Impact breakage of particle agglomerates

Ž .Int. J. Miner. Process. 61 2001 225–239www.elsevier.nlrlocaterijminpro

Impact breakage of particle agglomerates

B.K. Mishra), C. ThorntonSchool of Engineering and Applied Science, Aston UniÕersity, Birmingham, UK

Received 3 April 2000; received in revised form 5 September 2000; accepted 29 September 2000

Abstract

The paper examines the various factors that influence the breakage of particle agglomeratesresulting from impact. Numerical simulations of polydisperse spherical agglomerates impactingorthogonally on a target wall have been performed to study the effects of impact velocity, solidfraction, contact density, and the local arrangement of particles near the impact zone. Results ofsimulations show distinct fracture patterns for dense agglomerates above a critical impact velocitywhereas for loose agglomerates disintegration occurs under identical testing conditions. Eitherfracture or disintegration may occur for agglomerates with an intermediate packing density. It isalso demonstrated that, for agglomerates with intermediate packing densities, the mode of failurecan change from disintegration to fracture by either increasing the contact density or changing thelocation on the agglomerate surface, which is used as the impact site. q 2001 Elsevier ScienceB.V. All rights reserved.

Keywords: Agglomerates; Breakage; Discrete element method

1. Introduction

Powder materials in the form of particle agglomerates are commonly encountered in avariety of unit operations practiced by a wide range of industries such as iron and steel,chemical, pharmaceutical, cement, fertiliser, food, etc., where the material in powderform is intentionally agglomerated to develop specific product characteristics. Forexample, mineral processing engineers use agglomeration techniques to upgrade friablefine ore containing up to 60% iron to form pellets and sinters of sufficient strength to

) Corresponding author.Ž .E-mail address: [email protected] B.K. Mishra .

0301-7516r01r$ - see front matter q 2001 Elsevier Science B.V. All rights reserved.Ž .PII: S0301-7516 00 00065-X

( )B.K. Mishra, C. Thorntonr Int. J. Miner. Process. 61 2001 225–239226

withstand the mechanical load in the blast furnace. Agglomeration is a key process inthe fertiliser industry where the material is processed to obtain 90% of the granulesbetween y3 and q1 mm. Examples of other high-value added industries includeconsumer products. On the other hand, a common problem associated with the handlingof fine powders is the unintentional formation of agglomerates, which results in theclogging of feeders and prevents discharge from silos. In either situation, whetheragglomeration is achieved intentionally or otherwise, understanding of the formation,growth, and breakage of particle agglomerates is the key to the success of the associatedprocess engineering problems.

Various issues dealing with the mechanisms of agglomerate growth and prediction ofagglomerate size distribution are well documented in the mineral engineering literature.The relationship between the final performance of agglomerates and the physico-chemical properties of the powder is also available in the pharmaceutical literature. It isthe fracture and fragmentation behaviour of agglomerates, which is not adequatelyaddressed in the literature that needs further study. Breakage of particle agglomerates istraditionally studied by the free-fall impact test or drop test where the agglomerate isallowed to fall under gravity from a certain height onto a target platen. Under theseconditions, the impact AstrengthB of the agglomerate, is related to the maximum heightfrom which the agglomerate survives the drop without fracture. Impact test dataencompassing a wide range of spherical mineral materials such as iron ore, silica sand,graphite, limestone, zinc oxide, aluminium oxide, etc., are available in the literatureŽ .Pietsch, 1992; Capes, 1980 . These data show that the most important variable thatdetermines the AstrengthB of the agglomerate is the bonding mechanism.

The bonding mechanism between particles within an agglomerate is visualized asfollows: when two auto-adhesive particles collide, as in the case of adhesion of finepowders during storage, bonding takes place due to inter-molecular forces. The strengthof the bond is strongly dependent on the inter-particle cohesion and the size of theparticles. It has been observed that adhesive bonds are weaker than capillary bonds thatare responsible for balling of particles in a wet pelletization process. Theoreticalestimates of the actual strength of the bonds and their classifications are available in the

Ž .literature Rumpf, 1962 . However, the experimental determination of the forces ofcohesion has been found to be difficult due to the limitations resulting from the size ofthe particles.

Analysis of the fracture behaviour of agglomerates is often carried out to estimate thebond strength and identify the weakest link within the agglomerate. However, it isextremely difficult to experimentally capture each and every fracture event during thefracture process as it takes place within a very short timescale. Consequently, experi-mental investigation is usually restricted to post-impact analysis of the fragmentsproduced due to fracture. In contrast, numerical simulations of similar systems do notsuffer from such limitations. Solid fracture has been numerically studied to reveal the

Ž .detailed evolution of the fracture process. Using the discrete element method DEM ,Ž .Potapov and Campbell 1994 have numerically represented an elastic solid by gluing

together polyhedral elements such that the glued joints can only withstand a specifiedtensile stress until they break. This way, they have made it possible to correlate theobserved breakage pattern to various mechanisms of fracture. A similar approach to

( )B.K. Mishra, C. Thorntonr Int. J. Miner. Process. 61 2001 225–239 227

fracture of granular materials can also be studied using molecular dynamics techniquesŽ .Tsoungui et al., 1999; Kunn and Herrmann, 1996 .

Numerical simulations of agglomerate impact fracture using DEM was first studied atŽ .Aston University Yin, 1992; Thornton et al., 1996, 1999; Kafui and Thornton, 2000 .

The objective has been to carefully study the physics of fracture and fragmentation ofagglomerates under various testing conditions. The numerical results have made signifi-cant contributions towards the understanding of agglomerate fracture. Recently, re-

Ž .searchers at the University of Surrey Ghadiri et al., 1996; Subero et al., 1999 haveattempted to validate some of the numerical findings by experimental means. Thenumerical as well as experimental results of agglomerate fracture suggest that there areat least five parameters that affect the breakage behaviour of spherical agglomeratesupon impact: impact velocity, bond strength, porosity or solid fraction of the agglomer-ate, contact density, and the local arrangement of particles near the impact zone. Thepurpose of this paper is to show the individual effects of these parameters on agglomer-ate breakage in a unified manner.

2. Numerical methodology

The numerical method adopted here is called the discrete element method. Thistechnique was devised to analyse the behaviour of granular media in two dimensionsŽ .Cundall and Strack, 1979 . Since its inception, it has been upgraded and modified tosolve numerous problems in engineering disciplines involving particulate materials. Onesuch modification to the original TRUBAL program was successfully undertaken atAston University to simulate particle agglomerates. The computer program, which isnow called GRANULE, is capable of modelling elastic, frictional, adhesive or non-ad-hesive spherical primary particles, with or without plastic yield at the inter-particlecontacts. GRANULE is used in this study using the adhesive option with no plasticdeformation at the contacts.

2.1. Interaction laws

In DEM, particles are treated as discrete entities, which interact with each other at theinterface when they are in contact. The particle interaction rules are based on well-established contact mechanics theories, which relate the contact force to the relative

Ž .approach of particles. The Hertzian theory see Johnson, 1985 is used to describe theelastic particle interaction where the normal force–displacement relationship for spheri-cal particles 1 and 2 with elastic moduli E and E , Poisson’s ratios n and n , and1 2 1 2

radii R and R is given as1 2

4) )1r2 3r2Ps E R a . 1Ž .

3In the above expression, a is the relative approach that is related to the contact radius aby

)'as aR , 2Ž .) wŽ 2 . x wŽ 2 . x )where 1rE s 1yn rE q 1yn rE , and 1rR s1rR q1rR .1 1 2 2 1 2


The tangential interaction is non-linear and given by the theory developed by MindlinŽ . Ž .and Deresiewicz 1953 see Thornton, 1999 .

Ž .In the presence of adhesion, JKR theory is assumed Johnson et al., 1971 . It providesa relationship between the contact force and the relative approach as follows. Thecontact radius in the presence of adhesion is

1r3X)3R P

as 3Ž .)ž /4E

where PX is the effective Hertzian force, which would produce the same contact area. Itis related to the adhesive and applied force through the following

X 2(P sPq2 P " 4PP q4P 4Ž .c c c

where P is the applied force and P is the pull-off force. According to the JKR theory,c

the pull-off force is

P s3pg R) 5Ž .c

where g is the surface energy for each solid. The relative approach of the two spheres isrelated to the contact area a by

2a 4pg aas y . 6Ž .(

) )R E

The incremental normal force D F corresponding to an incremental relative approachDa is obtained as

'3 P y3 P( c)

D Fs2 E a Da . 7Ž .'3 P y P( c

The tangential interactions in the presence of adhesion are dealt with by a combina-Ž .tion of models Savkoor and Briggs, 1977; Mindlin and Deresiewicz, 1953 . Details of

these models and the implementation of the interaction laws have been reportedŽ .elsewhere Thornton and Ning, 1998; Thornton and Yin, 1991 .

3. Simulation procedure

The agglomerates that are used in this study are carefully prepared to retain realagglomerate properties as far as possible. At first, spherical particles are randomlygenerated in a pre-specified spherical region. Accepting particles that are centred withinthe spherical region ensures the formation of a spherical agglomerate. A centripetalgravity field is imposed to bring the particles in contact. The duration of imposition ofthe centripetal field determines the level of porosity or solid fraction within theagglomerate. At a desired level of solid fraction, each particle is assigned with therequired surface energy that ensures an adhesive bonding at the contact. Having formedthe agglomerate with the requisite properties, the centripetal gravity field is slowlyreduced to zero to complete the preparation of the agglomerate.


Table 1Agglomerate properties

Size distribution

Ž .Radius mm Wt.%

16 618 1020 5022 2224 12

Properties of the primary particles

Ž .Modulus of elasticity GPa 70Poisson’s ratio 0.3

3Ž .Density kgrm 2650Coefficient of friction 0.35

2Ž .Interface energy Jrm 1.0Total number of particles 5000

In this study, the agglomerate was composed of 5000 primary particles of fourdifferent sizes ranging from 24 to 16 mm. Several agglomerates over a range of solidfraction were prepared and four agglomerates were selected for impact simulations.These agglomerates had solid fractions of fs0.602, 0.583, 0.571, and 0.537; thecorresponding contact numbers were 12,400, 8329, 7653, and 6251, respectively. Thediameter of the agglomerate is a function of solid fraction and therefore it varied fromtest to test. However, the average radius of the agglomerates was 0.22 mm. Table 1shows all the other pertinent agglomerate properties that are common to all theagglomerates simulated. For the impact test, a stationary wall with the same elasticproperties as the primary particles was created and the desired impact velocity corre-sponding to a certain fall height was assigned to all the constituent primary particles.Computations proceeded until the kinetic energy of the system became constant after theimpact.

4. Results of simulation

Numerical results of agglomerate impact simulations are presented to show theinfluence on the breakage behaviour of the impact velocity, packing density, contact

Ždensity here defined, for simplicity, as the number of contacts or bonds existing in the.agglomerate prior to impact , and the location on the agglomerate surface selected for

the impact site. Before presenting the results, it is useful to clarify the terminology thatwill be adopted to describe the observed breakage phenomena.

The term AfractureB is reserved for breakage patterns in which clear fracture planesŽ .cracks are visible. This mode produces two or more large daughter fragments and isnormally accompanied by some fines production adjacent to the impact site. If, forexample, due to the high impact velocity used the large daughter fragments are


themselves broken into small clusters of primary particles then the term AshatteringB isused. An alternative mode of breakage, which will be illustrated later, is one in whichthere is no evidence from the simulation data of any attempted fracture and the endproducts consist of one large cluster centred in the upper part of the agglomerate withthe remainder of the agglomerate reduced to small clusters of 1–10 primary particles.This type of breakage behaviour is termed AdisintegrationB. If the impact velocity issufficiently high, for example, that disintegration extends throughout the agglomerateand there is no AlargeB surviving cluster then this mode of breakage is referred to asAtotal disintegrationB. Although the size distribution of the fragments may be similar tothat of shattering, the distinction between total disintegration and shattering is thedifference in the kinetic energy of the system at the end of the impact. When shatteringoccurs, a significant number of small daughter fragments are projected at relatively highspeeds away from the impact location. On the other hand, if total disintegration occurs,the agglomerate simply collapses into a heap on the target wall.

4.1. EÕolution of impact parameters

A vast amount of numerical data can be obtained from the simulation of a singleimpact test. Fig. 1 shows the results of a typical impact test where three of the mostimportant features of the agglomerate impact are illustrated. These are time evolutions ofthe force generated at the agglomerate–wall interface, the kinetic energy of the system

Fig. 1. Typical evolution of impact parameters; impact velocity s1.5 mrs; solid fractions0.602.


of primary particles composing the agglomerate, and the proportion of initial inter-par-Ž .ticle bonds broken damage ratio . The damage ratio is the ratio of the number of

adhesive bonds broken to the total number of adhesive bonds prior to impact andaccounts for degradation of the agglomerate due to bond breakage. In Fig. 1, thevariations in all three parameters are shown simultaneously. It is seen from the figurethat the damage ratio increases at an increasing rate at the beginning of the impact. Therate of bond breakage then decreases until the force on the wall is almost at itsmaximum value. There is then a sudden increase in the rate of bond breakage afterwhich the damage ratio increases at a decreasing rate as the wall force reduces to almostzero. Clearly, there are two stages to the bond breaking process during impact. Initiallybonds are broken primarily as a result of microstructural rearrangement associated withplastic deformation adjacent to the impact site, which occurs during the period when thewall force is increasing. This is followed by further bond breakage due to fracture duringthe ‘unloading’ stage as the wall force decreases. Finally, it is observed that when theforce on the wall reaches a maximum value, the rate of kinetic energy dissipation is amaximum and, thereafter, the kinetic energy decreases continuously at a decreasing rate,without any indication of recovery of kinetic energy as a consequence of agglomeratebreakage.

Results of all simulations show that, as expected, the maximum force on the wallincreases with increase in the impact velocity and the duration of the impact eventreduces. An important feature of all such tests is that fracture takes place within a fewmicroseconds.

4.2. Effect of solid fraction

Ž .For each of the four agglomerates different solid fractions , which were prepared asdescribed above, impact simulations were carried out at four different impact velocities:0.5, 1.0, 1.5, 2.0 mrs. In all cases, the interface energy was 1.0 Jrm2. It is worth notingthat apart from solid fraction, interfacial energy also plays a crucial role in determining

Žthe strength of the agglomerate. Several researchers Kafui and Thornton, 2000; Subero.et al., 1999 have adequately studied the effect of interfacial energy on the agglomerate

strength and fracture, which is not addressed here. In addition, the effect of impactvelocity on the breakage characteristics of dense agglomerate has also been reported

Ž .previously Thornton et al., 1999 . In the present study, the emphasis is directed to theeffect of solid fraction on the breakage behaviour of agglomerates impacted orthogo-nally against a target wall.

Visualisations of agglomerate breakage are provided by computer graphics images ofthe particle configuration at the end of an impact, with individual fragments indicated bydifferent shades of grey. Fig. 2 shows a set of snapshots taken after the impact of the

Ž .densest agglomerate fs0.602 with the wall at different impact velocities. It isinteresting to observe from the upper two snapshots shown on the left-hand side of thefigure that even up to an impact velocity of 1 mrs, the agglomerate under test suffersrelatively little damage. This fact is even more evident from the corresponding snapshotsshowing views from below the agglomerate on the right-hand side of the figure. Theextent of damage increases as the impact velocity is increased. It is also observed that at


Fig. 2. Fracture pattern at different impact velocities; solid fractions0.602. On the right-hand side, the toptwo images show views below the agglomerate, while the lower two images show views from above.


impact velocities of 1.5 and 2.0 mrs the agglomerate exhibits clear evidence of fractureplanes. The breakage of these agglomerates produces daughter fragments, spreadingover a wide size range as evident from the lower snapshots showing the fracturedagglomerate in elevation and as viewed from above. Further increase in the impactvelocity merely results in increased fragmentation of the already fragmented agglomer-ate without showing any visible evidence of change in the breakage mode.

Several more simulations were conducted for other agglomerates of different solidfractions in order to study the combined effect of solid fraction and impact velocity. Fig.3 shows a set of snapshots at the end of the impact simulations for four agglomerates ofdifferent solid fractions, which were tested at an impact velocity of 2.0 mrs. Thesnapshots on the left-hand side of the figure show both the fragments and the debrisformed due to the breakage of the agglomerate. The agglomerates shown in the top halfof the figure exhibit distinct fracture planes resulting in a number of largermediumsized residual fragments. In contrast, the agglomerate of solid fraction 0.537 tended todisintegrate upon impact resulting in one large surviving cluster and a lot of smalldebris. The agglomerate of solid fraction 0.571 exhibited mixed mode behaviour.Evidence of fracture, in the form of what may be described as AchippingB, can be seenbut, unlike the denser agglomerates, the resulting fracture product was mostly smalldebris. In order to clearly distinguish between the impact products, the images shown onthe left-hand side of Fig. 3 were reprocessed to eliminate the debris. The remaininglarger clusters are shown on the right-hand side of Fig. 3. These set of snapshots showthat decreasing the solid fraction results in fewer residual fragments and that fractureproduces several fragments of different sizes whereas disintegration results in just onelarge fragment surviving the impact event.

Quantitatively, the results of impact breakage can be examined by plotting the sizedistribution of the fragments produced. Fig. 4 shows a typical double logarithmic plot ofcumulative mass fraction undersize against normalised size. Here, the size of thefragments on the abscissa is represented by the mass of the cluster m normalised withrespect to the agglomerate mass M, which is equivalent to using the normalised size ofthe equivalent solid sphere. The size distributions of the fragments show two distinctregions with a sudden change in slope characteristic of bilinear grinding data that

Ž .distinguish the large fragments residue from the complement of small fragmentsŽ .debris . Earlier works and the result of the present investigation as shown in Fig. 4aindicate that while the exponent for the residue decreases with impact velocity, thecorresponding exponent for the debris is largely independent of impact velocity. It isalso observed that the transition between the residue and the complement becomessmooth and tends to disappear as the impact velocity increases. Experimental data

Ž .available in the literature Arbiter et al., 1969; Ghadiri et al., 1996 are in agreementwith these findings.

The effect of solid fraction on fragment size distribution is shown in Fig. 4b. Fromthe figure, it can be seen that for the same impact velocity, the amount of fine debrisincreases with decrease in solid fractions. It would also appear that the exponent for thecomplement is not significantly dependent on solid fraction. A further point worthnoting is the absence of data points in the residue part except for the densestagglomerate.


Ž .Fig. 3. Left: Fracture pattern obtained for different solid fraction impact velocity s2 mrs ; correspondingimages with small debris removed shown on the right-hand side.


Ž . Ž . Ž .Fig. 4. Fragment size distribution after impact; a effect of impact velocity f s0.602 , b effect of solidŽ .fraction V s1.5 mrs .

Examination of the results of all the sixteen impact simulations carried out leads tothe following observations. The agglomerate remains intact suffering very little damagebelow a threshold impact velocity. At higher impact velocities, the agglomerate break-


age mode may be one of fracture or disintegration. The results show that denseagglomerates fracture and loose agglomerates disintegrate, implying that at someintermediate packing fraction there is a transition from one breakage mode to the other.

4.3. Effect of contact density

When an agglomerate impacts a target wall, the force generated at the interfacepropagates through the agglomerate and the manner in which this propagation occurscontrols the distribution of initial kinetic energy converted into elastic stored energy.Force transmission through an agglomerate can only occur via the inter-particle contacts.Therefore, the number and locations of contacts within an agglomerate may be expectedto affect the agglomerate breakage behaviour; and the solid fraction does not account forthese characteristics of agglomerate microstructure. It has been shown by CiomocosŽ .1996 that if the contact density is increased for a dense agglomerate this results in very

Ždifferent fracture patterns for the same impact velocity and bond strength interfacial.energy . In this section, the effect of contact density is investigated for the agglomerate

with an intermediate solid fraction of 0.571.By careful manipulation during the preparation stage, a second agglomerate was

Žcreated with a solid fraction of 0.571 but with 8270 contacts 8% more than the 7653.contacts previously obtained . Both agglomerates were tested at an impact velocity of

1.5 mrs and the simulation results are presented in Fig. 5. The snapshots presented onthe right-hand side of the figure show the particle configuration at an elapsed time of0.68 ms when the simulations were terminated. It is clear from the figure that theagglomerate with higher contact density fractured whereas breakage of the agglomerate

Ž . Ž .Fig. 5. Effect of contact density on the breakage behaviour f s0.571, V s1.5 mrs ; a equivalent spaceŽ . Ž .lattice arrow indicates the orientation of the plane of fracture , b particle configuration.


with lower contact density occurred by disintegration. On the left-hand side of thefigure, the corresponding connection diagrams are shown at an elapsed time of 85 mswhen all the bond breaking had ended, after the wall force had reduced to almost zeroand before evidence of fracture became apparent from examining the particle configura-tion. Each of these connection diagrams represents the equivalent space lattice, which isformed by connecting the centres of particles, which were in contact at the start of theimpact. The light grey lines indicate existing contacts that have survived the impact andthe dark grey lines indicate contacts that have been broken. These diagrams clearly showŽ .i the existence of a fracture plane in the agglomerate with 8270 initial contacts which

Ž .corresponds to the breaking pattern shown on the right-hand side of the figure and iiclearly demonstrates that, for the agglomerate with 7653 initial bonds there was noattempted fracture process developed during the impact event.

5. Effect of impact site

In the previous section, it was demonstrated that contact density is a significantparameter, which affects the mode of breakage for agglomerates of intermediate solidfraction. The implication is that the contact density changes the potential pathwaysthrough the agglomerate which may be used for transmission of the force generated atthe agglomerate wall interface; and hence changes the distribution of elastic energystored. However, the contact density is a global scalar quantity that fails to reflect anyheterogeneity and anisotropy of the local contact orientations. Consequently, one mightexpect that the breakage behaviour may also be sensitive to the details of the localmicrostructure adjacent to the impact site. In this section, further impact simulations arereported in which, for each agglomerate, impacts were repeated but with the wallrepositioned so as to present a different location on the agglomerate surface as theimpact site.

Ž .No change in the breakage mode disintegration was observed for the loosestagglomerate as a consequence of varying the impact site location. However, minordifferences in the resulting particle size distribution occurred demonstrating the statisti-cal nature of impact breakage. When the densest agglomerate was repeatedly impactedwith different impact site locations, the agglomerate always fractured but the fracturepattern was sensitive to the impact site used. Consequently, there was a statisticalvariation in the resulting particle size distribution, particularly with regard to the size ofthe fragments comprising the residue. The effect of impact site was most pronounced foragglomerates of an intermediate packing density. This is illustrated by impacting theagglomerate of solid fraction of 0.571 and 8800 initial bonds at a velocity of 1.5 mrs.

The plan and elevation views of the particle configuration at the end of twosimulations in which the agglomerate was impacted at two different impact site locationsis shown in Fig. 6. The difference in the breakage behaviour is quite dramatic. In theupper part of the figure, the agglomerate clearly fractured producing a number ofrelatively large fragments plus small debris. In contrast, when impacted at a differentimpact site location, the lower part of the figure clearly shows no evidence of fractureand it is clear that the breakage mode is one of disintegration producing one large


Ž .Fig. 6. Breakage of one agglomerate f s0.571, Ns8800 when impacted at two different impact sitesŽ . Ž . Ž .V s1.5 mrs ; elevation left , top view right .

residual fragment plus fine debris that has been created from the lower hemisphericalpart of the agglomerate.

6. Conclusions

Agglomerate impacts have been simulated in order to examine how the breakagebehaviour is affected by impact velocity, solid fraction, contact density, and impact sitelocation on the agglomerate surface. The main findings of the study relate to thebreakage mode and how this is affected by solid fraction, contact density, and impactsite.

The results show that dense agglomerates fracture, loose agglomerates disintegrateand this remains true irrespective of impact site location. The breakage behaviour ofagglomerates with an intermediate packing density was found to be much morecomplicated. It has been shown that mixed mode behaviour may occur and that themode of breakage can change from disintegration to fracture by either increasing theoverall contact density or by changing the location of the impact site.

During all mineral-processing operations, adhesion of fine particles leading toformation of agglomerates is inevitable. Formation and breakage of the agglomeratesduring processing leads to operational problems. From the standpoint of what ispresented here and its relevance to the field of mineral engineering, two important issuesarise. From a practical standpoint, the simulation results illustrate a potential route tostudying a problem which is central to comminution research: prediction of the particle


size distribution in comminution devices. The DEM technique used is only strictlyapplicable to intergranular fracture, which may not be so relevant to particles that aremore strongly bonded than sandstone. Nevertheless, the technique may also prove to beuseful for predicting the particle size distribution due to breakage of other mineralparticles. Given the continued increase in computer hardware speeds, direct simulationof the entire comminution process will become possible in the near future and then,using the impact energy spectra and the breakage distribution data so obtained, morerational strategies for comminution device design and operation will become a realpossibility.

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Impact breakage of particle agglomerates