressionrdquoRock Mechanics and Rock Engineering vol 49 no 9pp 3481ndash3494 2016

[4] S J Zhao Q Zhang and L M Liu ldquoCrack initiationpropagation and coalescence experiments in sandstone Bra-zilian disks containing pre-existing flawsrdquo Advances in CivilEngineering vol 2019 Article ID 9816067 11 pages 2019

[5] A Bobet and H H Einstein ldquoFracture coalescence in rock-type materials under uniaxial and biaxial compressionrdquo In-ternational Journal of Rock Mechanics and Mining Sciencesvol 35 no 7 pp 863ndash888 1998

[6] E Hoek and C D Martin ldquoFracture initiation and propa-gation in intact rockmdasha reviewrdquo Journal of Rock Mechanicsand Geotechnical Engineering vol 6 no 4 pp 287ndash300 2014

[7] X Zhuang J Chun and H Zhu ldquoA comparative study onunfilled and filled crack propagation for rock-like brittlematerialrdquo=eoretical and Applied Fracture Mechanics vol 72pp 110ndash120 2014

Table 2 Types of cracks initiated from pre-cracked CSCFBD specimens under cyclic impact loading

Tested CSCFBDspecimen no

Crack typesType I tensile Type II tensile Type III tensile Type IV tensile-shear Type V shear Type VI shear Type VII shear

β 0deg radic radic radic radicβ 15deg radic radic radicβ 30deg radic radic radic radic radicβ 45deg radic radic radic radicβ 60deg radic radic radicβ 75deg radic radic radicβ 90deg radic radic radic

Advances in Materials Science and Engineering 9

[8] P Cao T Liu C Pu and H Lin ldquoCrack propagation andcoalescence of brittle rock-like specimens with pre-existingcracks in compressionrdquo Engineering Geology vol 187pp 113ndash121 2015

[9] 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

[10] 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

[11] M D Kuruppu ldquoFracture toughness measurement usingchevron notched semi-circular bend specimenrdquo InternationalJournal of Fracture vol 86 no 4 pp L33ndashL38 1997

[12] A M Shiryaev and A M Kotkis ldquoMethods for determiningfracture toughness of brittle porous materialsrdquo IndustrialLaboratory vol 48 no 9 pp 917-918 1983

[13] M -iercelin and J C Roegiers ldquoFracture toughness de-termination with the modified ring testrdquo in Proceedings of theInternational Symposium on Engineering in Complex RockFormations pp 1ndash8 Beijing China November 1986

[14] G R Irwin ldquoAnalysis of stress and strains near the end of acrack traversing a platerdquo Journal of AppliedMechanics vol 24no 3 pp 361ndash364 1957

[15] J B Walsh ldquo-e effect of cracks on the compressibility ofrockrdquo Journal of Geophysical Research vol 70 no 2pp 381ndash389 1965

[16] E Hoek and Z T Bieniawski ldquoBrittle fracture propagation inrock under compressionrdquo International Journal of FractureMechanics vol 1 no 3 pp 137ndash155 1965

[17] S Q Yang Y H Dai L J Han and Z Q Jin ldquoExperimentalstudy on mechanical behavior of brittle marble samplescontaining different flaws under uniaxial compressionrdquo En-gineering Fracture Mechanics vol 76 no 12 pp 1833ndash18452009

[18] C H Park and A Bobet ldquoCrack coalescence in specimenswith open and closed flaws a comparisonrdquo InternationalJournal of Rock Mechanics and Mining Sciences vol 46 no 5pp 819ndash829 2009

[19] R P Janeiro and H H Einstein ldquoExperimental study of thecracking behavior of specimens containing inclusions (underuniaxial compression)rdquo International Journal of Fracturevol 164 no 1 pp 83ndash102 2010

[20] S Q Yang ldquoCrack coalescence behavior of brittle sandstonesamples containing two coplanar fissures in the process ofdeformation failurerdquo Engineering Fracture Mechanics vol 78no 17 pp 3059ndash3081 2011

[21] M R M Aliha M Sistaninia D J Smith M J Pavier andM R Ayatollahi ldquoGeometry effects and statistical analysis ofmode I fracture in guiting limestonerdquo International Journal ofRock Mechanics and Mining Sciences vol 51 pp 128ndash1352012

[22] M R Ayatollahi and M R M Aliha ldquoOn the use of Braziliandisc specimen for calculating mixed mode I-II fracturetoughness of rock materialsrdquo Engineering Fracture Mechanicsvol 75 no 16 pp 4631ndash4641 2008

[23] A Ghazvinian H R Nejati V Sarfarazi and M R HadeildquoMixed mode crack propagation in low brittle rock-likematerialsrdquo Arabian Journal of Geosciences vol 6 no 11pp 4435ndash4444 2013

[24] N A Al-Shayea ldquoCrack propagation trajectories for rocksunder mixed mode I-II fracturerdquo Engineering Geology vol 81no 1 pp 84ndash97 2005

[25] H Haeri K Shahriar M F Marji and P MoarefvandldquoExperimental and numerical study of crack propagation andcoalescence in pre-cracked rock-like disksrdquo InternationalJournal of Rock Mechanics and Mining Sciences vol 67 no 6pp 20ndash28 2014

[26] H Haeri A Khaloo and M F Marji ldquoFracture analyses ofdifferent pre-holed concrete specimens under compressionrdquoActa Mechanica Sinica vol 31 no 6 pp 855ndash870 2015

[27] H Haeri V Sarfarazi and A Hedayat ldquoSuggesting a newtesting device for determination of tensile strength of con-creterdquo Structural Engineering and Mechanics vol 60 no 6pp 939ndash952 2016

[28] M R M Aliha and A Bahmani ldquoRock fracture toughnessstudy under mixed mode IIII loadingrdquo Rock Mechanics andRock Engineering vol 50 no 7 pp 1739ndash1751 2017

[29] D J Frew M J Forrestal and W W Chen ldquoPulse shapingtechniques for testing brittle materials with a split Hopkinsonpressure barrdquo Experimental Mechanics vol 42 no 1pp 93ndash106 2002

[30] D J Frew M J Forrestal and W Chen ldquoPulse shapingtechniques for testing elastic-plastic materials with a splitHopkinson pressure barrdquo Experimental Mechanics vol 45no 2 pp 186ndash195 2005

[31] X Li T Zhou and D Li ldquoDynamic strength and fracturingbehavior of single-flawed prismatic marble specimens underimpact loading with a split-Hopkinson pressure barrdquo RockMechanics and Rock Engineering vol 50 no 1 pp 29ndash442017

[32] Q Z Wang J R Yang C G Zhang et al ldquoSequential de-termination of dynamic initiation and propagation toughnessof rock using an experimental-numerical-analytical methodrdquoEngineering Fracture Mechanics vol 141 pp 78ndash94 2015

[33] F Dai S Huang K Xia and Z Tan ldquoSome fundamentalissues in dynamic compression and tension tests of rocksusing split Hopkinson pressure barrdquo Rock Mechanics andRock Engineering vol 43 no 6 pp 657ndash666 2010

[34] W Li and J Xu ldquoMechanical properties of basalt fiberreinforced geopolymeric concrete under impact loadingrdquoMaterials Science and Engineering A vol 505 no 1-2pp 178ndash186 2009

[35] Z L Wang H H Zhu and J G Wang ldquoRepeated-impactresponse of ultrashort steel fiber reinforced concreterdquo Ex-perimental Techniques vol 37 no 4 pp 6ndash13 2013

[36] X Chen S Wu and J Zhou ldquoExperimental and modelingstudy of dynamic mechanical properties of cement pastemortar and concreterdquo Construction and Building Materialsvol 47 pp 419ndash430 2013

[37] X D Chen L M Ge J K Zhou and S X Wu ldquoDynamicBrazilian test of concrete using split Hopkinson pressure barrdquoMaterials and Structures vol 50 no 1 2017

[38] M Zhang H J Wu Q M Li and F L Huang ldquoFurtherinvestigation on the dynamic compressive strength en-hancement of concrete-like materials based on split Hop-kinson pressure bar testsmdashpart I experimentsrdquo InternationalJournal of Impact Engineering vol 36 no 12 pp 1327ndash13342009

[39] W Chen and G Ravichandran ldquoFailure mode transition inceramics under dynamic multiaxial compressionrdquo In-ternational Journal of Fracture vol 101 no 1-2 pp 141ndash1592000

10 Advances in Materials Science and Engineering

[40] H Wang and K T Ramesh ldquoDynamic strength and frag-mentation of hot-pressed silicon carbide under uniaxialcompressionrdquo Acta Materialia vol 52 no 2 pp 355ndash3672004

[41] T Ficker ldquoQuasi-static compressive strength of cement-basedmaterialsrdquo Cement and Concrete Research vol 41 no 1pp 129ndash132 2011

[42] H Hao and B G Tarasov ldquoExperimental study of dynamicmaterial properties of clay brick and mortar at different strainratesrdquo Australian Journal of Structural Engineering vol 8no 2 pp 117ndash132 2008

[43] M Wu C Qin and C Zhang ldquoHigh strain rate splittingtensile tests of concrete and numerical simulation by meso-scale particle elementsrdquo Journal of Materials in Civil Engi-neering vol 26 no 1 pp 71ndash82 2014

[44] J Xiao L Li L Shen and C S Poon ldquoCompressive behaviourof recycled aggregate concrete under impact loadingrdquo Cementand Concrete Research vol 71 pp 46ndash55 2015

[45] W Wu W Zhang and G Ma ldquoMechanical properties ofcopper slag reinforced concrete under dynamic compressionrdquoConstruction and Building Materials vol 24 no 6 pp 910ndash917 2010

[46] H Su and J Xu ldquoDynamic compressive behavior of ceramicfiber reinforced concrete under impact loadrdquo Constructionand Building Materials vol 45 pp 306ndash313 2013

[47] Y Al-Salloum T Almusallam S M Ibrahim H Abbas andS Alsayed ldquoRate dependent behavior and modeling ofconcrete based on SHPB experimentsrdquo Cement and ConcreteComposites vol 55 pp 34ndash44 2015

[48] C A Ross P Y -ompson and J W Tedesco ldquoSplit-Hopkinson pressure-bar tests on concrete and mortar intension and compressionrdquo ACI Materials Journal vol 86no 5 pp 475ndash481 1989

[49] Q Z Wang X M Jia S Q Kou Z X Zhang andP-A Lindqvist ldquo-e flattened Brazilian disc specimen usedfor testing elastic modulus tensile strength and fracturetoughness of brittle rocks analytical and numerical resultsrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 41 no 2 pp 245ndash253 2004

[50] F Berto and J Gomez ldquoNotched plates in mixed modeloading (I+II) a review based on the local strain energydensity and the cohesive zone modelrdquo Engineering SolidMechanics vol 5 pp 1ndash8 2017

[51] D Huang Q Zhang and P Qiao ldquoDamage and progressivefailure of concrete structures using non-local peridynamicmodelingrdquo Science China Technological Sciences vol 54 no 3pp 591ndash596 2011

[52] D Huang Q Zhang P Z Qiao and F Shen ldquoA review onperidynamics (PD) method and its applicationsrdquo Advances inMechanics vol 40 no 4 pp 448ndash459 2010

[53] H Haeri K Shahriar M F Marji and P Moarefvand ldquoAcoupled numerical-experimental study of the breakage pro-cess of brittle substancesrdquo Arabian Journal of Geosciencesvol 8 no 2 pp 809ndash825 2015

[54] Y D Ha and F Bobaru ldquoStudies of dynamic crack propa-gation and crack branching with peridynamicsrdquo InternationalJournal of Fracture vol 162 no 1-2 pp 229ndash244 2010

Advances in Materials Science and Engineering 11

CorrosionInternational Journal of

Hindawiwwwhindawicom Volume 2018

Advances in

Materials Science and EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Analytical ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

ScienticaHindawiwwwhindawicom Volume 2018

Polymer ScienceInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Advances in Condensed Matter Physics

Hindawiwwwhindawicom Volume 2018

International Journal of

BiomaterialsHindawiwwwhindawicom

Journal ofEngineeringVolume 2018

Applied ChemistryJournal of

Hindawiwwwhindawicom Volume 2018

NanotechnologyHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

High Energy PhysicsAdvances in

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

TribologyAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

ChemistryAdvances in

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

Hindawiwwwhindawicom Volume 2018

BioMed Research InternationalMaterials

Journal of

Hindawiwwwhindawicom Volume 2018

Na

nom

ate

ria

ls

Hindawiwwwhindawicom Volume 2018

Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom

Wing crack

Wing crack

(e)

Wing crack

Wing crack

(f )

Wing crack

Wing crack

(g)

Figure 9 Experimental results of crack propagation paths in tested specimens with dierent inclination angles of pre-cracks (a) β 0(b) β 15deg (c) β 30deg (d) β 45deg (e) β 60deg (f ) β 75deg (g) β 90deg [4]

T

TType IT

T

Type II

T

T

Type IIIT

T

S

S

Type IV

S

S

Type V

S

Type VI

S

SType VII

Figure 10 Various crack types initiated from the pre-cracks identi ed in the present studies (Tand S denote tensile and shear cracks)Type Itensile crack Type II tensile crack Type III tensile crack Type IV mixed tensile-shear crack Type V shear crack Type VI shear crack(coplanar or quasi-coplanar shear crack) Type VII shear crack (oblique shear crack) [1 2]

8 Advances in Materials Science and Engineering

crack propagation fracture patterns and failure modes inbrittle materials but have not shown satisfactoryeffectiveness in modeling dynamic damage evolutionand crack propagation [51ndash53] Using mesh-free particlemethods to numerically study dynamic crack propagationmay be an effective way Especially in peridynamics cracksare part of the solution not part of the problem [54]-erefore using peridynamics to simulate dynamicmultiple crack propagation and fracture patterns in brittlematerials under impact or cyclic impact loading would bevery meaningful which we plan for in the future

5 Conclusions

In this paper we provide experimental results of dynamicfracture tests carried out on fine sandstone CSCFBDspecimens under cyclic impact loading by the Φ 74mm-diameter SHPB device Dynamic crack propagation andfracture mechanism are rather complicated processes Fromthe results presented and analyzed above the followingconclusions could be drawn

(1) Compared to static or quasi-static loading the dy-namic crack propagation and fracture behavior aremuch more complex and it presents multiple crackpropagation paths and directions in dynamicfracture

(2) Both tensile and shear cracks were observed most ofthemmainly initiated from tips of the pre-cracks andpropagated in a stable manner According to thedifferent geometries of pre-cracks the testedCSCFBD specimens experienced tensile or shearcrack propagation failure

(3) -e natural or artificial pre-existing defects canchange the crack propagation paths especially di-rections under impact loading compared to static orquasi-static loading However the geometries ofpre-cracks appear to play limited effects on crackstype of CSCFBD specimens under cyclic impactloading

(4) Dynamic crack propagation and fracture mecha-nism are rather complicated processes -is studyrevealed multiple dynamic crack propagationbehavior that had not been observed previouslyNumerical simulation is further needed to besummarized and explored which we plan for in thefuture

Data Availability

-e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-e research described in this paper was financially supportedby the National Key Technologies Research amp DevelopmentProgram (nos 2018YFC0406703 and 2017YFC1502600) theNational Natural Science Foundation of China (nos 11672101and 11372099) the Postgraduate Research amp Practice In-novation Program of Jiangsu Province (no KYLX16_0700)and the Fundamental Research Funds for the Central Uni-versities (no 2016B45214)

References

[1] L N Y Wong and H H Einstein ldquoCrack coalescence inmolded gypsum and Carrara marble part 1mdashmacroscopicobservations and interpretationrdquo Rock Mechanics and RockEngineering vol 42 no 3 pp 475ndash511 2009

[2] L N Y Wong and H H Einstein ldquoCrack coalescence inmolded gypsum and carrara marble part 2mdashmicroscopicobservations and interpretationrdquo Rock Mechanics and RockEngineering vol 42 no 3 pp 513ndash545 2009

[3] H Cheng X Zhou J Zhu and Q Qian ldquo-e effects of crackopenings on crack initiation propagation and coalescencebehavior in rock-like materials under uniaxial compressionrdquoRock Mechanics and Rock Engineering vol 49 no 9pp 3481ndash3494 2016

[4] S J Zhao Q Zhang and L M Liu ldquoCrack initiationpropagation and coalescence experiments in sandstone Bra-zilian disks containing pre-existing flawsrdquo Advances in CivilEngineering vol 2019 Article ID 9816067 11 pages 2019

[5] A Bobet and H H Einstein ldquoFracture coalescence in rock-type materials under uniaxial and biaxial compressionrdquo In-ternational Journal of Rock Mechanics and Mining Sciencesvol 35 no 7 pp 863ndash888 1998

[6] E Hoek and C D Martin ldquoFracture initiation and propa-gation in intact rockmdasha reviewrdquo Journal of Rock Mechanicsand Geotechnical Engineering vol 6 no 4 pp 287ndash300 2014

[7] X Zhuang J Chun and H Zhu ldquoA comparative study onunfilled and filled crack propagation for rock-like brittlematerialrdquo=eoretical and Applied Fracture Mechanics vol 72pp 110ndash120 2014

Table 2 Types of cracks initiated from pre-cracked CSCFBD specimens under cyclic impact loading

Tested CSCFBDspecimen no

Crack typesType I tensile Type II tensile Type III tensile Type IV tensile-shear Type V shear Type VI shear Type VII shear

β 0deg radic radic radic radicβ 15deg radic radic radicβ 30deg radic radic radic radic radicβ 45deg radic radic radic radicβ 60deg radic radic radicβ 75deg radic radic radicβ 90deg radic radic radic

Advances in Materials Science and Engineering 9

[8] P Cao T Liu C Pu and H Lin ldquoCrack propagation andcoalescence of brittle rock-like specimens with pre-existingcracks in compressionrdquo Engineering Geology vol 187pp 113ndash121 2015

[9] 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

[10] 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

[11] M D Kuruppu ldquoFracture toughness measurement usingchevron notched semi-circular bend specimenrdquo InternationalJournal of Fracture vol 86 no 4 pp L33ndashL38 1997

[12] A M Shiryaev and A M Kotkis ldquoMethods for determiningfracture toughness of brittle porous materialsrdquo IndustrialLaboratory vol 48 no 9 pp 917-918 1983

[13] M -iercelin and J C Roegiers ldquoFracture toughness de-termination with the modified ring testrdquo in Proceedings of theInternational Symposium on Engineering in Complex RockFormations pp 1ndash8 Beijing China November 1986

[14] G R Irwin ldquoAnalysis of stress and strains near the end of acrack traversing a platerdquo Journal of AppliedMechanics vol 24no 3 pp 361ndash364 1957

[15] J B Walsh ldquo-e effect of cracks on the compressibility ofrockrdquo Journal of Geophysical Research vol 70 no 2pp 381ndash389 1965

[16] E Hoek and Z T Bieniawski ldquoBrittle fracture propagation inrock under compressionrdquo International Journal of FractureMechanics vol 1 no 3 pp 137ndash155 1965

[17] S Q Yang Y H Dai L J Han and Z Q Jin ldquoExperimentalstudy on mechanical behavior of brittle marble samplescontaining different flaws under uniaxial compressionrdquo En-gineering Fracture Mechanics vol 76 no 12 pp 1833ndash18452009

[18] C H Park and A Bobet ldquoCrack coalescence in specimenswith open and closed flaws a comparisonrdquo InternationalJournal of Rock Mechanics and Mining Sciences vol 46 no 5pp 819ndash829 2009

[19] R P Janeiro and H H Einstein ldquoExperimental study of thecracking behavior of specimens containing inclusions (underuniaxial compression)rdquo International Journal of Fracturevol 164 no 1 pp 83ndash102 2010

[20] S Q Yang ldquoCrack coalescence behavior of brittle sandstonesamples containing two coplanar fissures in the process ofdeformation failurerdquo Engineering Fracture Mechanics vol 78no 17 pp 3059ndash3081 2011

[21] M R M Aliha M Sistaninia D J Smith M J Pavier andM R Ayatollahi ldquoGeometry effects and statistical analysis ofmode I fracture in guiting limestonerdquo International Journal ofRock Mechanics and Mining Sciences vol 51 pp 128ndash1352012

[22] M R Ayatollahi and M R M Aliha ldquoOn the use of Braziliandisc specimen for calculating mixed mode I-II fracturetoughness of rock materialsrdquo Engineering Fracture Mechanicsvol 75 no 16 pp 4631ndash4641 2008

[23] A Ghazvinian H R Nejati V Sarfarazi and M R HadeildquoMixed mode crack propagation in low brittle rock-likematerialsrdquo Arabian Journal of Geosciences vol 6 no 11pp 4435ndash4444 2013

[24] N A Al-Shayea ldquoCrack propagation trajectories for rocksunder mixed mode I-II fracturerdquo Engineering Geology vol 81no 1 pp 84ndash97 2005

[25] H Haeri K Shahriar M F Marji and P MoarefvandldquoExperimental and numerical study of crack propagation andcoalescence in pre-cracked rock-like disksrdquo InternationalJournal of Rock Mechanics and Mining Sciences vol 67 no 6pp 20ndash28 2014

[26] H Haeri A Khaloo and M F Marji ldquoFracture analyses ofdifferent pre-holed concrete specimens under compressionrdquoActa Mechanica Sinica vol 31 no 6 pp 855ndash870 2015

[27] H Haeri V Sarfarazi and A Hedayat ldquoSuggesting a newtesting device for determination of tensile strength of con-creterdquo Structural Engineering and Mechanics vol 60 no 6pp 939ndash952 2016

[28] M R M Aliha and A Bahmani ldquoRock fracture toughnessstudy under mixed mode IIII loadingrdquo Rock Mechanics andRock Engineering vol 50 no 7 pp 1739ndash1751 2017

[29] D J Frew M J Forrestal and W W Chen ldquoPulse shapingtechniques for testing brittle materials with a split Hopkinsonpressure barrdquo Experimental Mechanics vol 42 no 1pp 93ndash106 2002

[30] D J Frew M J Forrestal and W Chen ldquoPulse shapingtechniques for testing elastic-plastic materials with a splitHopkinson pressure barrdquo Experimental Mechanics vol 45no 2 pp 186ndash195 2005

[31] X Li T Zhou and D Li ldquoDynamic strength and fracturingbehavior of single-flawed prismatic marble specimens underimpact loading with a split-Hopkinson pressure barrdquo RockMechanics and Rock Engineering vol 50 no 1 pp 29ndash442017

[32] Q Z Wang J R Yang C G Zhang et al ldquoSequential de-termination of dynamic initiation and propagation toughnessof rock using an experimental-numerical-analytical methodrdquoEngineering Fracture Mechanics vol 141 pp 78ndash94 2015

[33] F Dai S Huang K Xia and Z Tan ldquoSome fundamentalissues in dynamic compression and tension tests of rocksusing split Hopkinson pressure barrdquo Rock Mechanics andRock Engineering vol 43 no 6 pp 657ndash666 2010

[34] W Li and J Xu ldquoMechanical properties of basalt fiberreinforced geopolymeric concrete under impact loadingrdquoMaterials Science and Engineering A vol 505 no 1-2pp 178ndash186 2009

[35] Z L Wang H H Zhu and J G Wang ldquoRepeated-impactresponse of ultrashort steel fiber reinforced concreterdquo Ex-perimental Techniques vol 37 no 4 pp 6ndash13 2013

[36] X Chen S Wu and J Zhou ldquoExperimental and modelingstudy of dynamic mechanical properties of cement pastemortar and concreterdquo Construction and Building Materialsvol 47 pp 419ndash430 2013

[37] X D Chen L M Ge J K Zhou and S X Wu ldquoDynamicBrazilian test of concrete using split Hopkinson pressure barrdquoMaterials and Structures vol 50 no 1 2017

[38] M Zhang H J Wu Q M Li and F L Huang ldquoFurtherinvestigation on the dynamic compressive strength en-hancement of concrete-like materials based on split Hop-kinson pressure bar testsmdashpart I experimentsrdquo InternationalJournal of Impact Engineering vol 36 no 12 pp 1327ndash13342009

[39] W Chen and G Ravichandran ldquoFailure mode transition inceramics under dynamic multiaxial compressionrdquo In-ternational Journal of Fracture vol 101 no 1-2 pp 141ndash1592000

10 Advances in Materials Science and Engineering

[40] H Wang and K T Ramesh ldquoDynamic strength and frag-mentation of hot-pressed silicon carbide under uniaxialcompressionrdquo Acta Materialia vol 52 no 2 pp 355ndash3672004

[41] T Ficker ldquoQuasi-static compressive strength of cement-basedmaterialsrdquo Cement and Concrete Research vol 41 no 1pp 129ndash132 2011

[42] H Hao and B G Tarasov ldquoExperimental study of dynamicmaterial properties of clay brick and mortar at different strainratesrdquo Australian Journal of Structural Engineering vol 8no 2 pp 117ndash132 2008

[43] M Wu C Qin and C Zhang ldquoHigh strain rate splittingtensile tests of concrete and numerical simulation by meso-scale particle elementsrdquo Journal of Materials in Civil Engi-neering vol 26 no 1 pp 71ndash82 2014

[44] J Xiao L Li L Shen and C S Poon ldquoCompressive behaviourof recycled aggregate concrete under impact loadingrdquo Cementand Concrete Research vol 71 pp 46ndash55 2015

[45] W Wu W Zhang and G Ma ldquoMechanical properties ofcopper slag reinforced concrete under dynamic compressionrdquoConstruction and Building Materials vol 24 no 6 pp 910ndash917 2010

[46] H Su and J Xu ldquoDynamic compressive behavior of ceramicfiber reinforced concrete under impact loadrdquo Constructionand Building Materials vol 45 pp 306ndash313 2013

[47] Y Al-Salloum T Almusallam S M Ibrahim H Abbas andS Alsayed ldquoRate dependent behavior and modeling ofconcrete based on SHPB experimentsrdquo Cement and ConcreteComposites vol 55 pp 34ndash44 2015

[48] C A Ross P Y -ompson and J W Tedesco ldquoSplit-Hopkinson pressure-bar tests on concrete and mortar intension and compressionrdquo ACI Materials Journal vol 86no 5 pp 475ndash481 1989

[49] Q Z Wang X M Jia S Q Kou Z X Zhang andP-A Lindqvist ldquo-e flattened Brazilian disc specimen usedfor testing elastic modulus tensile strength and fracturetoughness of brittle rocks analytical and numerical resultsrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 41 no 2 pp 245ndash253 2004

[50] F Berto and J Gomez ldquoNotched plates in mixed modeloading (I+II) a review based on the local strain energydensity and the cohesive zone modelrdquo Engineering SolidMechanics vol 5 pp 1ndash8 2017

[51] D Huang Q Zhang and P Qiao ldquoDamage and progressivefailure of concrete structures using non-local peridynamicmodelingrdquo Science China Technological Sciences vol 54 no 3pp 591ndash596 2011

[52] D Huang Q Zhang P Z Qiao and F Shen ldquoA review onperidynamics (PD) method and its applicationsrdquo Advances inMechanics vol 40 no 4 pp 448ndash459 2010

[53] H Haeri K Shahriar M F Marji and P Moarefvand ldquoAcoupled numerical-experimental study of the breakage pro-cess of brittle substancesrdquo Arabian Journal of Geosciencesvol 8 no 2 pp 809ndash825 2015

[54] Y D Ha and F Bobaru ldquoStudies of dynamic crack propa-gation and crack branching with peridynamicsrdquo InternationalJournal of Fracture vol 162 no 1-2 pp 229ndash244 2010

Advances in Materials Science and Engineering 11

CorrosionInternational Journal of

Hindawiwwwhindawicom Volume 2018

Advances in

Materials Science and EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Analytical ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

ScienticaHindawiwwwhindawicom Volume 2018

Polymer ScienceInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Advances in Condensed Matter Physics

Hindawiwwwhindawicom Volume 2018

International Journal of

BiomaterialsHindawiwwwhindawicom

Journal ofEngineeringVolume 2018

Applied ChemistryJournal of

Hindawiwwwhindawicom Volume 2018

NanotechnologyHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

High Energy PhysicsAdvances in

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

TribologyAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

ChemistryAdvances in

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

Hindawiwwwhindawicom Volume 2018

BioMed Research InternationalMaterials

Journal of

Hindawiwwwhindawicom Volume 2018

Na

nom

ate

ria

ls

Hindawiwwwhindawicom Volume 2018

Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom

crack propagation fracture patterns and failure modes inbrittle materials but have not shown satisfactoryeffectiveness in modeling dynamic damage evolutionand crack propagation [51ndash53] Using mesh-free particlemethods to numerically study dynamic crack propagationmay be an effective way Especially in peridynamics cracksare part of the solution not part of the problem [54]-erefore using peridynamics to simulate dynamicmultiple crack propagation and fracture patterns in brittlematerials under impact or cyclic impact loading would bevery meaningful which we plan for in the future

5 Conclusions

In this paper we provide experimental results of dynamicfracture tests carried out on fine sandstone CSCFBDspecimens under cyclic impact loading by the Φ 74mm-diameter SHPB device Dynamic crack propagation andfracture mechanism are rather complicated processes Fromthe results presented and analyzed above the followingconclusions could be drawn

(1) Compared to static or quasi-static loading the dy-namic crack propagation and fracture behavior aremuch more complex and it presents multiple crackpropagation paths and directions in dynamicfracture

(2) Both tensile and shear cracks were observed most ofthemmainly initiated from tips of the pre-cracks andpropagated in a stable manner According to thedifferent geometries of pre-cracks the testedCSCFBD specimens experienced tensile or shearcrack propagation failure

(3) -e natural or artificial pre-existing defects canchange the crack propagation paths especially di-rections under impact loading compared to static orquasi-static loading However the geometries ofpre-cracks appear to play limited effects on crackstype of CSCFBD specimens under cyclic impactloading

(4) Dynamic crack propagation and fracture mecha-nism are rather complicated processes -is studyrevealed multiple dynamic crack propagationbehavior that had not been observed previouslyNumerical simulation is further needed to besummarized and explored which we plan for in thefuture

Data Availability

-e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-e research described in this paper was financially supportedby the National Key Technologies Research amp DevelopmentProgram (nos 2018YFC0406703 and 2017YFC1502600) theNational Natural Science Foundation of China (nos 11672101and 11372099) the Postgraduate Research amp Practice In-novation Program of Jiangsu Province (no KYLX16_0700)and the Fundamental Research Funds for the Central Uni-versities (no 2016B45214)

References

[1] L N Y Wong and H H Einstein ldquoCrack coalescence inmolded gypsum and Carrara marble part 1mdashmacroscopicobservations and interpretationrdquo Rock Mechanics and RockEngineering vol 42 no 3 pp 475ndash511 2009

[2] L N Y Wong and H H Einstein ldquoCrack coalescence inmolded gypsum and carrara marble part 2mdashmicroscopicobservations and interpretationrdquo Rock Mechanics and RockEngineering vol 42 no 3 pp 513ndash545 2009

[3] H Cheng X Zhou J Zhu and Q Qian ldquo-e effects of crackopenings on crack initiation propagation and coalescencebehavior in rock-like materials under uniaxial compressionrdquoRock Mechanics and Rock Engineering vol 49 no 9pp 3481ndash3494 2016

[4] S J Zhao Q Zhang and L M Liu ldquoCrack initiationpropagation and coalescence experiments in sandstone Bra-zilian disks containing pre-existing flawsrdquo Advances in CivilEngineering vol 2019 Article ID 9816067 11 pages 2019

[5] A Bobet and H H Einstein ldquoFracture coalescence in rock-type materials under uniaxial and biaxial compressionrdquo In-ternational Journal of Rock Mechanics and Mining Sciencesvol 35 no 7 pp 863ndash888 1998

[6] E Hoek and C D Martin ldquoFracture initiation and propa-gation in intact rockmdasha reviewrdquo Journal of Rock Mechanicsand Geotechnical Engineering vol 6 no 4 pp 287ndash300 2014

[7] X Zhuang J Chun and H Zhu ldquoA comparative study onunfilled and filled crack propagation for rock-like brittlematerialrdquo=eoretical and Applied Fracture Mechanics vol 72pp 110ndash120 2014

Table 2 Types of cracks initiated from pre-cracked CSCFBD specimens under cyclic impact loading

Tested CSCFBDspecimen no

Crack typesType I tensile Type II tensile Type III tensile Type IV tensile-shear Type V shear Type VI shear Type VII shear

β 0deg radic radic radic radicβ 15deg radic radic radicβ 30deg radic radic radic radic radicβ 45deg radic radic radic radicβ 60deg radic radic radicβ 75deg radic radic radicβ 90deg radic radic radic

Advances in Materials Science and Engineering 9

[8] P Cao T Liu C Pu and H Lin ldquoCrack propagation andcoalescence of brittle rock-like specimens with pre-existingcracks in compressionrdquo Engineering Geology vol 187pp 113ndash121 2015

[9] 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

[10] 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

[11] M D Kuruppu ldquoFracture toughness measurement usingchevron notched semi-circular bend specimenrdquo InternationalJournal of Fracture vol 86 no 4 pp L33ndashL38 1997

[12] A M Shiryaev and A M Kotkis ldquoMethods for determiningfracture toughness of brittle porous materialsrdquo IndustrialLaboratory vol 48 no 9 pp 917-918 1983

[13] M -iercelin and J C Roegiers ldquoFracture toughness de-termination with the modified ring testrdquo in Proceedings of theInternational Symposium on Engineering in Complex RockFormations pp 1ndash8 Beijing China November 1986

[14] G R Irwin ldquoAnalysis of stress and strains near the end of acrack traversing a platerdquo Journal of AppliedMechanics vol 24no 3 pp 361ndash364 1957

[15] J B Walsh ldquo-e effect of cracks on the compressibility ofrockrdquo Journal of Geophysical Research vol 70 no 2pp 381ndash389 1965

[16] E Hoek and Z T Bieniawski ldquoBrittle fracture propagation inrock under compressionrdquo International Journal of FractureMechanics vol 1 no 3 pp 137ndash155 1965

[17] S Q Yang Y H Dai L J Han and Z Q Jin ldquoExperimentalstudy on mechanical behavior of brittle marble samplescontaining different flaws under uniaxial compressionrdquo En-gineering Fracture Mechanics vol 76 no 12 pp 1833ndash18452009

[18] C H Park and A Bobet ldquoCrack coalescence in specimenswith open and closed flaws a comparisonrdquo InternationalJournal of Rock Mechanics and Mining Sciences vol 46 no 5pp 819ndash829 2009

[19] R P Janeiro and H H Einstein ldquoExperimental study of thecracking behavior of specimens containing inclusions (underuniaxial compression)rdquo International Journal of Fracturevol 164 no 1 pp 83ndash102 2010

[20] S Q Yang ldquoCrack coalescence behavior of brittle sandstonesamples containing two coplanar fissures in the process ofdeformation failurerdquo Engineering Fracture Mechanics vol 78no 17 pp 3059ndash3081 2011

[21] M R M Aliha M Sistaninia D J Smith M J Pavier andM R Ayatollahi ldquoGeometry effects and statistical analysis ofmode I fracture in guiting limestonerdquo International Journal ofRock Mechanics and Mining Sciences vol 51 pp 128ndash1352012

[22] M R Ayatollahi and M R M Aliha ldquoOn the use of Braziliandisc specimen for calculating mixed mode I-II fracturetoughness of rock materialsrdquo Engineering Fracture Mechanicsvol 75 no 16 pp 4631ndash4641 2008

[23] A Ghazvinian H R Nejati V Sarfarazi and M R HadeildquoMixed mode crack propagation in low brittle rock-likematerialsrdquo Arabian Journal of Geosciences vol 6 no 11pp 4435ndash4444 2013

[24] N A Al-Shayea ldquoCrack propagation trajectories for rocksunder mixed mode I-II fracturerdquo Engineering Geology vol 81no 1 pp 84ndash97 2005

[25] H Haeri K Shahriar M F Marji and P MoarefvandldquoExperimental and numerical study of crack propagation andcoalescence in pre-cracked rock-like disksrdquo InternationalJournal of Rock Mechanics and Mining Sciences vol 67 no 6pp 20ndash28 2014

[26] H Haeri A Khaloo and M F Marji ldquoFracture analyses ofdifferent pre-holed concrete specimens under compressionrdquoActa Mechanica Sinica vol 31 no 6 pp 855ndash870 2015

[27] H Haeri V Sarfarazi and A Hedayat ldquoSuggesting a newtesting device for determination of tensile strength of con-creterdquo Structural Engineering and Mechanics vol 60 no 6pp 939ndash952 2016

[28] M R M Aliha and A Bahmani ldquoRock fracture toughnessstudy under mixed mode IIII loadingrdquo Rock Mechanics andRock Engineering vol 50 no 7 pp 1739ndash1751 2017

[29] D J Frew M J Forrestal and W W Chen ldquoPulse shapingtechniques for testing brittle materials with a split Hopkinsonpressure barrdquo Experimental Mechanics vol 42 no 1pp 93ndash106 2002

[30] D J Frew M J Forrestal and W Chen ldquoPulse shapingtechniques for testing elastic-plastic materials with a splitHopkinson pressure barrdquo Experimental Mechanics vol 45no 2 pp 186ndash195 2005

[31] X Li T Zhou and D Li ldquoDynamic strength and fracturingbehavior of single-flawed prismatic marble specimens underimpact loading with a split-Hopkinson pressure barrdquo RockMechanics and Rock Engineering vol 50 no 1 pp 29ndash442017

[32] Q Z Wang J R Yang C G Zhang et al ldquoSequential de-termination of dynamic initiation and propagation toughnessof rock using an experimental-numerical-analytical methodrdquoEngineering Fracture Mechanics vol 141 pp 78ndash94 2015

[33] F Dai S Huang K Xia and Z Tan ldquoSome fundamentalissues in dynamic compression and tension tests of rocksusing split Hopkinson pressure barrdquo Rock Mechanics andRock Engineering vol 43 no 6 pp 657ndash666 2010

[34] W Li and J Xu ldquoMechanical properties of basalt fiberreinforced geopolymeric concrete under impact loadingrdquoMaterials Science and Engineering A vol 505 no 1-2pp 178ndash186 2009

[35] Z L Wang H H Zhu and J G Wang ldquoRepeated-impactresponse of ultrashort steel fiber reinforced concreterdquo Ex-perimental Techniques vol 37 no 4 pp 6ndash13 2013

[36] X Chen S Wu and J Zhou ldquoExperimental and modelingstudy of dynamic mechanical properties of cement pastemortar and concreterdquo Construction and Building Materialsvol 47 pp 419ndash430 2013

[37] X D Chen L M Ge J K Zhou and S X Wu ldquoDynamicBrazilian test of concrete using split Hopkinson pressure barrdquoMaterials and Structures vol 50 no 1 2017

[38] M Zhang H J Wu Q M Li and F L Huang ldquoFurtherinvestigation on the dynamic compressive strength en-hancement of concrete-like materials based on split Hop-kinson pressure bar testsmdashpart I experimentsrdquo InternationalJournal of Impact Engineering vol 36 no 12 pp 1327ndash13342009

[39] W Chen and G Ravichandran ldquoFailure mode transition inceramics under dynamic multiaxial compressionrdquo In-ternational Journal of Fracture vol 101 no 1-2 pp 141ndash1592000

10 Advances in Materials Science and Engineering

[40] H Wang and K T Ramesh ldquoDynamic strength and frag-mentation of hot-pressed silicon carbide under uniaxialcompressionrdquo Acta Materialia vol 52 no 2 pp 355ndash3672004

[41] T Ficker ldquoQuasi-static compressive strength of cement-basedmaterialsrdquo Cement and Concrete Research vol 41 no 1pp 129ndash132 2011

[42] H Hao and B G Tarasov ldquoExperimental study of dynamicmaterial properties of clay brick and mortar at different strainratesrdquo Australian Journal of Structural Engineering vol 8no 2 pp 117ndash132 2008

[43] M Wu C Qin and C Zhang ldquoHigh strain rate splittingtensile tests of concrete and numerical simulation by meso-scale particle elementsrdquo Journal of Materials in Civil Engi-neering vol 26 no 1 pp 71ndash82 2014

[44] J Xiao L Li L Shen and C S Poon ldquoCompressive behaviourof recycled aggregate concrete under impact loadingrdquo Cementand Concrete Research vol 71 pp 46ndash55 2015

[45] W Wu W Zhang and G Ma ldquoMechanical properties ofcopper slag reinforced concrete under dynamic compressionrdquoConstruction and Building Materials vol 24 no 6 pp 910ndash917 2010

[46] H Su and J Xu ldquoDynamic compressive behavior of ceramicfiber reinforced concrete under impact loadrdquo Constructionand Building Materials vol 45 pp 306ndash313 2013

[47] Y Al-Salloum T Almusallam S M Ibrahim H Abbas andS Alsayed ldquoRate dependent behavior and modeling ofconcrete based on SHPB experimentsrdquo Cement and ConcreteComposites vol 55 pp 34ndash44 2015

[48] C A Ross P Y -ompson and J W Tedesco ldquoSplit-Hopkinson pressure-bar tests on concrete and mortar intension and compressionrdquo ACI Materials Journal vol 86no 5 pp 475ndash481 1989

[49] Q Z Wang X M Jia S Q Kou Z X Zhang andP-A Lindqvist ldquo-e flattened Brazilian disc specimen usedfor testing elastic modulus tensile strength and fracturetoughness of brittle rocks analytical and numerical resultsrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 41 no 2 pp 245ndash253 2004

[50] F Berto and J Gomez ldquoNotched plates in mixed modeloading (I+II) a review based on the local strain energydensity and the cohesive zone modelrdquo Engineering SolidMechanics vol 5 pp 1ndash8 2017

[51] D Huang Q Zhang and P Qiao ldquoDamage and progressivefailure of concrete structures using non-local peridynamicmodelingrdquo Science China Technological Sciences vol 54 no 3pp 591ndash596 2011

[52] D Huang Q Zhang P Z Qiao and F Shen ldquoA review onperidynamics (PD) method and its applicationsrdquo Advances inMechanics vol 40 no 4 pp 448ndash459 2010

[53] H Haeri K Shahriar M F Marji and P Moarefvand ldquoAcoupled numerical-experimental study of the breakage pro-cess of brittle substancesrdquo Arabian Journal of Geosciencesvol 8 no 2 pp 809ndash825 2015

[54] Y D Ha and F Bobaru ldquoStudies of dynamic crack propa-gation and crack branching with peridynamicsrdquo InternationalJournal of Fracture vol 162 no 1-2 pp 229ndash244 2010

Advances in Materials Science and Engineering 11

CorrosionInternational Journal of

Hindawiwwwhindawicom Volume 2018

Advances in

Materials Science and EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Analytical ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

ScienticaHindawiwwwhindawicom Volume 2018

Polymer ScienceInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Advances in Condensed Matter Physics

Hindawiwwwhindawicom Volume 2018

International Journal of

BiomaterialsHindawiwwwhindawicom

Journal ofEngineeringVolume 2018

Applied ChemistryJournal of

Hindawiwwwhindawicom Volume 2018

NanotechnologyHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

High Energy PhysicsAdvances in

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

TribologyAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

ChemistryAdvances in

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

Hindawiwwwhindawicom Volume 2018

BioMed Research InternationalMaterials

Journal of

Hindawiwwwhindawicom Volume 2018

Na

nom

ate

ria

ls

Hindawiwwwhindawicom Volume 2018

Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom

[8] P Cao T Liu C Pu and H Lin ldquoCrack propagation andcoalescence of brittle rock-like specimens with pre-existingcracks in compressionrdquo Engineering Geology vol 187pp 113ndash121 2015

[9] 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

[10] 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

[11] M D Kuruppu ldquoFracture toughness measurement usingchevron notched semi-circular bend specimenrdquo InternationalJournal of Fracture vol 86 no 4 pp L33ndashL38 1997

[12] A M Shiryaev and A M Kotkis ldquoMethods for determiningfracture toughness of brittle porous materialsrdquo IndustrialLaboratory vol 48 no 9 pp 917-918 1983

[13] M -iercelin and J C Roegiers ldquoFracture toughness de-termination with the modified ring testrdquo in Proceedings of theInternational Symposium on Engineering in Complex RockFormations pp 1ndash8 Beijing China November 1986

[14] G R Irwin ldquoAnalysis of stress and strains near the end of acrack traversing a platerdquo Journal of AppliedMechanics vol 24no 3 pp 361ndash364 1957

[15] J B Walsh ldquo-e effect of cracks on the compressibility ofrockrdquo Journal of Geophysical Research vol 70 no 2pp 381ndash389 1965

[16] E Hoek and Z T Bieniawski ldquoBrittle fracture propagation inrock under compressionrdquo International Journal of FractureMechanics vol 1 no 3 pp 137ndash155 1965

[17] S Q Yang Y H Dai L J Han and Z Q Jin ldquoExperimentalstudy on mechanical behavior of brittle marble samplescontaining different flaws under uniaxial compressionrdquo En-gineering Fracture Mechanics vol 76 no 12 pp 1833ndash18452009

[18] C H Park and A Bobet ldquoCrack coalescence in specimenswith open and closed flaws a comparisonrdquo InternationalJournal of Rock Mechanics and Mining Sciences vol 46 no 5pp 819ndash829 2009

[19] R P Janeiro and H H Einstein ldquoExperimental study of thecracking behavior of specimens containing inclusions (underuniaxial compression)rdquo International Journal of Fracturevol 164 no 1 pp 83ndash102 2010

[20] S Q Yang ldquoCrack coalescence behavior of brittle sandstonesamples containing two coplanar fissures in the process ofdeformation failurerdquo Engineering Fracture Mechanics vol 78no 17 pp 3059ndash3081 2011

[21] M R M Aliha M Sistaninia D J Smith M J Pavier andM R Ayatollahi ldquoGeometry effects and statistical analysis ofmode I fracture in guiting limestonerdquo International Journal ofRock Mechanics and Mining Sciences vol 51 pp 128ndash1352012

[22] M R Ayatollahi and M R M Aliha ldquoOn the use of Braziliandisc specimen for calculating mixed mode I-II fracturetoughness of rock materialsrdquo Engineering Fracture Mechanicsvol 75 no 16 pp 4631ndash4641 2008

[23] A Ghazvinian H R Nejati V Sarfarazi and M R HadeildquoMixed mode crack propagation in low brittle rock-likematerialsrdquo Arabian Journal of Geosciences vol 6 no 11pp 4435ndash4444 2013

[24] N A Al-Shayea ldquoCrack propagation trajectories for rocksunder mixed mode I-II fracturerdquo Engineering Geology vol 81no 1 pp 84ndash97 2005

[25] H Haeri K Shahriar M F Marji and P MoarefvandldquoExperimental and numerical study of crack propagation andcoalescence in pre-cracked rock-like disksrdquo InternationalJournal of Rock Mechanics and Mining Sciences vol 67 no 6pp 20ndash28 2014

[26] H Haeri A Khaloo and M F Marji ldquoFracture analyses ofdifferent pre-holed concrete specimens under compressionrdquoActa Mechanica Sinica vol 31 no 6 pp 855ndash870 2015

[27] H Haeri V Sarfarazi and A Hedayat ldquoSuggesting a newtesting device for determination of tensile strength of con-creterdquo Structural Engineering and Mechanics vol 60 no 6pp 939ndash952 2016

[28] M R M Aliha and A Bahmani ldquoRock fracture toughnessstudy under mixed mode IIII loadingrdquo Rock Mechanics andRock Engineering vol 50 no 7 pp 1739ndash1751 2017

[29] D J Frew M J Forrestal and W W Chen ldquoPulse shapingtechniques for testing brittle materials with a split Hopkinsonpressure barrdquo Experimental Mechanics vol 42 no 1pp 93ndash106 2002

[30] D J Frew M J Forrestal and W Chen ldquoPulse shapingtechniques for testing elastic-plastic materials with a splitHopkinson pressure barrdquo Experimental Mechanics vol 45no 2 pp 186ndash195 2005

[31] X Li T Zhou and D Li ldquoDynamic strength and fracturingbehavior of single-flawed prismatic marble specimens underimpact loading with a split-Hopkinson pressure barrdquo RockMechanics and Rock Engineering vol 50 no 1 pp 29ndash442017

[32] Q Z Wang J R Yang C G Zhang et al ldquoSequential de-termination of dynamic initiation and propagation toughnessof rock using an experimental-numerical-analytical methodrdquoEngineering Fracture Mechanics vol 141 pp 78ndash94 2015

[33] F Dai S Huang K Xia and Z Tan ldquoSome fundamentalissues in dynamic compression and tension tests of rocksusing split Hopkinson pressure barrdquo Rock Mechanics andRock Engineering vol 43 no 6 pp 657ndash666 2010

[34] W Li and J Xu ldquoMechanical properties of basalt fiberreinforced geopolymeric concrete under impact loadingrdquoMaterials Science and Engineering A vol 505 no 1-2pp 178ndash186 2009

[35] Z L Wang H H Zhu and J G Wang ldquoRepeated-impactresponse of ultrashort steel fiber reinforced concreterdquo Ex-perimental Techniques vol 37 no 4 pp 6ndash13 2013

[36] X Chen S Wu and J Zhou ldquoExperimental and modelingstudy of dynamic mechanical properties of cement pastemortar and concreterdquo Construction and Building Materialsvol 47 pp 419ndash430 2013

[37] X D Chen L M Ge J K Zhou and S X Wu ldquoDynamicBrazilian test of concrete using split Hopkinson pressure barrdquoMaterials and Structures vol 50 no 1 2017

[38] M Zhang H J Wu Q M Li and F L Huang ldquoFurtherinvestigation on the dynamic compressive strength en-hancement of concrete-like materials based on split Hop-kinson pressure bar testsmdashpart I experimentsrdquo InternationalJournal of Impact Engineering vol 36 no 12 pp 1327ndash13342009

[39] W Chen and G Ravichandran ldquoFailure mode transition inceramics under dynamic multiaxial compressionrdquo In-ternational Journal of Fracture vol 101 no 1-2 pp 141ndash1592000

10 Advances in Materials Science and Engineering

[40] H Wang and K T Ramesh ldquoDynamic strength and frag-mentation of hot-pressed silicon carbide under uniaxialcompressionrdquo Acta Materialia vol 52 no 2 pp 355ndash3672004

[41] T Ficker ldquoQuasi-static compressive strength of cement-basedmaterialsrdquo Cement and Concrete Research vol 41 no 1pp 129ndash132 2011

[42] H Hao and B G Tarasov ldquoExperimental study of dynamicmaterial properties of clay brick and mortar at different strainratesrdquo Australian Journal of Structural Engineering vol 8no 2 pp 117ndash132 2008

[43] M Wu C Qin and C Zhang ldquoHigh strain rate splittingtensile tests of concrete and numerical simulation by meso-scale particle elementsrdquo Journal of Materials in Civil Engi-neering vol 26 no 1 pp 71ndash82 2014

[44] J Xiao L Li L Shen and C S Poon ldquoCompressive behaviourof recycled aggregate concrete under impact loadingrdquo Cementand Concrete Research vol 71 pp 46ndash55 2015

[45] W Wu W Zhang and G Ma ldquoMechanical properties ofcopper slag reinforced concrete under dynamic compressionrdquoConstruction and Building Materials vol 24 no 6 pp 910ndash917 2010

[46] H Su and J Xu ldquoDynamic compressive behavior of ceramicfiber reinforced concrete under impact loadrdquo Constructionand Building Materials vol 45 pp 306ndash313 2013

[47] Y Al-Salloum T Almusallam S M Ibrahim H Abbas andS Alsayed ldquoRate dependent behavior and modeling ofconcrete based on SHPB experimentsrdquo Cement and ConcreteComposites vol 55 pp 34ndash44 2015

[48] C A Ross P Y -ompson and J W Tedesco ldquoSplit-Hopkinson pressure-bar tests on concrete and mortar intension and compressionrdquo ACI Materials Journal vol 86no 5 pp 475ndash481 1989

[49] Q Z Wang X M Jia S Q Kou Z X Zhang andP-A Lindqvist ldquo-e flattened Brazilian disc specimen usedfor testing elastic modulus tensile strength and fracturetoughness of brittle rocks analytical and numerical resultsrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 41 no 2 pp 245ndash253 2004

[50] F Berto and J Gomez ldquoNotched plates in mixed modeloading (I+II) a review based on the local strain energydensity and the cohesive zone modelrdquo Engineering SolidMechanics vol 5 pp 1ndash8 2017

[51] D Huang Q Zhang and P Qiao ldquoDamage and progressivefailure of concrete structures using non-local peridynamicmodelingrdquo Science China Technological Sciences vol 54 no 3pp 591ndash596 2011

[52] D Huang Q Zhang P Z Qiao and F Shen ldquoA review onperidynamics (PD) method and its applicationsrdquo Advances inMechanics vol 40 no 4 pp 448ndash459 2010

[53] H Haeri K Shahriar M F Marji and P Moarefvand ldquoAcoupled numerical-experimental study of the breakage pro-cess of brittle substancesrdquo Arabian Journal of Geosciencesvol 8 no 2 pp 809ndash825 2015

[54] Y D Ha and F Bobaru ldquoStudies of dynamic crack propa-gation and crack branching with peridynamicsrdquo InternationalJournal of Fracture vol 162 no 1-2 pp 229ndash244 2010

Advances in Materials Science and Engineering 11

CorrosionInternational Journal of

Hindawiwwwhindawicom Volume 2018

Advances in

Materials Science and EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Analytical ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

ScienticaHindawiwwwhindawicom Volume 2018

Polymer ScienceInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Advances in Condensed Matter Physics

Hindawiwwwhindawicom Volume 2018

International Journal of

BiomaterialsHindawiwwwhindawicom

Journal ofEngineeringVolume 2018

Applied ChemistryJournal of

Hindawiwwwhindawicom Volume 2018

NanotechnologyHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

High Energy PhysicsAdvances in

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

TribologyAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

ChemistryAdvances in

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

Hindawiwwwhindawicom Volume 2018

BioMed Research InternationalMaterials

Journal of

Hindawiwwwhindawicom Volume 2018

Na

nom

ate

ria

ls

Hindawiwwwhindawicom Volume 2018

Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom

[40] H Wang and K T Ramesh ldquoDynamic strength and frag-mentation of hot-pressed silicon carbide under uniaxialcompressionrdquo Acta Materialia vol 52 no 2 pp 355ndash3672004

[41] T Ficker ldquoQuasi-static compressive strength of cement-basedmaterialsrdquo Cement and Concrete Research vol 41 no 1pp 129ndash132 2011

[42] H Hao and B G Tarasov ldquoExperimental study of dynamicmaterial properties of clay brick and mortar at different strainratesrdquo Australian Journal of Structural Engineering vol 8no 2 pp 117ndash132 2008

[43] M Wu C Qin and C Zhang ldquoHigh strain rate splittingtensile tests of concrete and numerical simulation by meso-scale particle elementsrdquo Journal of Materials in Civil Engi-neering vol 26 no 1 pp 71ndash82 2014

[44] J Xiao L Li L Shen and C S Poon ldquoCompressive behaviourof recycled aggregate concrete under impact loadingrdquo Cementand Concrete Research vol 71 pp 46ndash55 2015

[45] W Wu W Zhang and G Ma ldquoMechanical properties ofcopper slag reinforced concrete under dynamic compressionrdquoConstruction and Building Materials vol 24 no 6 pp 910ndash917 2010

[46] H Su and J Xu ldquoDynamic compressive behavior of ceramicfiber reinforced concrete under impact loadrdquo Constructionand Building Materials vol 45 pp 306ndash313 2013

[47] Y Al-Salloum T Almusallam S M Ibrahim H Abbas andS Alsayed ldquoRate dependent behavior and modeling ofconcrete based on SHPB experimentsrdquo Cement and ConcreteComposites vol 55 pp 34ndash44 2015

[48] C A Ross P Y -ompson and J W Tedesco ldquoSplit-Hopkinson pressure-bar tests on concrete and mortar intension and compressionrdquo ACI Materials Journal vol 86no 5 pp 475ndash481 1989

[49] Q Z Wang X M Jia S Q Kou Z X Zhang andP-A Lindqvist ldquo-e flattened Brazilian disc specimen usedfor testing elastic modulus tensile strength and fracturetoughness of brittle rocks analytical and numerical resultsrdquoInternational Journal of Rock Mechanics and Mining Sciencesvol 41 no 2 pp 245ndash253 2004

[50] F Berto and J Gomez ldquoNotched plates in mixed modeloading (I+II) a review based on the local strain energydensity and the cohesive zone modelrdquo Engineering SolidMechanics vol 5 pp 1ndash8 2017

[51] D Huang Q Zhang and P Qiao ldquoDamage and progressivefailure of concrete structures using non-local peridynamicmodelingrdquo Science China Technological Sciences vol 54 no 3pp 591ndash596 2011

[52] D Huang Q Zhang P Z Qiao and F Shen ldquoA review onperidynamics (PD) method and its applicationsrdquo Advances inMechanics vol 40 no 4 pp 448ndash459 2010

[53] H Haeri K Shahriar M F Marji and P Moarefvand ldquoAcoupled numerical-experimental study of the breakage pro-cess of brittle substancesrdquo Arabian Journal of Geosciencesvol 8 no 2 pp 809ndash825 2015

[54] Y D Ha and F Bobaru ldquoStudies of dynamic crack propa-gation and crack branching with peridynamicsrdquo InternationalJournal of Fracture vol 162 no 1-2 pp 229ndash244 2010

Advances in Materials Science and Engineering 11

CorrosionInternational Journal of

Hindawiwwwhindawicom Volume 2018

Advances in

Materials Science and EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Analytical ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

ScienticaHindawiwwwhindawicom Volume 2018

Polymer ScienceInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Advances in Condensed Matter Physics

Hindawiwwwhindawicom Volume 2018

International Journal of

BiomaterialsHindawiwwwhindawicom

Journal ofEngineeringVolume 2018

Applied ChemistryJournal of

Hindawiwwwhindawicom Volume 2018

NanotechnologyHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

High Energy PhysicsAdvances in

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

TribologyAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

ChemistryAdvances in

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

Hindawiwwwhindawicom Volume 2018

BioMed Research InternationalMaterials

Journal of

Hindawiwwwhindawicom Volume 2018

Na

nom

ate

ria

ls

Hindawiwwwhindawicom Volume 2018

Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom

CorrosionInternational Journal of

Hindawiwwwhindawicom Volume 2018

Advances in

Materials Science and EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Analytical ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

ScienticaHindawiwwwhindawicom Volume 2018

Polymer ScienceInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Advances in Condensed Matter Physics

Hindawiwwwhindawicom Volume 2018

International Journal of

BiomaterialsHindawiwwwhindawicom

Journal ofEngineeringVolume 2018

Applied ChemistryJournal of

Hindawiwwwhindawicom Volume 2018

NanotechnologyHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

High Energy PhysicsAdvances in

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

TribologyAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

ChemistryAdvances in

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

Hindawiwwwhindawicom Volume 2018

BioMed Research InternationalMaterials

Journal of

Hindawiwwwhindawicom Volume 2018

Na

nom

ate

ria

ls

Hindawiwwwhindawicom Volume 2018

Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom