experimentalstudyonlimestonecohesiveparticlemodeland...

Research ArticleExperimental Study on Limestone Cohesive Particle Model andCrushing Simulation

Huaiying Fang 1 Dawei Xing 2 Jianhong Yang 1 Fulin Liu 1 Junlong Chen 2

and Jiansheng Li 2

1Key Laboratory of Process Monitoring and System Optimization for Mechanical and Electrical Equipment Huaqiao UniversityXiamen 361021 China2Fujian South Highway Machinery Co Ltd Quanzhou 362021 China

Correspondence should be addressed to Huaiying Fang happenhqueducn

Received 21 May 2018 Revised 26 August 2018 Accepted 10 October 2018 Published 1 November 2018

Academic Editor Baozhong Sun

Copyright copy 2018Huaiying Fang et alis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

is study investigates the effect of impact velocity and particle size on crushing characteristics We use a discrete-element methodsimulation and construct cohesive limestone particles with internal microinterfaces and cracks for impact crushing experi-mentatione simulation model follows the same process as the impact crushing experiment Results show that after crushing atimpact velocities of 30 and 40ms the simulated particle-size distribution curve matches experimental results as closely as 95For different particle sizes results are more than 90 in agreement ese results indicate the feasibility of the cohesive-particlecrushing simulation model When the particle size is 15mm an approximate linear relationship exists on impact velocity andcrushing ratio For a constant impact velocity the particle size of 18mm results in the maximum crushing ratio

1 Introduction

e discrete-element method (DEM) is an effective nu-merical simulation method for investigating crushing par-ticles [1] For DEM numerical simulation of particlebreakage it is necessary to construct a model of the ma-terialrsquos particle mechanics e quality of the model stronglyaffects the simulation results [2] In the mineral ore fieldPotyondya and Cundall built a DEM modelmdashbased ona bonded particle modelmdashthat simulated rock crushing [3]e rock is filled with assembly of spherical particles ofdifferent sizes and the contact point is added with theparallel bond Bonding differently sized particles into co-hesive particlese cohesive particles are used in the impactcrushing experiment Schubert et al showed that experi-mental results had similarities with DEM simulationsproving the feasibility of this approach [4] Price et alproposed a filling method using the particlesrsquo mesh verticesto automatically derive the 3D surface thereby convertingfour points into a sphere [5] However the random samplingtechnique required to select four points from a large number

of mesh vertices affects the computational efficiency Al-Khasawneh proposed a newmodel based on the DEM [6] Insimulations and experiments their model avoided theproblems caused by calculating too many cohesive particlesHowever it also ignored the changes of micromorphology inthe grain-crushing process

Jiang et al developed the numerical model of rockfragmentation via waste-jet impact based on the finite-element method e results showed that the theoreticalscopes of the crushing and damage zone were slightlysmaller than those of the numerical method because thestress wave reflection and superposition were ignored in thedeveloped theoretical model [7] Quist and Evertsson builtan ore particle model for simulating cone crushing ina virtual environment with a collection of particles usinga bimodal model [8] Lei built a cohesive-particle model witha single particle that can dynamically simulate the wholeprocess of a jaw crusher crushing the material [9] Liestablished a model of a collection of particles to simulateasphalt pavement He used uniaxial compression and in-direct tensile test parameters to calibrate the DEM

HindawiAdvances in Materials Science and EngineeringVolume 2018 Article ID 3645720 12 pageshttpsdoiorg10115520183645720

improving the established theories of milling operations[10] e internal parameters of the above mode only begiven one group of bond parameters and more researchesonly are carried out compression crushing It is difficult toreflect the internal strength of many kinds of mineralsbinding the surface and different minerals in the ores Due toparticle breakage and fracture that can only be fully un-derstood at the particle scale DEM has been widely used inthe past few years [11ndash13] In this paper we constructeda cohesive-particle model with internal microinterfaces andcracks to simulate the crushing process of a single materiale particle size distribution after crushing was analyzede real crushing ratio and sand forming rate were com-pared and analyzed

2 Materials and Methods

21 HertzndashMindlin (No Slip) Nonsliding Contact Model and3eory HertzndashMindlin (no slip) is a DEM simulationmodel with the normal force based on Hertz contact theoryand the tangential force based on the work of MindlinndashDeresiewicz e contact between granular cells is modeledby a spring-damping system e spring represents theelasticity of the unit Damping is force attenuation or objectin the energy dissipation of the movement e dampingrepresents the inelasticity and the sliding block with frictioncoefficient represents the friction between elements econtact model between particle elements is shown in Fig-ure 1 e contact model is efficient and accurate for cal-culation of the forces [14ndash17]

From Hertz contact theory [18ndash20] the normal force Fnbetween the particles is

Fn 43Elowast

Rlowast

1113968δ32n

1Elowast

1minus ]2aEa

+1minus ]2b

Eb

1Rlowast

1Ra

+1

Rb

(1)

where Elowast is equivalent Youngrsquos modulus Rlowast is equivalentradius δn is normal overlap Ea ]a and Ra and Eb ]b and Rbare Youngrsquos modulus Poissonrsquos ratio and the radius of thecontact sphere respectively

e tangential force Ft between the particles is

Ft minusStδt

Sτ 8Glowast

Rlowastδn

1113969

d 1113944i

xBi minusxAi1113872 1113873 xBi minus xAi1113872 1113873⎛⎝ ⎞⎠

12

(i 1 2)

(2)

where St is the shear stiffness δt is the tangential overlap Glowast

is the equivalent shear modulus xAi and xBi are the centercoordinates of A and B of particle units respectively and d isthe distance between the centers of the two particle units

e contact stiffnesses between two particles aremodeled as a set of elastic springs with a constant normaland shear stiffness at the contact point (Figure 2) Whentwo particles overlap a normal and shear contact forcedevelop at the contact point causing a relative motion tooccur between two balls during each calculation stepParallel bond replaces cohesion between different tissueswith polymerization in rock material particleserefore the numerical calculation model of the crushedrock material particles the cohesive particle model isobtained

e normal overlap δn of two particle units can becalculated as

δn RA + RB minus d (3)

where RA and RB are bonding radii of particle A andparticle B

e stiffness coefficient of the two particle units is

kn 2Elowast

Rlowastδn

1113969

ks 12minus13

1113874 1113875kn

(4)

where kn is the normal stiffness coefficient and ks is thetangential stiffness coefficient

22 HertzndashMindlin Model with Bonding Particle Adhesione HertzndashMindlin with the bonding contact model canuse a finite bond force to calculate the bonded particlemodel e bonding forcemoment is an additionalHertzndashMindlin force is model is especially suitable forsimulating the fracture failure of concrete and rock-likematerials [21 22]

e interaction between particles is calculated by theHertzndashMindlin contact model using DEM software beforethe particles are bonded together during bond generationAfter bond generation the force (Fnt)torque (Tnt) on theparticle is set to 0 and (5)ndash(8) are calculated

δFn minusυnSnAψt (5)

δFt minusυtStAψt (6)

δTn minusωnStJψt (7)

δTt minusωtStJ

2ψt (8)

where A πR2B J (12)πR4

B RB is the bonding radius Snand St are the normal stiffness and tangential stiffness re-spectively ψt is the time step υn and υt are the normalvelocity and tangential velocity of the particle respectivelyωn and ωt are the normal angular velocity and tangentialangular velocity of the particle respectively

e bond breaks when the normal and tangential stressesexceed preset values

2 Advances in Materials Science and Engineering

σmax ltminusFn

A+2Mt

JRB

τmax ltminusFt

A+Mn

JRB

(9)

23 Construction of Cohesive Model of Limestone Owing tothe complex internal structure and diverse composition ofrock the bond strength diers even between dierentsamples of the same mineral Using the HertzndashMindlinwith the bonding model we use multiple-strength bondkeys to distribute bonds randomly to construct the initialdefects in the interior of the particles e particle-ballmodel is then divided into four partse shared surfaces ofeach part represent internal cracks and can simulate thedierences in cohesion between both similar and dierentminerals e discrete-element model of rock particlesneeds to determine the physical parameters and contactparameters e physical parameters and contact param-eters of limestone discrete-element model are determinedthrough a series of experiments e results are shown inTables 1 and 2

e cohesive-particle model is established with in-ternal microinterfaces and cracks as shown in Figure 3 In

Figure 3(a) four dierent color combinations red-darkgreen blue-light green green-brown and pink-black rep-resent the distributions of four same-sized particle typesebonding surface of each structure is the internal crack of theparticle which is composed of two small particles of dif-ferent sizes e dierent cohesive force between smallparticles and the initial crack in the cohesive particles is set toa smaller bond strength In Figure 3(b) the dierent colors

AParticle B

Particle

Contact surface

RA

RB

δn δn

Contact point

2RFin

Fis

Min

Mis

Parallel bond

Figure 2 Parallel bond lying on the contact surface between two particles

Table 1 e material properties of limestone and steel

Material Poissonrsquos ratio Shearmodulus (Pa)

Density(kgmiddot(m3)minus1)

Limestone 025 209e + 8 2650Steel 030 7e + 10 7800

Particle B

Ftangential

RA

XAlocal

ZAlocal

YAlocalFnormal

kn

kt

μ

cn

ct

XBlocal

ZBlocal

YBlocalRB

Particle stiffness (spring)Damping

Friction coefficient

Particle A

Figure 1 Diagram of HertzndashMindlin contact model

Table 2 Contact parameter table

Mutualcontact

Coecient ofrestitution

Coecient ofstaticfriction

Rollingfriction

coecientLimestone-limestone 0208 077 01

Limestone-steel 0557 061 007

Advances in Materials Science and Engineering 3

lengths and thicknesses of the link bar indicates the differentbond strength of bond keys

e bonding surface of the initial crack in the material iseasily broken owing to the mechanical properties of rockWe determine a set of appropriate parameters through theimpact crushing experiment and simulation experimentetype and value of the contact model parameters are shown inTable 3

24 Impact Crushing Experiment Platform Figure 4 showsa schematic of the single-particle impact crushing experi-mentematerial particles are accelerated by high-pressuregas and impact a stationary plate We obtain the requiredparticle impact velocity by adjusting the pressure e im-pact velocity is calculated using a high-speed camera tomeasure the distance between points A and B and the timedifference between the two frames After collecting thecrushed material the size distribution is obtained Formaterial less than 475mm in diameter standard sieves areused to screen the distribution of particle sizes For largerparticles a video size-detection system is used e impactsimulation experimental device is shown in Figure 5 In theexperimental device the MROM110 CMOS high-speedcamera and the MACRO100F28D manual focus lens areusede shooting rate can reach 10000 framess which canfully capture the position information of high-speed shotparticles Since the camerarsquos light-receiving rate is relativelylow at high resolution a carbon lamp is added to fill thecamera to achieve a clear speed image e light source usedin this test is a 1000W carbon lampe high-pressure gas inthe high-pressure gasholder is equivalent to the powersystem of the experimental device and the limestone drivenby the high-pressure gas is sufficiently accelerated in theacceleration pipeline to enter the crushing chamber and hitthe impact plate of the crushing chamber at a higher linearvelocitye impact plate has a speed acquisition window onthe surface of the crushing chamber and is sealed withbulletproof glass e speed of the limestone particles before

impact can be calculated from the pictures taken by the high-speed camera e aggregated particles can also be collectedefficiently after crushing e crushed particles are collectedand processed by a combination of mechanical screeningand image processing to calculate the mass distribution andthe true crush ratio of the particle size interval

In this paper we construct cohesive-particle modelsusing a variety of bond-key combinations based on previousresearch on the parameters of a single bond key DEM isused to simulate impact experiments with different velocitiesand different particle sizes e simulation of the impactprocess is shown in Figure 6 e 15mm model cohesive

(a) (b)

Figure 3 Cohesive particles model-limestone cohesive model ball (a) and different intensity bond keys (b)

Table 3 e type and value of the contact model parameters

Contact type BPM parameter type Values

Red-dark green

Normal stiffness per unitarea

(Nm3)6e + 11

Shear stiffness per unit area(Nm3) 3e + 11

Critical normal stress (Pa) 8e + 6Critical shear stress (Pa) 4e + 6Bonded disk radius (mm) 06

Blue-light green green-brown


(Nm3)6e + 11


Critical normal stress (Pa) 7e + 6

Critical shear stress (Pa) 35e +6

Bonded disk radius (mm) 06

Pink-black


(Nm3)6e + 11




particle with internal initial crack and microstructure isimpacted at dierent velocities and an image size-detectionsystem is used to measure the distribution of particles sizeafter crushing In addition at 45ms dierent sizes of

limestone cohesive particles are modeled and the experimentis repeated e limestone material with a particle size ofabout 15mm is rounded and then a single-particle activeimpact crushing experiment is performed A limestone

Aggregate particle inlet

High-pressure gasholder

Dust export

Crushingchamber

Outlet

Impact plate

(a) (b)

Figure 5 e impact crushing experiment device e schematic diagram of pneumatic experimental device (a) and single-particle impactcrushing experiment diagram (b)

Bondinggeneration

Impactcrushing

Figure 6 e simulation of the impact crushing process

Broken materials

Point of impact

Impact plate

Distance D

Position BCrack

Position A

Material initial positionVentilation pipe

Adjustable pressure

Image processing with particle size larger than 475mm

Sieving with particle size less than 475mm

Figure 4 Principle diagram of the single-particle impact crushing experiment


crushing process is recorded using a high-speed camera(Figure 7)

3 Results and Discussion

31 Simulation and Experimental Analysis of Different ImpactVelocities We accelerate the 15mm single-particle lime-stone material with different air pressures to reach thedesired impact velocities We then observe the particle-sizedistribution after crushing and analyze the degree offragmentation and crushing effect After 10 crushing ex-periments we take the crushed limestone and calculate thegrain mass proportions using sieve screening and theimage size-detection system e DEM simulation is usedto count the bonded-particle aggregate after each particleis completely crushed e cohesive particlesrsquo model di-ameter of the simulation experiment is 15mm eparticle-size fractions are determined using imageprocessing

311 Effect of Impact Velocity on Particle-Size Distributionafter Crushing Impact velocities of 20ms 30ms 40msand 50ms are used to crush materials with similar particlesizes and the granularity characteristics are analyzed Withincreasing impact velocity particles are broken furthere characteristics of the particle-size distribution areanalyzed

For impact velocity 20ms ore particles break from themiddle into two pieces When impact velocity is increased to30ms the particles break into 3-4 parts For impact velocity40ms the particles break into 4-5 parts e particle-sizedistribution of the simulated fracture is close to the realcrushing condition so the internal structure of the initialmicrostructure and the crack of our particle model simulatesthe impact crushing process well For impact velocity 50msthe particles break into 7-8 parts similar to the simulatione particles with particle size 475ndash132mm accounts forthe majority fewer particles are lt236mm or gt132mm indiameter e particle-size distribution curve is close toa normal distribution When the particle size is almost thesame Figures 8ndash11 show that the morphology of the brokenmaterial is similar With increasing impact velocity theparticle-size distribution curve is skewed to the left overallthe grain size is decreased and the particle-size distributioncurve is closer to a normal distribution after breaking esimulation results are close to the experimental results

312 Effect of Impact Velocity on Crushing Ratio and SandForming Rate To investigate the relationship between im-pact velocity and particle-size distribution the present studyuses experimental and DEM simulation data A particlediameter of 15mm is chosen for the single-particle impactcrushing experiment performed at different impact veloc-ities e real crushing ratio i is the ratio of the arithmetic

(a) (b)

(c) (d)

Figure 7 e impact crushing process of different times (a) 0 μs (b) 78 μs (c) 152 μs (d) 295 μs


mean particle size DM of the particles before crushing to thearithmetic mean particle size dM of the particles aftercrushing e formula is as follows

i DM

dM (10)

e purpose of mechanical sand is to increase pro-duction for industrially produced sand and the particle sizeshould be lt475mm us it is important to study theparticle-size statistics e sand forming ratio Sp formula isas follows

Sp m1

m0times 100 (11)

where m1 is the mass of the particles smaller than 475mmafter crushing and m0 is the total mass of aggregate aftercrushing

Figure 12 shows the comparison of experimental andsimulation real crushing ratios for limestone of particle size15mm at an impact velocity of 20ndash50ms e averageparticle size of the ore materials for the experiment and thesimulation was obtained by the weighted arithmetic av-erage method and used to calculate the real crushing ratioWith increasing impact velocity the real crushing ratio andsand forming ratio increases proportionally is re-lationship has the same trend for simulation and experi-mental results is shows that the establishment of theinternal initial crack and the microinterface of the particlemodel are reasonable

32 Simulation and Experimental Analysis of Dierent Par-ticle Sizes For dynamic loads such as impact crushing theinitial particle size has a signicant eect on the physicalproperties of the particles which are nonuniform solids withmany internal cracks e random distribution of the cracks

(a) (b)

0ndash236

60

50

40

30

20

10

0236ndash475 475ndash95

Particle size (mm)

Mas

s per

cent

age (

)


ExperimentSimulation

(c)

Figure 8 Experimental crushing eect of 20ms (a) simulation crushing eect of 20ms (b) and particle-size distribution curve of20ms (c)

(a) (b)

0ndash236

60

70

50

40

30

20

10


Particle size (mm)

Mas

s per

cent

age (

)



(c)



determines if the local macroscopic strength of the particle isless than the nominal strength e larger the particle themore the internal cracks and the more likely it is to bedamaged owing to a weak point

To standardize comparisons of fragmentation of dif-ferent particle sizes we introduce the concept of unit impactcrushing energy to account for energy consumption per unitvolume and crack density Hu et al discussed the re-lationship between energy consumption and size distribu-tion of original coal particles and crushing products and theresults show that there is an optimum size of the original coalparticle at which the specic impact energy reaches mini-mum [23] Guo et al set up the relation models betweencoecient of energy utilization and the degree of crushingas well as the models between the coecient and inputenergy by simulating the fragmentation process of rockblasting [24] To study the eect of particle size on energyconsumption per unit volume and the fragility of the

particles we mill limestone particles into 10mm 14mm18mm and 22mm balls using a small round mill (DM-IIIAbrasion Tester) en we set the impact velocity to keepunit impact crushing energy in a similar range and use theDEM to simulate the process of the experiment e co-hesive particles model diameters are 10mm 14mm 18mmand 22mm in the DEM simulation experiment

e0 Etotal

V(12)mv2ρ

m 05ρv2 (12)

where e0 is the unit impact crushing energy Etotal is theimpact crushing energy m is the particle mass V is theparticle volume v is the impact velocity and ρ is the particledensity

321 Eect of Particle Size on Particle-Size Distribution afterCrushing In the DEM simulation 10mm 14mm 18mm

(a) (b)

0ndash236

50

40

30

20

10


Particle size (mm)

Mas

s per

cent

age (

)



(c)


(a) (b)


0ndash2360

10

20

30

40

50

60

70

80

236ndash475 475ndash95Particle size (mm)


Mas

s per

cent

age (

)

(c)



and 22mm balls are accelerated to 45ms to make their unitimpact crushing energy consistent Using statisticalmethods we analyze and compare the particle-size distri-butions after crushing as shown in Figures 13ndash16

In the experiment for the 14mmmaterial particle sizethe material breaks into 4-5 parts similar to the simulationresults At impact velocity 45ms particle size 475ndash132mm accounts for most material and fewer particleshave diameters gt132mm or lt236mm Figures 13ndash16show the particle-size distribution curve after experi-ment and simulation under the same impact velocityWhen unit impact crushing energy of the material is keptconstant the particle-size distribution curve is shifted tothe right as the particle size increases the ne aggregategradually decreases the larger particle size increases andthe probability density curve after crushing tends toa normal distribution is simulation result is similar tothe experimental result

322 Eect of Particle Size on Crushing Ratio and SandForming Rate To investigate the relationship betweenparticle-size distribution and particle size after impactcrushing the present study uses experimental and DEMsimulation data Limestone single particles with diameter10ndash22mm are used in the impact crushing experiment at thesame velocity to maintain constant unit impact crushingenergy From the experiment and simulation results weobtain the average particle size of the crushed material andcalculate the crushing ratio e curve relationship betweenthe crushing ratio and the particle size is established theresults are shown in Figure 17(a) To calculate the brokensand ratio we establish the particles size and sand ratio curveand compare with the results of the impact crushing ex-periment as shown in Figure 17(b)

Figure 17(a) shows the comparison of experimentaland simulated crushing ratios of 10ndash22mm limestoneparticles at 45ms e average particle size for the

(a) (b)

0ndash2360

102030405060708090

100



Mas

s per

cent

age (

)


(c)

Figure 13 Experimental crushing eect of 10mm (a) simulation crushing eect of 10mm (b) and 10mm particle-size distributioncurve (c)

28

26

Real

crus

hing

ratio

() 24

22

20

18

16

14

12

20 25 30Impact velocity (ms)

35 40 45 50


(a)

Sand

form

ing

ratio

()

20

25

30

15

35

10

5

020 25 30

Impact velocity (ms)35 40 45 50


(b)

Figure 12 Real crushing ratio (a) and sand forming ratio (b)


experiment and the simulation was obtained using theweighted arithmetic average method and used to calculatethe crushing ratio As particle size increases the crushingratio rst increases to a maximum and then decreasesFigure 17(b) shows the inverse proportional relationshipbetween the percentage of sand formation and the particlesize of materials after crushing e trend is the same forboth the simulation and the experiment showing that theparticle model with the internal initial crack and micro-structure is reasonable

4 Conclusions

In this paper we constructed a cohesive-particle modelwith internal microinterfaces and cracks using a DEM

simulation After simulating the impact crushing process ofthe single-particle material and using experiments to verifythe rationality of the model we reach the followingconclusions

(1) e proposed model can simulate the internal de-fects of rock materials and the strength can beadjusted according to dierent materials e modelis suitable for the impact fracture of anisotropicbrittle materials and is a modication of the bondedparticle model

(2) For constant particle size there is a linear re-lationship between impact velocity and crushingratio Sand formation rate increases as impact ve-locity increases

(a) (b)

0ndash2

36

0

10

20

30

40

50

60

70

236

ndash47

5

475

ndash95

Particle size (mm)

95ndash

132

132

ndash16

16ndash2

0

Mas

s per

cent

age (

)


(c)


(a) (b)

0ndash236

60

50

70

40

30

20

10


Particle size (mm)

Mas

s per

cent

age (

)

95ndash132 132ndash16 16ndash20


(c)



(3) Up to a certain impact velocity there is an optimumparticle size which has the highest degree of frag-mentation and the maximum crushing ratio

(4) For constant unit impact crushing energy there isan approximate inverse relation between sandformation rate and particle size e entireparticle-size distribution curve is shifted to theright with the increasing particle size e pro-portion of ne aggregate to larger particles grad-ually decreases

e cohesive-particle model with internal micro-interfaces and cracks is feasible for simulating the impactcrushing process of limestone particles e DEM has animportant application value in the simulation of material

fragmentation and is used as the basis for a new method forfurther research on the eciency of impact crushingconsumption of crushing energy and material character-istics after crushing

Data Availability

e data used to support the ndings of this study are in-cluded within the article

Conflicts of Interest

e authors declare that there are no conbrvbaricts of interestregarding the publication of this paper

30

28

26

24

22

20

18

16

14

12

1010 12 14

Impact particle size (mm)

Real

crus

hini

g ra

tio (

)

16 18 20 22


(a)

10

5

15

20

25

30

35Sa

nd fo

rmin

g ra

tio (

)

10 12 14Impact particle size (mm)

16 18 20 22


(b)

Figure 17 Crushing ratio (a) and sand forming ratio (b)

(a) (b)

0ndash236

50

40

30

20

10


Particle size (mm)

Mas

s per

cent

age (

)



(c)



Acknowledgments

is work was financially supported by the InternationalScience and Technology Cooperation and Exchange Pro-gram in Fujian Province (2018I1006) Major Project ofIndustry-University-Research Cooperation in Fujian Prov-ince (2016H6013) and the Subsidized Project for CultivatingPostgraduatesrsquo Innovative Ability in Scientific Research ofHuaqiao University (1611403006) e project received re-search start-up fee from Huaqiao University (17BS305) andFujian Natural Science Foundation Project (2017J01108)

References

[1] L Zheng and Z Zhao ldquoReview of particle breakage of rockand soil under DEM analysis techniquesrdquo Science amp Tech-nology Information vol 13 no 3 pp 84ndash87 2015

[2] Y Liu X Z Li and S C Wu ldquoNumerical simulation ofparticle crushing for rockfill of different particles shape underrolling compactionrdquo Rock and Soil Mechanics vol 35 no 11pp 3269ndash3280 2014

[3] D O Potyondya and P A Cundall ldquoA bonded-particle modelfor rockrdquo International Journal of RockMechanics andMiningSciences vol 41 no 8 pp 1329ndash1364 2004

[4] W Schubert M Khanal and J Tomas ldquoImpact crushing ofparticle-particle compounds-experiment and simulationrdquoInternational Journal of Mineral Processing vol 75 no 1-2pp 41ndash52 2005

[5] M Price V Murariu and G Morrison ldquoSphere clumpgeneration and trajectory comparison for real particlesrdquo Der-chen Chang Irina Markina and Alexander Vasilrsquoev vol 51no 4 pp 105ndash113 2007

[6] Y Al-Khasawneh Beitrag zur Ermittlung von Zielgroszligen furdie Auslegung und den Betrieb von Rotorschleuderbrechern mitder Diskret-Aquivalent-Element-Methode (DEEM) Techni-sche Universitat Bergakademie Freiberg Freiberg Germany2009

[7] H X Jiang C L Du and Z H Liu ldquoeoretical and nu-merical investigation on rock fragmentation under high-pressure water-jet impactrdquo Iranian Journal of Science andTechnology Transactions of Civil Engineering vol 41 no 3pp 305ndash315 2017

[8] J Quist and C M Evertsson ldquoCone crusher modelling andsimulation using DEMrdquo Minerals Engineering vol 85pp 92ndash105 2015

[9] Q Lei Research on Material Crushing Mechanism Based onDiscrete Element Method Jiangxi University of Science andTechnology Ganzhou Jiangxi China 2012

[10] Y P Li Simulation Study on Milling Device of Road MillingMachine Based on the Discrete Element Method Jilin Uni-versity Changchun Jilin China 2015

[11] P A Cundall and O D L Strack ldquoA discrete numericalmodel for granular assembliesrdquo Geotechnique vol 29 no 1pp 47ndash65 1979

[12] K Iwashita and M Oda ldquoRolling resistance at contacts insimulation of shear band development by DEMrdquo Journal ofEngineering Mechanics vol 124 no 3 pp 285ndash292 1998

[13] J F Ferellec and G RMcdowell ldquoAmethod tomodel realisticparticle shape and inertia in DEMrdquo Granular Matter vol 12no 5 pp 459ndash467 2010

[14] N S Weerasekara M S Powell P W Cleary et al ldquoecontribution of DEM to the science of comminutionrdquo PowderTechnology vol 248 pp 3ndash24 2013

[15] M Ucgul J M Fielke and C Saunders ldquoree-dimensionaldiscrete element modelling of tillage determination ofa suitable contact model and parameters for a cohesionlesssoilrdquo Biosystems Engineering vol 121 pp 105ndash117 2014

[16] A Elmekati and U E Shamy ldquoA practical co-simulationapproach for multiscale analysis of geotechnical systemsrdquoComputers and Geotechnics vol 37 no 4 pp 494ndash503 2010

[17] Y Q Tan D M Yang and Y Sheng ldquoDiscrete elementmethod (DEM) modeling of fracture and damage in themachining process of polycrystalline SiCrdquo Journal of theEuropean Ceramic Society vol 29 no 6 pp 1029ndash1037 2009

[18] R D Mindlin ldquoCompliance of elastic bodies in contactrdquoJournal of AppliedMechanics vol 16 no 3 pp 259ndash268 1949

[19] S Lommen D Schott and G Lodewijks ldquoDEM speedupstiffness effects on behavior of bulk materialrdquo Particuologyvol 12 pp 107ndash112 2014

[20] R Moreno-Atanasio ldquoEnergy dissipation in agglomeratesduring normal impactrdquo Powder Technology vol 223pp 12ndash18 2012

[21] G K P Barrios R M D Carvalho A Kwade andL M Tavares ldquoContact parameter estimation for DEMsimulation of iron ore pellet handlingrdquo Powder Technologyvol 248 pp 84ndash93 2013

[22] N Cho C D Martin and D C Sego ldquoA clumped particlemodel for rockrdquo International Journal of Rock Mechanics andMining Sciences vol 44 no 7 pp 997ndash1010 2007

[23] Z Z Hu Y M Zhuang T Y Cai and X P Chen ldquoEx-perimental study on energy consumption and particle sizedistribution of single particle coal under impact crushingrdquoJournal of China Coal Society vol 40 pp 230ndash234 2015

[24] L Guo A Shao D Zhang et al ldquoResearch on energy con-sumption characteristics and energy density per unit time ofrock crushing by impact loadrdquo in Proceedings of the 4th Asian-Pacific Symposium on Blasting Techniques 2014


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improving the established theories of milling operations[10] e internal parameters of the above mode only begiven one group of bond parameters and more researchesonly are carried out compression crushing It is difficult toreflect the internal strength of many kinds of mineralsbinding the surface and different minerals in the ores Due toparticle breakage and fracture that can only be fully un-derstood at the particle scale DEM has been widely used inthe past few years [11ndash13] In this paper we constructeda cohesive-particle model with internal microinterfaces andcracks to simulate the crushing process of a single materiale particle size distribution after crushing was analyzede real crushing ratio and sand forming rate were com-pared and analyzed

2 Materials and Methods

21 HertzndashMindlin (No Slip) Nonsliding Contact Model and3eory HertzndashMindlin (no slip) is a DEM simulationmodel with the normal force based on Hertz contact theoryand the tangential force based on the work of MindlinndashDeresiewicz e contact between granular cells is modeledby a spring-damping system e spring represents theelasticity of the unit Damping is force attenuation or objectin the energy dissipation of the movement e dampingrepresents the inelasticity and the sliding block with frictioncoefficient represents the friction between elements econtact model between particle elements is shown in Fig-ure 1 e contact model is efficient and accurate for cal-culation of the forces [14ndash17]

From Hertz contact theory [18ndash20] the normal force Fnbetween the particles is

Fn 43Elowast

Rlowast

1113968δ32n

1Elowast

1minus ]2aEa

+1minus ]2b

Eb

1Rlowast

1Ra

+1

Rb

(1)

where Elowast is equivalent Youngrsquos modulus Rlowast is equivalentradius δn is normal overlap Ea ]a and Ra and Eb ]b and Rbare Youngrsquos modulus Poissonrsquos ratio and the radius of thecontact sphere respectively

e tangential force Ft between the particles is

Ft minusStδt

Sτ 8Glowast

Rlowastδn

1113969

d 1113944i

xBi minusxAi1113872 1113873 xBi minus xAi1113872 1113873⎛⎝ ⎞⎠

12

(i 1 2)

(2)

where St is the shear stiffness δt is the tangential overlap Glowast

is the equivalent shear modulus xAi and xBi are the centercoordinates of A and B of particle units respectively and d isthe distance between the centers of the two particle units

e contact stiffnesses between two particles aremodeled as a set of elastic springs with a constant normaland shear stiffness at the contact point (Figure 2) Whentwo particles overlap a normal and shear contact forcedevelop at the contact point causing a relative motion tooccur between two balls during each calculation stepParallel bond replaces cohesion between different tissueswith polymerization in rock material particleserefore the numerical calculation model of the crushedrock material particles the cohesive particle model isobtained

e normal overlap δn of two particle units can becalculated as

δn RA + RB minus d (3)

where RA and RB are bonding radii of particle A andparticle B

e stiffness coefficient of the two particle units is

kn 2Elowast

Rlowastδn

1113969

ks 12minus13

1113874 1113875kn

(4)

where kn is the normal stiffness coefficient and ks is thetangential stiffness coefficient

22 HertzndashMindlin Model with Bonding Particle Adhesione HertzndashMindlin with the bonding contact model canuse a finite bond force to calculate the bonded particlemodel e bonding forcemoment is an additionalHertzndashMindlin force is model is especially suitable forsimulating the fracture failure of concrete and rock-likematerials [21 22]

e interaction between particles is calculated by theHertzndashMindlin contact model using DEM software beforethe particles are bonded together during bond generationAfter bond generation the force (Fnt)torque (Tnt) on theparticle is set to 0 and (5)ndash(8) are calculated

δFn minusυnSnAψt (5)

δFt minusυtStAψt (6)

δTn minusωnStJψt (7)

δTt minusωtStJ

2ψt (8)

where A πR2B J (12)πR4

B RB is the bonding radius Snand St are the normal stiffness and tangential stiffness re-spectively ψt is the time step υn and υt are the normalvelocity and tangential velocity of the particle respectivelyωn and ωt are the normal angular velocity and tangentialangular velocity of the particle respectively

e bond breaks when the normal and tangential stressesexceed preset values


σmax ltminusFn

A+2Mt

JRB

τmax ltminusFt

A+Mn

JRB

(9)




AParticle B

Particle

Contact surface

RA

RB

δn δn

Contact point

2RFin

Fis

Min

Mis

Parallel bond






Particle B

Ftangential

RA

XAlocal

ZAlocal

YAlocalFnormal

kn

kt

μ

cn

ct

XBlocal

ZBlocal

YBlocalRB



Particle A



Mutualcontact



Rollingfriction









(a) (b)




Red-dark green


(Nm3)6e + 11





(Nm3)6e + 11





Pink-black


(Nm3)6e + 11








Dust export

Crushingchamber

Outlet

Impact plate

(a) (b)


Bondinggeneration

Impactcrushing


Broken materials

Point of impact

Impact plate

Distance D

Position BCrack

Position A


Adjustable pressure











(a) (b)

(c) (d)




i DM

dM (10)


Sp m1

m0times 100 (11)




(a) (b)

0ndash236

60

50

40

30

20

10


Particle size (mm)

Mas

s per

cent

age (

)



(c)


(a) (b)

0ndash236

60

70

50

40

30

20

10


Particle size (mm)

Mas

s per

cent

age (

)



(c)






e0 Etotal

V(12)mv2ρ

m 05ρv2 (12)



(a) (b)

0ndash236

50

40

30

20

10


Particle size (mm)

Mas

s per

cent

age (

)



(c)


(a) (b)


0ndash2360

10

20

30

40

50

60

70

80



Mas

s per

cent

age (

)

(c)







(a) (b)

0ndash2360

102030405060708090

100



Mas

s per

cent

age (

)


(c)


28

26

Real

crus

hing

ratio

() 24

22

20

18

16

14

12


35 40 45 50


(a)

Sand

form

ing

ratio

()

20

25

30

15

35

10

5

020 25 30



(b)




4 Conclusions





(a) (b)

0ndash2

36

0

10

20

30

40

50

60

70

236

ndash47

5

475

ndash95

Particle size (mm)

95ndash

132

132

ndash16

16ndash2

0

Mas

s per

cent

age (

)


(c)


(a) (b)

0ndash236

60

50

70

40

30

20

10


Particle size (mm)

Mas

s per

cent

age (

)



(c)







Data Availability




30

28

26

24

22

20

18

16

14

12

1010 12 14


Real

crus

hini

g ra

tio (

)

16 18 20 22


(a)

10

5

15

20

25

30

35Sa

nd fo

rmin

g ra

tio (

)


16 18 20 22


(b)


(a) (b)

0ndash236

50

40

30

20

10


Particle size (mm)

Mas

s per

cent

age (

)



(c)



Acknowledgments


References




























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls




σmax ltminusFn

A+2Mt

JRB

τmax ltminusFt

A+Mn

JRB

(9)




AParticle B

Particle

Contact surface

RA

RB

δn δn

Contact point

2RFin

Fis

Min

Mis

Parallel bond






Particle B

Ftangential

RA

XAlocal

ZAlocal

YAlocalFnormal

kn

kt

μ

cn

ct

XBlocal

ZBlocal

YBlocalRB



Particle A



Mutualcontact



Rollingfriction









(a) (b)




Red-dark green


(Nm3)6e + 11





(Nm3)6e + 11





Pink-black


(Nm3)6e + 11








Dust export

Crushingchamber

Outlet

Impact plate

(a) (b)


Bondinggeneration

Impactcrushing


Broken materials

Point of impact

Impact plate

Distance D

Position BCrack

Position A


Adjustable pressure











(a) (b)

(c) (d)




i DM

dM (10)


Sp m1

m0times 100 (11)




(a) (b)

0ndash236

60

50

40

30

20

10


Particle size (mm)

Mas

s per

cent

age (

)



(c)


(a) (b)

0ndash236

60

70

50

40

30

20

10


Particle size (mm)

Mas

s per

cent

age (

)



(c)






e0 Etotal

V(12)mv2ρ

m 05ρv2 (12)



(a) (b)

0ndash236

50

40

30

20

10


Particle size (mm)

Mas

s per

cent

age (

)



(c)


(a) (b)


0ndash2360

10

20

30

40

50

60

70

80



Mas

s per

cent

age (

)

(c)







(a) (b)

0ndash2360

102030405060708090

100



Mas

s per

cent

age (

)


(c)


28

26

Real

crus

hing

ratio

() 24

22

20

18

16

14

12


35 40 45 50


(a)

Sand

form

ing

ratio

()

20

25

30

15

35

10

5

020 25 30



(b)




4 Conclusions





(a) (b)

0ndash2

36

0

10

20

30

40

50

60

70

236

ndash47

5

475

ndash95

Particle size (mm)

95ndash

132

132

ndash16

16ndash2

0

Mas

s per

cent

age (

)


(c)


(a) (b)

0ndash236

60

50

70

40

30

20

10


Particle size (mm)

Mas

s per

cent

age (

)



(c)







Data Availability




30

28

26

24

22

20

18

16

14

12

1010 12 14


Real

crus

hini

g ra

tio (

)

16 18 20 22


(a)

10

5

15

20

25

30

35Sa

nd fo

rmin

g ra

tio (

)


16 18 20 22


(b)


(a) (b)

0ndash236

50

40

30

20

10


Particle size (mm)

Mas

s per

cent

age (

)



(c)



Acknowledgments


References




























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls









(a) (b)




Red-dark green


(Nm3)6e + 11





(Nm3)6e + 11





Pink-black


(Nm3)6e + 11








Dust export

Crushingchamber

Outlet

Impact plate

(a) (b)


Bondinggeneration

Impactcrushing


Broken materials

Point of impact

Impact plate

Distance D

Position BCrack

Position A


Adjustable pressure











(a) (b)

(c) (d)




i DM

dM (10)


Sp m1

m0times 100 (11)




(a) (b)

0ndash236

60

50

40

30

20

10


Particle size (mm)

Mas

s per

cent

age (

)



(c)


(a) (b)

0ndash236

60

70

50

40

30

20

10


Particle size (mm)

Mas

s per

cent

age (

)



(c)






e0 Etotal

V(12)mv2ρ

m 05ρv2 (12)



(a) (b)

0ndash236

50

40

30

20

10


Particle size (mm)

Mas

s per

cent

age (

)



(c)


(a) (b)


0ndash2360

10

20

30

40

50

60

70

80



Mas

s per

cent

age (

)

(c)







(a) (b)

0ndash2360

102030405060708090

100



Mas

s per

cent

age (

)


(c)


28

26

Real

crus

hing

ratio

() 24

22

20

18

16

14

12


35 40 45 50


(a)

Sand

form

ing

ratio

()

20

25

30

15

35

10

5

020 25 30



(b)




4 Conclusions





(a) (b)

0ndash2

36

0

10

20

30

40

50

60

70

236

ndash47

5

475

ndash95

Particle size (mm)

95ndash

132

132

ndash16

16ndash2

0

Mas

s per

cent

age (

)


(c)


(a) (b)

0ndash236

60

50

70

40

30

20

10


Particle size (mm)

Mas

s per

cent

age (

)



(c)







Data Availability




30

28

26

24

22

20

18

16

14

12

1010 12 14


Real

crus

hini

g ra

tio (

)

16 18 20 22


(a)

10

5

15

20

25

30

35Sa

nd fo

rmin

g ra

tio (

)


16 18 20 22


(b)


(a) (b)

0ndash236

50

40

30

20

10


Particle size (mm)

Mas

s per

cent

age (

)



(c)



Acknowledgments


References




























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls








Dust export

Crushingchamber

Outlet

Impact plate

(a) (b)


Bondinggeneration

Impactcrushing


Broken materials

Point of impact

Impact plate

Distance D

Position BCrack

Position A


Adjustable pressure











(a) (b)

(c) (d)




i DM

dM (10)


Sp m1

m0times 100 (11)




(a) (b)

0ndash236

60

50

40

30

20

10


Particle size (mm)

Mas

s per

cent

age (

)



(c)


(a) (b)

0ndash236

60

70

50

40

30

20

10


Particle size (mm)

Mas

s per

cent

age (

)



(c)






e0 Etotal

V(12)mv2ρ

m 05ρv2 (12)



(a) (b)

0ndash236

50

40

30

20

10


Particle size (mm)

Mas

s per

cent

age (

)



(c)


(a) (b)


0ndash2360

10

20

30

40

50

60

70

80



Mas

s per

cent

age (

)

(c)







(a) (b)

0ndash2360

102030405060708090

100



Mas

s per

cent

age (

)


(c)


28

26

Real

crus

hing

ratio

() 24

22

20

18

16

14

12


35 40 45 50


(a)

Sand

form

ing

ratio

()

20

25

30

15

35

10

5

020 25 30



(b)




4 Conclusions





(a) (b)

0ndash2

36

0

10

20

30

40

50

60

70

236

ndash47

5

475

ndash95

Particle size (mm)

95ndash

132

132

ndash16

16ndash2

0

Mas

s per

cent

age (

)


(c)


(a) (b)

0ndash236

60

50

70

40

30

20

10


Particle size (mm)

Mas

s per

cent

age (

)



(c)







Data Availability




30

28

26

24

22

20

18

16

14

12

1010 12 14


Real

crus

hini

g ra

tio (

)

16 18 20 22


(a)

10

5

15

20

25

30

35Sa

nd fo

rmin

g ra

tio (

)


16 18 20 22


(b)


(a) (b)

0ndash236

50

40

30

20

10


Particle size (mm)

Mas

s per

cent

age (

)



(c)



Acknowledgments


References




























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls










(a) (b)

(c) (d)




i DM

dM (10)


Sp m1

m0times 100 (11)




(a) (b)

0ndash236

60

50

40

30

20

10


Particle size (mm)

Mas

s per

cent

age (

)



(c)


(a) (b)

0ndash236

60

70

50

40

30

20

10


Particle size (mm)

Mas

s per

cent

age (

)



(c)






e0 Etotal

V(12)mv2ρ

m 05ρv2 (12)



(a) (b)

0ndash236

50

40

30

20

10


Particle size (mm)

Mas

s per

cent

age (

)



(c)


(a) (b)


0ndash2360

10

20

30

40

50

60

70

80



Mas

s per

cent

age (

)

(c)







(a) (b)

0ndash2360

102030405060708090

100



Mas

s per

cent

age (

)


(c)


28

26

Real

crus

hing

ratio

() 24

22

20

18

16

14

12


35 40 45 50


(a)

Sand

form

ing

ratio

()

20

25

30

15

35

10

5

020 25 30



(b)




4 Conclusions





(a) (b)

0ndash2

36

0

10

20

30

40

50

60

70

236

ndash47

5

475

ndash95

Particle size (mm)

95ndash

132

132

ndash16

16ndash2

0

Mas

s per

cent

age (

)


(c)


(a) (b)

0ndash236

60

50

70

40

30

20

10


Particle size (mm)

Mas

s per

cent

age (

)



(c)







Data Availability




30

28

26

24

22

20

18

16

14

12

1010 12 14


Real

crus

hini

g ra

tio (

)

16 18 20 22


(a)

10

5

15

20

25

30

35Sa

nd fo

rmin

g ra

tio (

)


16 18 20 22


(b)


(a) (b)

0ndash236

50

40

30

20

10


Particle size (mm)

Mas

s per

cent

age (

)



(c)



Acknowledgments


References




























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls





i DM

dM (10)


Sp m1

m0times 100 (11)




(a) (b)

0ndash236

60

50

40

30

20

10


Particle size (mm)

Mas

s per

cent

age (

)



(c)


(a) (b)

0ndash236

60

70

50

40

30

20

10


Particle size (mm)

Mas

s per

cent

age (

)



(c)






e0 Etotal

V(12)mv2ρ

m 05ρv2 (12)



(a) (b)

0ndash236

50

40

30

20

10


Particle size (mm)

Mas

s per

cent

age (

)



(c)


(a) (b)


0ndash2360

10

20

30

40

50

60

70

80



Mas

s per

cent

age (

)

(c)







(a) (b)

0ndash2360

102030405060708090

100



Mas

s per

cent

age (

)


(c)


28

26

Real

crus

hing

ratio

() 24

22

20

18

16

14

12


35 40 45 50


(a)

Sand

form

ing

ratio

()

20

25

30

15

35

10

5

020 25 30



(b)




4 Conclusions





(a) (b)

0ndash2

36

0

10

20

30

40

50

60

70

236

ndash47

5

475

ndash95

Particle size (mm)

95ndash

132

132

ndash16

16ndash2

0

Mas

s per

cent

age (

)


(c)


(a) (b)

0ndash236

60

50

70

40

30

20

10


Particle size (mm)

Mas

s per

cent

age (

)



(c)







Data Availability




30

28

26

24

22

20

18

16

14

12

1010 12 14


Real

crus

hini

g ra

tio (

)

16 18 20 22


(a)

10

5

15

20

25

30

35Sa

nd fo

rmin

g ra

tio (

)


16 18 20 22


(b)


(a) (b)

0ndash236

50

40

30

20

10


Particle size (mm)

Mas

s per

cent

age (

)



(c)



Acknowledgments


References




























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls







e0 Etotal

V(12)mv2ρ

m 05ρv2 (12)



(a) (b)

0ndash236

50

40

30

20

10


Particle size (mm)

Mas

s per

cent

age (

)



(c)


(a) (b)


0ndash2360

10

20

30

40

50

60

70

80



Mas

s per

cent

age (

)

(c)







(a) (b)

0ndash2360

102030405060708090

100



Mas

s per

cent

age (

)


(c)


28

26

Real

crus

hing

ratio

() 24

22

20

18

16

14

12


35 40 45 50


(a)

Sand

form

ing

ratio

()

20

25

30

15

35

10

5

020 25 30



(b)




4 Conclusions





(a) (b)

0ndash2

36

0

10

20

30

40

50

60

70

236

ndash47

5

475

ndash95

Particle size (mm)

95ndash

132

132

ndash16

16ndash2

0

Mas

s per

cent

age (

)


(c)


(a) (b)

0ndash236

60

50

70

40

30

20

10


Particle size (mm)

Mas

s per

cent

age (

)



(c)







Data Availability




30

28

26

24

22

20

18

16

14

12

1010 12 14


Real

crus

hini

g ra

tio (

)

16 18 20 22


(a)

10

5

15

20

25

30

35Sa

nd fo

rmin

g ra

tio (

)


16 18 20 22


(b)


(a) (b)

0ndash236

50

40

30

20

10


Particle size (mm)

Mas

s per

cent

age (

)



(c)



Acknowledgments


References




























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls








(a) (b)

0ndash2360

102030405060708090

100



Mas

s per

cent

age (

)


(c)


28

26

Real

crus

hing

ratio

() 24

22

20

18

16

14

12


35 40 45 50


(a)

Sand

form

ing

ratio

()

20

25

30

15

35

10

5

020 25 30



(b)




4 Conclusions





(a) (b)

0ndash2

36

0

10

20

30

40

50

60

70

236

ndash47

5

475

ndash95

Particle size (mm)

95ndash

132

132

ndash16

16ndash2

0

Mas

s per

cent

age (

)


(c)


(a) (b)

0ndash236

60

50

70

40

30

20

10


Particle size (mm)

Mas

s per

cent

age (

)



(c)







Data Availability




30

28

26

24

22

20

18

16

14

12

1010 12 14


Real

crus

hini

g ra

tio (

)

16 18 20 22


(a)

10

5

15

20

25

30

35Sa

nd fo

rmin

g ra

tio (

)


16 18 20 22


(b)


(a) (b)

0ndash236

50

40

30

20

10


Particle size (mm)

Mas

s per

cent

age (

)



(c)



Acknowledgments


References




























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls





4 Conclusions





(a) (b)

0ndash2

36

0

10

20

30

40

50

60

70

236

ndash47

5

475

ndash95

Particle size (mm)

95ndash

132

132

ndash16

16ndash2

0

Mas

s per

cent

age (

)


(c)


(a) (b)

0ndash236

60

50

70

40

30

20

10


Particle size (mm)

Mas

s per

cent

age (

)



(c)







Data Availability




30

28

26

24

22

20

18

16

14

12

1010 12 14


Real

crus

hini

g ra

tio (

)

16 18 20 22


(a)

10

5

15

20

25

30

35Sa

nd fo

rmin

g ra

tio (

)


16 18 20 22


(b)


(a) (b)

0ndash236

50

40

30

20

10


Particle size (mm)

Mas

s per

cent

age (

)



(c)



Acknowledgments


References




























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls








Data Availability




30

28

26

24

22

20

18

16

14

12

1010 12 14


Real

crus

hini

g ra

tio (

)

16 18 20 22


(a)

10

5

15

20

25

30

35Sa

nd fo

rmin

g ra

tio (

)


16 18 20 22


(b)


(a) (b)

0ndash236

50

40

30

20

10


Particle size (mm)

Mas

s per

cent

age (

)



(c)



Acknowledgments


References




























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls




Acknowledgments


References




























Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls






Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls




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