Powder Technology 203 (2010) 482–488

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Powder Technology

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Uniaxial compaction behaviour and elasticity of cohesive powders

M. Stasiak a,⁎, J. Tomas b, M. Molenda a, R. Rusinek a, P. Mueller b

a Institute of Agrophysics, Polish Academy of Sciences, P.O. Box 201, 20-290 Lublin 27, Polandb Otto-von-Guericke University, Magdeburg, P.O. Box 4120, 39106 Magdeburg, Germany

⁎ Corresponding author.E-mail address: mstasiak@ipan.lublin.pl (M. Stasiak)

0032-5910/$ – see front matter © 2010 Elsevier B.V. Adoi:10.1016/j.powtec.2010.06.010

a b s t r a c t

a r t i c l e i n f o

Article history:Received 4 February 2010Received in revised form 19 May 2010Accepted 14 June 2010Available online 21 June 2010

Keywords:Compression testPowder compactionModulus of elasticityTablet densityTablet strength

The compression and compaction behaviour of bentonite, limestone and microcrystalline cellulose (MCC) —three cohesive powders widely used in industry were studied. Uniaxial compression was performed in acylindrical die, 40 mm in diameter and 70 mm high, for three selected cohesive powder samples. The initialdensity, instantaneous density and tablet density were determined. The influence of maximum pressure anddeformation rate was examined. The secant modulus of elasticity Esec was calculated as a function ofdeformation rate v, maximum pressure p and powder sample. After compaction experiments in hydraulicpress at three pressures – p=30, 45 and 60 MPa – and two different deformation rates, the strength of theproduced tablets was examined in a material strength testing machine.From uniaxial compression tests performed on the universal testing machine for loading and unloading, themodulus of elasticity E was calculated on the basis of the first linear phase of unloading. The total elasticrecovery of tablets was also obtained.

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© 2010 Elsevier B.V. All rights reserved.

1. Introduction

Powders and bulk solids are produced, handled and applied infood, pharmaceutical, chemical and building material industries. Thevolume and range of bulk solids used in industry are still increasing,and simultaneously powder handling remains one of the leastunderstood areas associated with solid processing plants. Predictableprocessing, increase of quality and reduction of losses of products arestill the main issues [4]. Process design and optimisation determinethe properties and quality of products. With increasing scale ofindustrial operations, the design of reliable processes and efficientequipment requires more precise information about physical proper-ties and on how different process conditions change them [25]. Themost important technologies of process engineering involvingpowders and bulk solids, as listed in handbooks, are e.g.: pneumaticconveying, transport, size reduction, screening, coating, mixing,segregation, dust collection, feeding, weighing, metering, packagingand bagging, storage, instrumentation and quality control. Predictableprocessing, increase of quality and reduction of product losses are themain issues addressed in last few decades [9]. Process design andoptimisation generate the need to determine properties and qualityparameters measures of powders and bulk solids. Mechanicalproperties that serve as design parameters for storage systems orprocessing plants usually depend on the properties of individual

grains or particles, adhesion and friction between particles, interpar-ticle contact geometry and prior history of loading [20].

Compressibility and compactability of a powder are influenced bythe flow properties, and in the microscale, by the adhesion andfriction forces between the particles. Compressibility is the ability toreduce the volume under pressure and compactability is the ability tobuild a solid tablet under pressure, with sufficient mechanicalstrength and stability. Powders are often compacted to make themeasier to handle and transport and also to reduce dust problems. Oneof the most important processes is press agglomeration. The pressagglomeration process of powders is also influenced by feedproperties such as particle size and shape distribution, modulus ofelasticity, moisture content, flow properties and temperature[6,12,24,27].

Most frequently the design of efficient processing equipmentrequires the data of tablet density ρ, angle of internal friction φ,coefficient of wall friction between powders and apparatus ormachine wall μ, modulus of elasticity E and lateral stress ratio k.Modulus of elasticity E characterises the elastic deformation ofpowder under compression load and is one of the parametersrequired for numerical modelling of uniaxial compression using thediscrete element method (DEM) [5]. For structural engineer itdetermines how much a bar will sag under its own weight or undera loading when used as a beamwithin its limit of proportionality [17].These parameters are in particular interest of professionals usingcomputer aided design that recently has become very common tool[3]. Equipment design for handling and processing requires experi-mental values of this parameter that depends on moisture, pressure,load history, density, porosity, internal structure and kind of material

Fig. 1. Particle size distributions of bentonite, limestone and microcrystalline cellulose.

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[15,18,22,27]. Eurocode 1 part 4 [7] recommends to determine twovalues of effective modulus of elasticity. One, denoted Eload, ismeasured during loading of the sample and the second, Eunload,during unloading. Calculation of values require two ratios of change inlateral stress to change in the vertical stress Kload and Kunload that aredetermined during loading and unloading using uniaxial compression

Table 1Granulometric characteristics of powder samples.

Material d50

in μmXw

in %Sm in m2/g(BET)

Sm in m2/g(Blaine)

ρs inkg/m3

Limestone 20 0.56 2.28 0.45 2590Bentonite 7.4 4.65 16.51 0.8 2640MCC 70.2 5.09 4.84 0.434 1551

Fig. 2. Hydraulic press and unia

test with additional measurement of lateral stress. Eurocode 1 [7]recommends the uniaxial compression test under loads similar tothose occurring in the full-scale process.

The modulus of elasticity E was found to be strongly influenced bymoisture content, compacted density and porosity. Liu [15] measuredthe modulus of elasticity E of sand and found approximately threefoldchange in the values with varying experimental parameters. Investiga-tions on agricultural bulk solids by Moya et al. [18,19] confirmed verystrong influence of moisture content and pressure level on the value ofmodulus of elasticity E.

The objective of this study was to determine essential processparameters of three cohesive powders during compaction: thecompacted ρ and instantaneous density ρi, the modulus of elasticityE and strength of the press agglomerate σB. These parameters areuseful to design effective and reliable processes with granularmaterials as well as for numerical modelling of mechanical behaviourof granular materials.

2. Powder samples

Reported project was performed for bentonite, limestone andmicrocrystalline cellulose (MCC). Powder particle size distributions arepresented in Fig. 1 [11]. The particle size distribution was determinedby Mastersizer 2000 (Malvern).

Themean diameter d50, moisture content XW specific surface Sm bygas adsorption (BET) and air permeation methods (Blaine) as well astrue particle density ρs are listed in Table 1 [11]. The large differencesin surface areas of both test methods, especially at bentonite andMCC,show the large influence of internal pores and asperities of theparticles. Only materials at equilibrium moisture content wereinvestigated because the main interest of the project was tocharacterize parameters of powders useful industrial conditions ofoperation, namely roller press agglomeration.

xial compression chamber.

Fig. 3. Universal testing machine (TIRAtest) with equipment to determine the tensile strength of tablets applying diametrical compression force.

484 M. Stasiak et al. / Powder Technology 203 (2010) 482–488

3. Methods

3.1. Uniaxial compression in hydraulic press

First, the compaction behaviour of cohesive powders duringcompression in hydraulic press was analysed to determine the initialdensity ρ0, the compacted density ρ and the instantaneous density ρiduring powder compression. The influence of maximum pressure anddeformation rate was examined. Experiments address the problem ofagglomerate quality obtained in compaction tests. The secant modulusof elasticity Esec was calculated as dependant on deformation rate v andmaximum pressure p.

The uniaxial compression tests of bentonite, limestone and MCCwere performed in a hydraulic press, in a 40 mm in diameter chamber,70 mm high (Fig. 2). All experiments were conducted for the initialheight of powder sample of 60 mm. The displacement was measuredby an inductive sensor having accuracy of 0.01 mm. The sensor wasmounted with a rubber coupling to avoid moments generated byeccentric forces occurring during the experiments.

The tests were performed at two deformation rates v=3.5 and9.5 mm/s for maximum pressure p in a range from 30 to 60 MPa withthe step of increase of 5 MPa. Speed v=3.5 mm/s is the minimalwhich could be obtained in hydraulic press and comparable with

Fig. 4. Typical pressure–displacement relationship from hydraulic compression testsand method to determine secant modulus Esec during loading.

speed v=2 mm/s in universal testing machine while v=9.5 mm/minis characteristic for speed of deformation in roller press duringproduction of agglomerates. All experiments were performed in threereplications and the results were statistically elaborated.

3.2. Testing the agglomerate strength

After compaction experiments, the tablet strength was tested by auniversal testing machine. The strength of agglomerates was obtainedfor tablets compacted at pressures of p=30, 45 and 60 MPa and for twodeformation rates v of 3.5 and 9.5 mm/s. The tablets were diametricallycompressed between circular plate and stamp as shown in Fig. 3.

During the experiments, the stamp was moving down withconstant deformation rate v of 0.033 mm/s. The real time, compres-sion force in N and displacement in mm of the moving stamp wererecorded continuously.

3.3. Uniaxial compression in universal testing machine

The uniaxial compression tests of powder samples for loading andunloading were performed using the same universal testing machineto determine the strength of agglomerates. From these tests the

Fig. 5. Influence of powder sample on the modulus of elasticity Esec calculated on thebasis of loading. Points denote mean values and vertical bars the 0.95 confidenceinterval.

Fig. 6. Influence of maximum compaction pressure on the modulus of elasticity Esec.Points denote mean values and vertical bars the 0.95 confidence intervals.

Fig. 7. Compacted density of powder agglomerates versus compression pressure.

Fig. 8. Density of powder agglomerates versus deformation rate obtained in uniaxialcompression tests on hydraulic press.

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modulus of elasticity E of powders was calculated based on the firstlinear part of unloading curve (see Fig. 2). At this phase of unloadingonly elastic response of thematerial takes place [21,22]. Themethod isalso recommended by European Standard [7]. These tests were alsoperformed to determine the elastic recovery Δh of tablets afterunloading. The powder was filled into the test chamber withoutvibrations or another compression effects. The sample was 60 mmhigh and 40 mm in diameter. The bed was loaded to the referencevertical stress σz of 10 and 20 MPa. The top cover of the apparatus wasmoving down at a constant deformation rate of 2 mm/s, while thedisplacement wasmeasuredwith an inductive sensor having accuracy

of 0.01 mm. Next, the sample was unloaded at the same deformationrate until zero stress level was reached. The tests were conducted inthree replications.

For data evaluation the model, equation of Sawicki [21] was used.During the loading both reversible (elastic) and irreversible (plastic)strains develop in the sample: εz=εze+εzp. Two phases of unloadingcan be observed (see Fig. 2). The first phase is characterised by apurely elastic deformation and was used to determine the modulus ofelasticity E. The second stage of unloading is characterised by bothelastic and plastic deformations. During the first phase of unloading,the sample shows linear response which is characteristic forreversible elastic deformation. Thus εz may be expressed as [21]:

εz =σz

E1− 2ν2

1−ν

!: ð1Þ

4. Results

4.1. Secant modulus of elasticity by uniaxial compression in hydraulicpress

Based on the experimental curves (pressure versus relativedisplacement) the secant modulus of elasticity Esec was determinedas recommended by European Standard Eurocode 1 [7] (Fig. 4).

Fig. 5 presents the secant modulus of elasticity Esec calculated foreach maximum pressure and for the two deformation rates. Variance

Fig. 9. Compression force–displacement tests of bentonite, limestone and MCCagglomerates obtained for three maximum compaction pressures at v=3.5 mm/s.

Fig. 10. Breakage strength of bentonite, limestone and MCC agglomerates obtained forthree maximum compaction pressures at v=9.5 mm/s.

Fig. 11. Typical experimental data obtained for loading and unloading cycle of bentonitepowder in universal testing machine for two maximum compression pressures p=10and 20 MPa. Straight lines represent tangents of the first parts of unloading curves.

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analysis was performed to estimate the influence of deformation rateon modulus of elasticity Esec. No significant effect of deformation rate(F-ratio=0.33) was observed for three experimental materials.Significant differences were found in modulus of elasticity Esecbetween powders (see Fig. 5). The highest value of modulus ofelasticity Esec=255 MPa was obtained for limestone, the lowest forMCC. For bentonite the modulus of elasticity Esec=90 MPa was foundto be nearly two times higher than for MCC. The elongated fibre-likeshape of the largest MCC particles could be the reason for higherdeformability of this powder bed. The limestone powder consists ofcrushed particles with rough surface and shows lower deformability.

From all considered factors influence of compression pressure wasthe strongest. The results are presented in Fig. 6. For bentonite andMCC an increase in pressure from 30 to 60 MPa resulted in significantincrease of modulus of elasticity Esec. Values of modulus of elasticity

for bentonite Esec were obtained in the range from 75 to 106 MPa, andlow values — from 47 to 62 MPa for MCC, while for limestoneEsec=209 to 276 MPa. Relationships between secant modulus ofelasticity Esec and compression pressure p were fitted by linearapproximation. Coefficient of determination of R2=0.68 for bentoniteand MCC was higher than that R2=0.12 obtained for limestone.

In Fig. 6 results of calculated Esec from experiments on universaltesting machine at 10 and 20 MPa of maximum pressure arepresented for comparison. These values are lower than linear fits ofvalues of secant modulus obtained by uniaxial compression inhydraulic press at the pressures ranging from 30 to 60 MPa.

4.2. Compression function by hydraulic press

Li and Puri [14] presented an empirical relationship between thecompression behaviour and the initial bulk density. The authors foundthat limestone had the highest bulk density for loose packing (approx.900 kg/m3). The microcrystalline cellulose had the lowest initial bulkdensity (approx. 300 kg/m3)but its compressibility indexwas thehighest.

The aim of the final part of the experiments was to determine theinitial density ρ0, the instantaneous density ρ0 and density of powdersduring the process of compaction ρ in hydraulic press. For allexperiments the relationships between instantaneous densities andvertical deformation were determined, but the most importantparameter in tablet production is the agglomerate density ρ (Fig. 7).

The highest values of density ρ in the range of maximum pressurefrom 30 to 60 MPa and at the two constant deformation rates of v 3.5and 9.5 mm/s were found for limestone. The lowest values of ρ wereobtained for MCC in a range from 860 kg/m3 for p=30 MPa to

Fig. 12. Sequence of micro-processes and deformation mechanism during press agglomeration.

Table 2Modulus of elasticity E calculated on the basis of linear part of unloading and elasticrecovery Δh determined in uniaxial compaction tests at universal testing machine.

Powdermaterial

Maximum pressurep in MPa

Modulus ofelasticity E in MPa

Elastic recovery oftablets Δh in mm

Bentonite 10 48.4±2.5 1.66±0.0820 71.4±2.8 2.10±0.54

Limestone 10 55.6±3.1 2.05±0.0720 81.2±3.0 4.02±0.08

MCC 10 30.4±3.5 2.60±0.0520 56.5±7.2 2.79±0.09

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1100 kg/m3 for p=60 MPa and were strongly affected by maximumcompaction pressure. For limestone and bentonite an increase inpressure resulted in a small increase of ρ from 1820 to 1880 kg/m3

and from 1700 to 1840 kg/m3, respectively. Practically no influence ofdeformation rate on density ρ was noted (Fig. 8). Using thecompression function on physical basis, [26], defined the compress-ibility index n, as:

ρρ0

= 1 +pσ0

� �n

: ð2Þ

In current investigations its values of 0.092 (for limestone), 0.175 (forbentonite) and 0.650 for MCC was found higher than those obtained by[10,11]. Tablet density was analyzed in detail by Sinka et al. [23] and byWu et al. [27]. Sinka et al. [23] examined compaction of microcrystallinecellulose and concluded that that non-uniform density distribution wasmainly caused by wall friction within the die. Factors such as friction,geometry, loading schedule and method of filling the die all influencecompaction but conclusions regarding density distribution cannot begeneralized. Eachpractical situation requires individual analysis.Wuet al.[27] analyzed compaction of lactose powder and pointed out tolocalization of intensive shear stresses during unloading that causedbreaking of tablets upon ejection. A set of reported effects was a probablereasonofdiscrepancies inour results and thoseobtainedbyother authors.Obtaining of coherent results in different laboratories require similarity ofequipment as well as precise control of condition of compaction.

4.3. Strength and compaction function of agglomerates

During the experiments different types of deformation wereobserved, Fig. 9. MCC was reported as a mainly plastic deformingpowder by Inghelbrecht and Remon [13] who analysed rollercompaction and tabletting of MCC.

Using the maximum compression force at breakage point B thetensile or breakage strength of agglomerates σB was calculated as in Felland Newton [8] (FB — breakage force, d — tablet diameter, and h —

height of tablet), Fig. 10:

σB =2⋅FBπ⋅d⋅h : ð3Þ

The highest values of σB, 1.14 and 3.95 MPa for respectively 30 and60 MPa of maximum pressure, were obtained for MCC tablets while the

lowest,σB=0.012 and 0.027 MPa, for limestone tablets. Values ofσB forMCC were higher than those estimated by [10]. The largest increase ofbreakage strength approximately 200% with increasing compactionpressure was observed for bentonite and MCC tablets. In the case oflimestone tablets σB increased only of nearly 120%. No significantinfluence of the deformation rate was observed on tablet strength σB.

4.4. Modulus of elasticity by uniaxial compression in universal testingmachine

Elastic constants were determined using experimental results fromlinear phase of unloading. Fig. 11 shows the relationships between thecompression stress σz and the relative displacement εz for loading–unloading cycles of bentonite powder at maximum compressionpressures of 10 and 20 MPa. In Fig. 12 schematic of change modes ofdeformation is illustrated. The first part of the loading curve reflectscompaction of the sample with translation and rotation movements ofparticles, at relatively small contact deformations, Fig. 12b) and c). Thesecond, steeper part of the curve shows a sharp increase in the elastic–plastic contact stresses associated with deformations of entire particlesand their breakage, Fig. 12d) and e) [1,2]. During loading, deformationtakes place in contacts as well as volume deformations of particles.Controlling the elastic recovery is very important in the processing ofpowders compacts because defects, such as cracks and fractures ofpowder compacts may occur as an effect of faster elastic recovery orspring back. According to Wu et al. [27] the phenomenon requiresfurther research. Obtained values of modulus of elasticity E and elasticrecovery Δh of the tablets are presented in Table 2.

Tested parameters E and Δh were found to be dependent on thepowder and on the maximum stress. For all samples tested, themodulus of elasticity E increased with increasing maximum pressure

488 M. Stasiak et al. / Powder Technology 203 (2010) 482–488

p. The highest values of modulus of elasticity E=55.6 MPa for 10 MPaof compression pressure and E=81.2 MPa for p=20 MPa, wereobtained in the case of limestone, while the lowest values wereobtained for MCC. Modulus of elasticity E of MCC ranged from30.4 MPa to 56.5 MPa and that of bentonite ranged from 48.4 MPa to71.4 MPa. Modulus of elasticity of MCC was also determined byMichrafy et al. [16] by a four-point beam bending test at differentdensities. The authors obtained modulus of elasticity E=90 MPa forpressure of 60 MPa, in good agreement with our results.

Experiments performed on the universal testing machine allowed toobtain elastic recovery Δh of tablets after uniaxial compression [Fig. 11].Values of this parameter are presented in Table 2. The lowest value ofelastic recoveryΔh=1.66 mmwasobtained for bentonite atp=10MPa,and the largest, Δh=4.02 mm, for limestone at p=20MPa.

5. Summary and conclusions

The highest value of secant modulus of elasticity Esec=255 MPadetermined at hydraulic press was obtained for limestone and thelowest Esec=55 MPa for MCC. No influence of deformation rate onmodulus of elasticity Esec was found. For bentonite and MCC anincrease in pressure from 30 to 60 MPa resulted in significant increaseof secant modulus of elasticity Esec even for 41% and 32% adequately.

The highest compressibility index n=0.350 was obtained for MCCwhile the lowest n=0.092 for limestone.

The highest value of tablet density ρ from 1820 to 1880 kg/m3 wasobtained in the case of limestone. Lower for 45% for MCC, and for thismaterial it was strongly affected (increase 28%) by maximumcompaction pressure. No influence of deformation rate on thisparameter was observed.

Values of σB were found to increase with an increase incompaction pressure p more than two times. The highest values ofbreakage strength σB=1.14 and 3.95 MPa for p=30 and 60 MPawere obtained for MCC tablets, and the lowest adequately 0.012 and0.027 MPa for limestone tablets. Deformation rate during compactionhad no significant influence on tablets breakage strength.

The largest values of modulus of elasticity E=55.6 MPa for 10 MPaof compression pressure and E=81.2 MPa for p=20 MPa calculatedon the basis of the first phase of unloading were obtained in the caseof limestone, while the lowest ranged from 30.4 MPa to 56.5 MPawere values obtained for MCC.

The lowest value of elastic recovery Δh=1.66 mm was obtainedfor bentonite and more than 200% higher for limestone.

Acknowledgment

This project was supported by DFG in the frame of project DFGproject (TO 156/18–2): Modeling of cohesive powder compaction inthe roller press.

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